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Phase equilibrium in systems containing fluorocarbons

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Title:
Phase equilibrium in systems containing fluorocarbons
Creator:
Kyle, B. G ( Benjamin Gayle ), 1927-
Place of Publication:
Gainesville
Publisher:
[s.n.]
Publication Date:
Language:
English
Physical Description:
ix, 186 l. : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Calibration ( jstor )
Fluorocarbons ( jstor )
Fractions ( jstor )
Free energy ( jstor )
Hydrocarbons ( jstor )
Liquids ( jstor )
Solubility ( jstor )
Solvents ( jstor )
Trucks ( jstor )
Vapor pressure ( jstor )
Fluorocarbons ( lcsh )
Hydrocarbons ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis - University of Florida.
Bibliography:
Bibliography: l. 183-185.
General Note:
Manuscript copy.
General Note:
Vita.
Statement of Responsibility:
by Benjamin G. Kyle.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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030111969 ( ALEPH )
ACH2362 ( NOTIS )
11045679 ( OCLC )

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PHASE EQUILIBRIUM IN SYSTEMS

CONTAINING FLUOROCARBONS









By
BENJAMIN G. KYLE


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
FEBRUARY, 1958
















ACXXOVL19DGNKII


The author wishes to thank Dr. T. N. Reed
for his advice and guidance throughout this investigation.

Appreciation is expressed to the supervisory comiLttee

members, Dr. Iack Tyner, Dr. W. S. Brey, Dr. E. X. mschlitz,

and Dr. R. B. Bennett for their aid and cooperation.














TABLE OF CONTENTS




LIST OF TABL . iv

LIST OF ILLUSTRATIONS vi

CHAPTER
I PURPOSE . 1

II NOMENCLATURE .. 2

III INTRODUCTION 5

IV BINARY SYSTEMS FORMING TWO LIQUID PHASES 9

V TOTAL VAPOR PRESSURE OF BINARY MIXTURES 18

VI VOLUME CHANGES IN MIXING FLUOROCARBONS AND
HyROCABOS 30
VII ESTIMATION OF THERMODYNAMIC PROPERTIES 45

VIII TERNARY LIQUID-LIQUID SOLUBILITY STUDIES 55

IX EXTRACTIVE DISTILLATION STUDIES 67

X EVALUATION OF METHODS OF SEPARATING FLUORO-
CARBON MIXTURES 79

XI CONCLUSIONS . 82
APPENDIX . 85

TABLES . 91

FIGURES . 129

REFERENCES . 183

BIOGRAPHICAL ITEMS 186


iii













LIST OF TABLES


TABLE Page


I TEST OF THE CONSOLUTE TEMPERATURE CRITERION
II CHECK RUN IN TWO LIQUID PHASE STILL .
III ISOTHERMAL COMPRESSIBILITIES FOR USE IN
EQUATION 34 .
IV O8LVENT SELECTIVITIES .
V COMPARISON OF DIFFERENCE .

VI CALCULATION OF d3 FROM EQUATION 64 .

VII PHYSICAL PROPERTIES OF HYDROCARBONS USED
IN THIS WORK .

VIII PHYSICAL PROPERTIES OF FLUOROCARBONS USED
IN THIS WORK .

IX THERMOCOUPLE AND THERMOMETER CALIBRATIONS

X PYCNOMETER CALIBRATIONS .

XI VAPOR PRESSURES OF PURE FLUOROCARBONS .

XII SOLUBILITY DATA 1

XIII COMPARISON OF CALCULATED AND OBSERVED
CONSOLUTE TEMPERATURES AND COMPOSITIONS 1


XIV TOTAL VAPOR PRESSURE-TEMPERATURE DATA
XV COMPARISON OF VAN LAAR ACTIVITIES WITH
ACTIVITY RANGE CALCULATED FROM
EQUATION 15a .

XVI VOLUME OF MIXTURES OF PERFLUOROHEPTANE
AND CARBON TETRACHLORIDE; PERFLUORO-
CYCLIC OXIDE AND CARBON TETRACHLORIDE;
PERFLUOROCYCLIC OXIDE AND n-HEPTANE;
AND PERFLUOROHEPTANE AND nEPANE .
iv


1


1




1


16
19

41
59
63

75

91


92

93

95

96

.01

.07

.08


09




11










TABLE Page

XVII TOTAL VOLUME CHANGE AND PARTIAL MOLAL
VOLUME CHANGE ON MIXING 114
XVI11 CALIBRATION DATA FOR ANALYSIS OF SYSTEMS:
C7716-C.1s60F-CC14; Cr716-'CgF16o-C7H 16s
AND C6Hs5C.-C6H11CH3-C7F15COOCCa 118

XIX TIE LINE DATA 120
XX ACTIVITIES CALCULATED FROM EQUATION 59 122
XXI ACTIVITIES CALCULATED FROM EQUATION 61 123
XXII CHARACTERISTICS OF CHROMATOGRAPHY COLUMNS
USED IN EXTRACTIVE DISTILLATION STUDIES 124
XXIII APPEARANCE TIME OF C7F16, C8F160, -C7H16
AND C6HlCH3 IN THE VARIOUS PARTITIONING
LIQUIDS 124

XXIV RELATIVE VOLATILITY OF THE C7F16-C8F160
SOLVET AND n-C7H16-C6H11CH3 SOLVENT
STSTSs .. s25

XXV ACTIVITY COEFFICIENT RATIOS BASED ON
AVERAGE RELATIVE VOLATILITY FOR ALL
SOLVNTS................ 125
XXVI PROPERTIES OF PURE COMPOUNDS FOR USE IN
EQUATION 684 126
XXVII DATA FOR USE IN EQUATIONS 37, 40, AND 46 127
XXVIII DATA USED IN ESTABLISHING EMPIRICAL COR-
RELATION FOR EXCESS FREE ENERGY 128













LIST OF FIGURES


Figure Page
1. Vapor Pressure Data for Fluorocarbons 129

2. Solubility Cell .. .. 130

3. Binary Solubility Curves Systems Containing
CyF16 . 131
4. Binary Solubility Curves Systems Containing
C8F160 132

5. Binary Solubility Curves Systems Containing
(C4F9)3N . 133
6. Binary Solubility Curves Systems Containing
C7F15C000C3 134

7. Binary Solubility Curves Systems Containing
C7F5l H 135

8. Activity Isotherms 136

9. Two Liquid Phase Still 137

10. Van Laar Constants Versus Temperature 138

11. Total Vapor Pressure Plot System: Per-
fluorocyclic OKide-n-Beptane 139

12. Total Vapor Pressure Plot System: Per-
fluorocyclic Oxide-Toluene 140

13. Total Vapor Pressure Plot System: Per-
fluorocyclic Oxide-Methylcyclohexane 141

14. Total Vapor Pressure Plot System: Per-
fluorocyclic Oxide-Carbon Tetrachloride 142

15. Total Vapor Pressure Plot System: Per-
fluoroheptane-Carbon Tetrachloride 143










Figure Page

16. Total Vapor Pressure Plot System: Per-
fluorobeptane-n-Heptane 144
17. Activity Coefficients System: C5H12-C5F12
T = 262.40 K. 145
18. Excess Free Energy of Mixing System:
CS3FI2C.12H .. 146
19. Excess Free Energy of Mixing System:
C4F10-C4HlO a & 147
20. Excess Free Znergy of Mixing System:
C7F16-._C8H18 at 300 C. 148

21. Van Laar Activity Coefficients 149

22. Van Laar Activity Coefficients Temperature
Dependence . 150
23. Pycnometer Filling Arrangement 151

24. Volume Change on Mixing System:
C8F160-CCI4 at 50 C. .. 152

25. Volume Change on Mixing System:
C7Fl6-C7H16 at 50 C. 153
26. Volume Change on Mixing System:
C7FI6-CC14 at 60 C. 154
27. Volume Change on Mixing System:
C8F160-a-C71H6 at 50 C. 155

28. Partial Molal Volume Change System:
CF 160-n e at 500 C. i6

29. Partial Nolal Volumg Change System:
C8F160-CC14 at 50 C. .. 157
30. Partial Molal Volume Change System:
C7Fl6-CC14 at 60 C. 158

31. Partial Molal Volume Change System:
C7F16-n-C7H16 at 50 C. .. 159


vii











Figure Page

32. Partial Molal Volume Change 160
33. Thermal Coefficient of Expansion System:
C7F16-CC14 . 161

34. Thermal Coefficient of Expansion System:
C7F16-n-C716 161

35. Thermal Coefficient of Expansion System:
C8F160-CC14 162
36. Thermal Coefficient of Expansion System:
C8F160-n-C7H16 ... 162
37. Volume of Mixing System: C7F16-CC14 163

38. Volume of Mixing System: C7F16-C7H16 164

39. Volume of Mixing System: C7F16.--CH 18 165
40. Calibration of System C8F160-C 716 166

41. Calibration for System CC14-C8F160 167

42. Calibration for System C8F160-n-CH16 168

43. Calibration for System C6H~E3-C6H5CH3 169

44. Calibration for System C6H 11C3-CF C150OCH3 170

45. Phase Diagram System C7F16-C8F160-CC14
at 30 C. . 171
46. Phase Diagram System: C7F16-CsF160-n-C7H16
at 30 C. . 172
47. Phase Diagram System: C6H5CH3-C6H11CH3-
C7F1]COOC% at 25 C. 173
48. Phase Diagram System: C6H5C%-C6H11CH3-
C7Fl5COOCH3 at 10 C. 1. 74


viii











Figure Page

49. Heat of Mixing System: C7F16-an-C7H16
at 500 C. . 175

50. Heat of Mixing System: C7F16-CC14 at 600 C. 176

51. Heat of Mixing System: C F -i-C H
7 16 8 18
at 300 C. . 177

52. Heat of Mixing System: CF 10-C H10 178

53. Heat of Mixing System: C5F12-C5H12 179

54. Excess Free Energy of Mixing system;,
C7F16-CC14 . 180

55. Free Energy Correlation for Fluorocarbons
and Paraffin Hydrocarbons 181
56. Excess Entropy of Mixing System:
C F 6--C8 H18 at 300 C. 182














CHAPTER I


PURPOSE

The purpose of this work is twofold:
1. The determination of the necessary phase equili-
brium data for the evaluation of various methods of separat-

ing fluorocarbon mixtures and hydrocarbon mixtures, partic-

ular emphasis being given to the methods of liquid extrac-

tion, extractive distillation, and aseotropic distillation.

2. The calculation of the thermodynamic properties

of some flurocarbon-hydrocarbon mixtures and the comparison

of these calculated properties with properties predicted from

various theories of solutions.














CHAPTER II


NOMENCLATURE

a Activity, standard state taken as pure substance
A Van Laar constant

B Van Laar constant
d Distance between centers of nearest-neighbor mole-

cules
H Partition coefficient, defined as the ratio of

solute per unit volume of solvent to solute per

unit volume of gas phase
I Ionization potential
N Number of theoretical plates
pi Inlet pressure in chromatography column

po Outlet pressure in chromatography column
P0 Vapor pressure of pure compound

R Gas constant
T Absolute temperature, oK.
V Nolal volume, cc
Vg Volume occupied by vapor phase in chromatography
column

Vr Retention volume, defined as the volume of carrier
gas passed through chromatography column when solute
peak appears











3
Vs Volume occupied by stationary solvent phase in
chromatography column
Vs Molar volume of stationary solvent phase, cc
v Weight fraction
x Mole traction

y Mole fraction of a component in vapor phase
z Correction factor
AA Change in Helmholtz Free Energy

As Change in Internal Energy

A F Change in Gibbs Free Energy
A H Change in Enthalpy

AS Change in Entropy
Xo Coefficient of thermal expansion
0( Relative volatility

Isothermal compressibility
3 Solvent selectivity
Y Activity coefficient, standard state taken as pure

substance
0C Solubility parameter, ( V/y)1/2 (calories/cc)1/2
TT Total vapor pressure

Volume fraction
6 Retention time, defined as time for appearance of
solute peak













Subscripts

1

2 Refer to components

3
C Refers to consolute properties
D Refers to distillate composition

9 Refers to mixture properties

0 Refers to ideal solution properties

P Refers to constant pressure process

V Refers to constant volume process

W Refers to composition of material in distillation

pot


Superscripts
* Refers to excess properties

M Refers to mixing process

V Refers to vaporization process
I Refers to hydrocarbon-rich phase














CHAPTER III


INTRODUCTION

Before any e equipment affecting physical separation

of two or more components can be designed, phase equilibrium

data must be available. Since the majority of the unit

operations involve the contacting of two phases under condi-

tions approaching equilibrium, the determination, correla-

tion, and prediction of phase equilibrium data play an im-

portant role in the field of chemical engineering.

A most desirable method of obtaining necessary phase
equilibrium data would involve the calculation of the pro-

perties of the mixture from those of the pure components;

however, to be used with confidence, any such method should

have some sound theoretical basis. At present there are

several approaches to the theory of solutions, most of which

have a statistical mechanical basis and require many assump-

tions and approximations and yield equations which are com-

plex and cumbersome.

A simple theory that has achieved considerable suc-

cess in the treatment of solutions of nonelectrolytes is one
developed independently by Scatchard and by Hildebrand (11).

By making four simple assumptions, Scatchard and Bildebrand










6
arrived at the following expression for the energy of mix-
ing in a binary system:*

X : (x *1 xV2) ( Q :2 2 2 (1)

The four assumptions were:

1. The energy of a system can be expressed by sum-
mation of the interaction energies of all possible pairs of
molecules. This interaction energy was assumed to depend
only on the distance between the two molecules.

2. The distribution of molecules is random with
respect to position and orientation.

3. There is no volume change on mixing at constant
pressure.

4. The interaction energy between 1-2 pairs of mole-
cules is the geometric mean of the interaction energy between
1-1 and 2-2 pairs. Strictly speaking this theory applies
only to systems containing nonpolar molecules between which
only dispersion forces are operating.

By further assuming that the entropy of mixing has
the same value as that of an ideal solution (a solution obey-
ing Raoult's law) it is possible to write for the free
energy of mixing


*A tabulation of the nomenclature used in this work
is given in Chapter II.












AP x (11 x2V2)( 2l ) { 1 2 + RT(xln x1 X2 inx2)

(2)
and for the activity coefficients

RT InY = VI(C1 i 2) 2 + ) 2

RT laY2 V2 ) 2 ) >i, 2 (3)
From its inception in 1932 until about 1950 the
success of the Scatchard-Hildebrand theory had been measured
by its prediction of the properties of hydrocarbon systems.
Since 1950 much work has appeared concerning fluorocarbon-
hydrocarbon systems which were not adequately accounted for
by the theory. These systems have such larger positive de-
viations from aoult's law than are predicted. For some
systems these positive deviations are large enough so that
at room temperature two liquid phases exist.
Because of their nonconformity to the existing
theory, fluorocarbon-hydrocarbon systems have stimulated the
interest of many investigators. The first comprehensive
study of fluorocarbon-hydrocarbon systems was made by Simons
and Dunlap (39) followed later by Simons and Mausteller (40);
these investigators determined the thermodynamic properties
of CSF2I-C5H12 and C4110-C4H10 systems respectively.
Simons and Dunlap found the Scatchard-Hildebrand
theory to be inadequate in predicting the thermodynamic











8
properties of their system, and improved the agreement by

rederiving equation 1 omitting the assumption of no volume

change on mixing. Later Reed (32) showed that for fluoro-

carbon-hydrocarbon mixtures the interaction energy between

unlike pairs of molecules is not the geometric mean of

like pairs as was also assumed in the derivation of equation

1. Reed also rederived equation 1 omitting the assumptions

of the geometric mean and no volume change. Be was alle to

calculate values of the heat of mixing which agreed very well

with the experimental data of Simons and Dunlap, and Simons

and Mausteller.

Since most fluorocarbon-hydrocarbon mixtures do not
conform to the present theory, their study should prove use*

ful toward further development and evolution of the theory

and the understanding of solution processes.












CHAPTER IV


BINARY SYSTEMS FORMING TWO LIQUID PHASES


The study of binary systems forming two liquid

phases was undertaken for two reasons:

1. To determine solubility relationships which

might be useful in selecting a solvent for separating

fluorocarbon-fluorocarbon mixtures and hydrocarbon-hydro-

carbon mixtures.

2. To obtain a measure of the positive deviations

from Raoult's law exhibited by binary mixtures of two par-

tially miscible liquids.

Experimental.--The properties of the pure compounds

used in this study are tabulated in the appendix under

Tables VII and VIII.

The unmixing temperature of a known binary mixture

was determined by heating the mixture until the two liquids

were completely miscible, then cooling the solution slowly

and observing the temperature at which the second liquid

phase appeared. The appearance of the second phase on cool-

ing is marked by cloudiness; this cloudiness is sometimes

masked by an opalescence which occurs about 2 or 3 degrees

above the consolute temperature. Due to this opalescence,

the determination of the unmixing temperature depends to some










10
extent on the judgment of the observer.

The solubility apparatus shown in Figure 2 consisted
of a heavy-walled glass test tube clamped between two staen-

less steel flanges by means of four brwas bolts. A Teflon

gasket placed between the open end of the tube and the top

flange was used to seal the tube. A thermaocouple, which

passed through the top flange, was used to measure the tem-

perature of the mixture. The whole tube assembly was ia-
mersed in an oil or water bath, which provided the necessary

temperature control.

The solubility data are tabulated in Table XII and
the solubility curves, which were obtained by plotting the

unmixing temperature-composition data, are shown on Figures
3-7. Published data are available for the two perfluorohep-

tane systems (17); these points are plotted on Figure 3

along with the present data. The agreement between the two

sets of data is satisfactory.

Due to the presence of air in the solubility tube,
the values of the unaixing temperatures so determined per-

tain to the mixture saturated with air and at a pressure in
excess of the equilibrium vapor pressure of the mixture. The

difference between these values and those of the mixture under

its own equilibrium vapor pressure is generally assumed to be
negligible, but in order to justify this assumption the un-












sixing temperature was determined for a degassed ixture
of toluee and perfluorocyclic oxide* in a sealed glass
tube under its own equilibrium vapor pressure. This value
of the unmixing temperature is plotted on Figure 4 along with
those obtained in the presence of air and it can be seen that
there is no significant difference.

Theoretical Calculation of Consolute Temperature and
Composition.--The thermodynamic conditions necessary to de-
fine the consolute temperature are

da1 ag
"Ia 0 da io
W or \(4)
dls 421a i 1
-- 0 00"


This requirement can be seen from examination of Figure 8,
where three isothermal curves of activity are plotted versus
composition. For illustrative purposes the activity is cal.
culated from the following equation
n a1 = In X BK2 (5)

At T1, a temperature below Tc (conaslute temperature), there
exist two liquid phases having the same activity. These

*A description of this material is given in the
appendix.










12
phases correspond to points A and B. The dashed portion
of the curve has no physical significance and corresponds
to the Van der Waals isotherm in the two phase region on a
pressure-volume diagram of a pure substance. As the tem-
perature is increased, the length of the line AD decreases
until the consolute temperature Tc is reached and a point
of inflection, C, is observed in the activity curve. At
this point the first and second derivatives of the activity
are equal to zero. At a temperature T2, above Tc, the
deviations from Raoult's law become smaller and the activity
is a single valued function of composition.
The value of the activity as predicted by the Scatch.
ard Hildebrand theory is

In a1 = In x1 4 (C1 d 2 422 (6)

Using equation 6 for the activity and applying the condi-
tions of equation 4, the following expressions result for
the consolute temperature and composition.

RTc xSaa2V22 (fl )2 (7)
R TC ....(.. + ...

XI a (Vi 2 2 2 '2 V ), 1/2. V
V2 m 1

By using the entropy of nixing for molecules of different


I










13
sisMe as calculated from a lattice model along with the
energy of aixing as given by equation 1, Hildebrand (18)
derived expressions for the consolute temperature and com-
position somewhat different from equations 7 and 8

OTN 2jlV2 2>2/ -/2 1 V/22 (9)

2 1/2/2 1/2 V1/2
9i : 2V1Y2(dj 4) / (VS -- ) (9)
1/2



The consolute temperatures and compositions have
been calculated from equations 7 aud 8, and 9 and 10 for the
Systems rcreted in this work and are tabulated in Table XIII.
The values of the consolute composition in Table XIII are
given only to two figures because of the uncertainty in locat-
iag the composition corresponding to the maxima temperature.
From Table XIII it is obvious that equations 8 and 10 predict
the consolute composition quite well while equations 7 and 9
provide poor estimates of the consolute temperature. Only
for the system perfluorocyclic oxide-toluene was the consolute
temperature correctly predicted by equation 7.

The fact that equations 8 and 10 predict the consolute
composition would indicate that the volume fraction is a use-
ful variable in correlating solution behavior. This is borne
out by the successful correlation of experimental activity












coefficients by the Van LUar equation, which 18 similar in
form to equation 3, but contains two adjustable parameters
instead of constants which are fixed by the physical proper-
ties of the pure components.
The failure of equations 7 and 9 to predict the
consolute temperature is probably due partly to the failure
of fluoroearbon-hydrocarbon mixtures to eofomer to the
geometric easn aseeaption which is implicit in these equa.
tions. Equation 9 predicts lower temperatures than equau-
tion 7 because the exeoss entropy of nixing due to different
volumes is always positive and therefore the deviatonas
from aoult's law due to this correction are always negative.
Sioe f luorocarbonahydrocarbon mixtures show auch larger
positive deviations than predicted, the entropy correction
Iapairs the agreement between the observed and predicted
temperatures. It can not be stated, however, that the use of
the entropy term for unequal volumes is incorrect since the
small effect it contributes is ovoershadoed by the larger
effect probably duo to the geometric mesa assumption.
It should be mentioned that, although often used in
the literature, couparlson of the calculated and observed
conaolate temperature is not a good criterion for testing
the applicability of the Scatchard-Hldebrand theory. It










15
equations 7 and 8 predict the correct temperature and com-
position, this means that the first and second derivatives
of the true activity coefficient with respect to composition
are equal to the corresponding derivatives of the activity
coefficient as given by equation 3. This is a necessary,
but not a sufficient condition which must be fulfilled by
equation 3, for it is conceivable that two different func-
tions could have equal first and second derivatives at a

given composition. This reasoning can be substantiated by
comparing activity coefficients calculated by equation 3
with experimental values for some systems which conform to
the consolute temperature criterion. This is done below.

In a two liquid phase system the activity of a comm
ponent is equal in both phases and we can write

xi 1 a Y a(1)

In many fluorocarbon-hydrocarbon systems which form two
liquid phases the mole fraction of hydrocarbon in the hydro.
carbon-rich phase approaches unity at low temperatures and
the activity coefficient also approaches unity. Thus by set-
ting Y1' equal to unity, the activity coefficient of the

hydrocarbon in the fluorocarbon-rich phase ( TY) is equal to

the ratio xl'/xl. Values of In Y 1 so calculated are com-
pared in Table I with values predicted by equation 3 for










16
three systems in which the observed and calculated conso-

lute temperatures are in good agreement.


TABLE I
TEST OF THE CONSOLUTE TEMPERATURE CRITERION



Tc0 InY
SYSTEM obe. eq.7 C) x x'1 eq. eq. 2J2.
(C) 11 3

I 323.5 325 26.3 0.306 0.960 1.14 0.913 19
II 358.5 360 61.1 0.320 0.956 1.09 0.900 19
III 386 377 69.0 0.256 0.981 1.34 0.977 this
work

I. perfluoromethylcyclohexane and chloroform

II. perfluoromethylcyclohexane and benzene
III. perfluorocyclicoxide and toluene


One would expect the same percentage difference be-
tween the logarithm of the activity coefficients as between
the two temperatures in Table I since both Tc and In V are

directly proportional to the (1 6 )2 term. Inspection of
Table I reveals that the percentage difference between the
logarithms of the activity coefficients is much greater than
between the consolute temperatures. Since the values of InYl










17
and To in Table I are compared at different toperaturea.,
the possibility arises that the activity coefficients pre-
dicted by equation 3 are equal to the true activity coof-
ficients at the consolute temperature only, and not at other

temperatures. From consideration of the consolute tempera-

ture alone one would erroneously aassme that the three systems
in Table I closely conformed to the theory.












CHAPTER V
TOTAL VAPOR PRESSURE OF BINARY MIXTURES

ExperWiental.--Total vapor pressure versus temperam
ture data were obtained for six binary fluorocarbon-.hydro-
carbon fixtures. The physical properties of these compounds
are listed in Tables VII and VIII.
The measurements were made in the two liquid phase
region since liquid compositions could be determined from
the temperature and the experimentally established soli.-
bility curve.
A dynamic boiling still was used for these measure*
eants, the design details of which should be obvious from
examination of Figure 9. The still was designed so that
vigorous boiling and low liquid level would prevent super-
heating while the insulating vapor space would prevent any
heat lose by the vapor in the inside tube. Daurinag operation
of the still undor equilibrium conditions no condensation was
observed inside the ianer tube. A calibrated thermocouple
was used to measure the vapor temperature; the calibration
data for this thermocouple is reported in Table IX. The still
was connected to a vacuum system contain a mercury mnaome-
ter which could be read to the nearest tenth of a millimeter













by use of a cathetometer.

As a check on the performance of the still the total
pressure of the system 2 butanone-water was determined at

two temperatures. These values compare favorably with the
reported literature values (29) as shown in Table II.

TABLU II

CHUCK RUN IN TWO LIQUID PHASE STILL

System: 2 butanone-wvater reference 29


Literature This Work

Pressure Temperature Pressure Temperature
M oC m OC

760 73.3 768 73.6

500 62.0 503 62.0

The experimental total vapor pressure versus temperature

data are reported in Table XIV.

Calculation of Activity Coefficients from Liquid.
Liquid Solubility Data.-The following method for calculat-
ing activity coefficients has been described by Carlson and

Colburn (6). In a two liquid phase system the activity of a
component is equal in both liquid phases and we can write

xI 1 x' 1' (11)
z21 : z2' 2'










20
The mole fractions are known from the solubility data and
we have two equations containing four unknown quantities.
The number of unknowns can be reduced to two if it is an-
sumed that a twomcoustant equation can be found vhich correct-

ly expresses the activity coefficients as a function of
composition. One such equation which has proved useful in
correlating experimental activity coefficients is the Van
Lear equation.

Y "2 113)



la Y 8 (14)



Ift equations 13 and 14 are substituted into equations 11 and
12 written in logarithamic form, values of the constants A
and B can be found. This procedure can be repeated at several
temperatures so that the temperature dependence of A and B
can be determined. The Van Lear A and B have been calculated
for several of the fluorocarbon-hydrocarbon systems for which

the solubility curves were determined and it was found that
the constants were always linear functions of temperature.
Figure 10 shows several of these linear plots.
In order to have confidence in values of the activity











21
coefficient as calculated from equations 13 and 14, some
method should be available for determining whether the Van
Laar equation accurately predicts the activity coefficients.
One method of accomplishing this is to compare experimentally
determined total vapor pressures with thost calculated from
equation 15 using the vapor pressures of the pure compounds,
solubility data, and the Van Laar equation to determine the
activity coefficients.

TT : x1 TIPl + x2 2po (15)
A graphical comparison of calculated and experimental total
vapor pressures is given in Figures 11-16, where it is re-
vealed that the agreement is quite good at lower tempera-
tures, but becomes poorer as the temperature increases. The
fact that calculated and experimental values of the total
vapor pressure agree should not be taken as conclusive proof
that the activity coefficients predicted by equations 13 and
14 are correct, however, since there is an infinite number of
combinations of Y1 and T2 which will satisfy equation 15.

By rearranging equation 15 we see that the activity
of component two is a linear function of the activity of
component one.

a2 T/P2o alPlo/p20 (15a)










22
By using equation 15a we can establish limits for the ac-

tivity of the fluorocarbon (component 2) from the limits of

the hydrocarbon activity. The upper limit for the ac-

tivity of the hydrocarbon will be set at unity and since

these mixtures all exhibit positive deviations from Raoult's

law, the lower limit will be set at the mole fraction of

hydrocarbon in the hydrocarbon-rich phase. Table XV shows

the activity limits of the fluorocarbon as determined from

equation 15a along with the values calculated from the Van

Laar equation for all six systems for which the total vapor

pressure was determined. Table XV reveals that for most

systems the calculated activities fall within the range cal-

culated by equation 15a at the low temperatures, but deviate

at higher temperatures following a pattern similar to the

observed and calculated total vapor pressures.

The Van Laar activity coefficients determined from

the solubility data of Simons and Dunlap (39) are plotted

on Figure 17 along with their activity coefficients determined

from partial pressure data for the system perfluoropentane-

n-pentane. The value of the total vapor pressure in the two

liquid phase region for this system at 262.4K., calculated

from the Van Laar equation, is 214 ma. as compared to the

reported value of 216 am., and the Van Laar activity of

0.766 falls within the 0.718 to 0.855 range calculated from

equation 15a. It can be seen from Fig. 17 that the Van Laar










23
equation with constants determined from solubility data

predicts values of the activity coefficients which agree

very well with the experimental ones. The Van Laar equa-

tion with constants determined from solubility data has

successfully predicted excess free energies of mixing in

other fluorocarbon-hydrocarbon systems for which the ther-

modynamic properties have been determined. Figures 18-20

show that the calculated and experimental excess free

energies of mixing for the systems n-perfluoropentane and

n-pentane (39), n-perfluorobutane and n-butane (40) and

perfluoroheptane and iso-octane (26) are in good agreement.

These experimental values of the excess free energy of

mixing were determined from partial pressure data.

The solubility data for the system perfluorohep-

tane and isooctane were taken from reference (17); calcu-

lated values of A Fe for this system were made from the

solubility data and the Van Laar equation at 170 a while

the reported data are at 30 C. The excess free energy

data of Simons and Dunlap and Simons and Mausteller are

the averages of several temperatures in the ranges 262 to

293 K. and 233 to 260 K., respectively, while those cal-

culated from solubility data are at 262.4 and 220 K. re-

spectively. The small difference in temperature between

calculated and observed free energies is negligible since










24
the temperature derivative of the excess free energy of

mixing is the excess entropy of mixing at constant pressure.

Values of excess entropy of mixing are tabulated below for

several systems.



System at x 2 0.5, cal./mole OK Reference

C4'1O C410 1.00 40

CS12 CSH12 0.43 39

C716 i-CS.18 0.24 26

This entropy term does not usually exceed one entropy unit

and a change of ten degrees would result in less than a

10 calories per mole change in the free energy term.
The partial molal heat of mixing can also be cal

culated from the Van Laar equation and the temperature deriva-

tives of its constants

ANL -L A (16)
T -T Ax1l 12
Lk.B2










25
Beats of mixing calculated from the Van Laar equation are

approximately twice as large as those determined experi-
mentally in the three fluorocarbon-hydrocarbon systems

cited above. Wood (48) has calculated the thermodynamic
properties for the system cyclohexane-methanol from solu-

bility data alone, but using a two-constant Scatchard equa-

tion instead of the Van Lear equation to represent activity

coefficients. He found that his calculated excess free

energies of mixing were in line with those reported for the
methanol-benzene and methanol-carbon tetrachloride systems,

but his calculated heat of mixing values were about twice as

large as those for the two reported methanol systems.

Besides the Van Laar equation, two-constant Margules

and Scatchard equations were used in this work for substi-

tution into equations 11 and 12, but these equations pre-

dicted total vapor pressures that did not agree with the ob.

served vapor pressures as well as did those predicted from

the Van Laar equation. These two types of equation also

predicted heats of mixing which were in poorer agreement with

the experimental values than those predicted by the Van Lear
equation.

Since the temperature derivative of the free energy

is needed for calculation of the heat of mixing, mall errors

in the free energy will produce larger errors in the heat of












mixing. The disagreement between experimental heats of
mixing and those calculated from the Van Laar equation could
be attributed to small errors in the free energy as predicted
by the Van Laar equation. However, these errors are not of
a random nature since the calculated value is always about
two times as large as the experimental values.
In order to determine why the Van Laar equation fails
we should consider in detail the process by which the Van
Laar constants are determined. Figure 21 illustrates
graphically the conditions required to obtain the Van Laar
constants. Equations 11 and 12 can be rearranged to

In YI In Tl' : In x1'/x1 (lla)

In Y2 In Y2' lan x2'/x2 (12a)

The differences In1 In YT' and In 2 In Y2' are rep-
resented on Figure 21 by ab and cd respectively. Using equa-
tions 11, 12, 13, and 14 is equivalent to finding the con-
stants A and B such that at x1 and xl* the differences
In Y 1 In Y I' and In 2 In 2' given by the Van Laar

equation are equal to the corresponding differences between
the true activity coefficients. This does not mean that the
actual values of the Van Laar activity coefficients are cor-
rect or that the Van Laar curve is identical with the true











27
activity coefficient versus composition curve.

At lower temperatures the composition of the con-
jugate phases approaches that of the pure compounds and the

true activity coefficient and Van Laar activity coefficient

both approach unity. This means that at lower temperatures

the activity coefficients Y1' and Y2 corresponding to

points a and c on Figure 21 can be predicted by the Van Lar

equation. Since the Van Lear activity coefficients and true

activity coefficients approach each other at a and c, and

since ab and cd as given by the Van Laar equation are equal

to ab and cd corresponding to the true values of In Y^
In Y 1' and In Y 2 In Y2', the Van Lar and true ac-

tivity coefficients also approach each other at b and d.

This is manifested by the very good agreement between ob-
served and calculated total vapor pressures at lover tempera-

tures. As the temperature increases the concentration of

the major component in each phase decreases causing the ac.

tivity coefficients to differ from unity and it is possible

that differences occur between the Van Laar and true ac-
tivity coefficients at a and c. This would result in dif-
ferences at b and d and would cause the values of the observed

and calculated total vapor pressures to diverge,

One reason why the Van Laar equation does not correct-
ly predict heats of mixing can be seen from examination of










28
Figure S22. Curves 1 and 2 on Figure 22 represent the Van

Lear equation at two temperatures, curve 1 being at the
lower temperature. Curves 3 and 4 represent the true ac-

tivity coefficient curves, where curves 3 and 1, and 2 and 4

are at the same temperatures. Only the curves for one

component are shown for the sake of simplicity. The shape

of the two types of curves is greatly exaggerated for

illustrative purposes. At the temperature T1, the Van Lear
equation (1) predicts correct values of the activity coef-

ficient at a and b even though its form is different from

the true activity coefficient curve (3) at that temperature.

Increasing the temperature to T2 causes only a slight change

in the true activity coefficient curve (4), but due to the

difference in form the Van Lear curve (2) must change by a

greater amount in order that it may predict the activity

coefficients at c and d. Since the heat of mixing is de-

termined from the temperature derivative of the logarithm of

the activity coefficient at constant composition, it can be

seen that larger heats of mixing would be obtained by the Van

Lear equation. We see that the inability of the Van Lear
equation to predict heats of mixing could be due to a dif-

ference in form between the calculated and true activity coef-

ficient curve. This difference is undoubtedly small since the










29
excess free energy of mixing curves calculated from the

solubility data using the Van Lear equation agree in aag-

nitude and in shape with experimentally determined excess

free energy.curves.

Based on the preceding considerations it is con-

cluded that the Van Lear equation can be used to estimate
free energies in systems which form two liquid phases if

the constants are determined at temperatures where the com-

positions of the two coexisting phases approach the pure

compounds. Of course more confidence can be placed in the

Van iLar equation if total pressure data are available.
Since the temperature derivative of the free energy is small,

these estimated free energies can be used without appreciable

error at other temperatures within 20 or 30 C. of the tem-

perature at which the estimate was made. It is further con-

cluded that the heats of mixing predicted by the Van Laar

equation are unreliable.













CHAPTER VI


VOLUME CHANGES IN MIXING FLUOROCARBONS AND HYDROCARBONS

Experimental.-The molal volumes as a function of

composition were determined for four fluorocarbon-hydro-

carbon systems. The physical properties of the pure com-

pounds are given in Tables VII and VIII. Pycnometers de-

scribed by Lipkin (22) and having a nominal capacity of

5 milliliters were used to measure the volumes of mix.

tures of known composition. These pycnometers were cali-

brated with distilled mercury at 40, 450, 50, and 600 C.;

the calibration data are given in Table X.

The molal volumes of the fluorocarbon-hydrocarbon

solutions were measured over the entire composition range

at a temperature slightly above the consolute temperature

of each system. The molal volumes were also measured over

the limited composition range at two other temperatures

5 and 10 C. below the complete isotherm. For the systems

perfluorocyclic oxide-n-heptane, perfluorocyclic oxide-

carbon tetrachloride, and perfluoroheptane-n-heptane the

isothermal volume measurements were made at 400, 450, and

50o C. while for the system perfluoroheptane-carbon tetra-











31
chloride they were made at 50, 55, and 600 C. The thermal

coefficient of expansion of the materials limited the teon-

perature range to ten degrees for one filling of the pyonom-
eter.

Since some of the mixtures were two liquid phases
at room temperature it was necessary to fill the pycnonoeter

at a temperature above the consolute temperature. Figure 23
shows the arrangement for filling the pycnometer. The de-

sired mixture was weighed out into the transfer tube,

which was then closed off by means of a ground glass stopper

and placed in the water bath at a temperature above the

consolute temperature of the system. After remaining in

the water bath several minutes the tube was shaken until

mixing was complete and the ground glass stopper was replaced
by the syphon tube, which had been heated to the bath tem-

perature. The pycnometer was connected to the transfer

tube by a small section of Tygon tubing and was filled by

applying auction to the other arm. The pycnometer was al-

ways filled at the highest temperature of each series. The

pycnometer reading was taken after approximately fifteen min-
utes at the bath temperature, then the bath temperature was

lowered five degrees to the next temperature.

The water bath temperature was controlled manually











32
by meaas of an electrical heating element connected through

a Variac. The mercury-in-glass thermometer measuring the

bath temperature could be read to + 0.02 C. and was checked

against a thermocouple calibrated by the National Bureau of

Standards. The temperature of the bath never varied more

than 0.05 C. from the desired temperature while the pyc-

nometer was approaching thermal equilibrium. After the pyc-

nometer reading was made at the three temperatures the pyc-

noaeter was removed from the bath and allowed to cool to

room temperature. The pycnometer was then weighed, emptied,

and weighed empty; all weights were corrected to weights

in vacuo, Knowing the weight of material in the pycnometer,

the composition of the material, and the pycnometer read*

ingas it is a simple matter to find the molal volumes of the

mixture at the three temperatures.

The molal volume-composition data is tabulated in
Table XVI. The volume change on mixing was calculated by
equation 17

AV*= V IM x" LV 22 T (17)

The partial molal volume change on mixing was determined

by plotting the total volume change versus mole fraction
of hydrocarbon, graphically taking the tangent to the curve

at the desired composition, and determining the value of the











33

intercepts of the tangent line at x, : 0 and x, : 1.

These values of the intercepts are the partial molal volume

changes of mixing of components 2 and 1 respectively.

Plots of the total volume change on mixing ( AVM) versus

mole fraction of hydrocarbon are shown on Figures 24-27,

Values of the partial molal volume changes on mixing are

tabulated in Table XVII and plotted versus composition on

Figures 28-31.

Figure 32 shows the plots of partial molal volume

changes versus composition for the systems perfluorocyclie

oxide-n-heptane and perfluoroheptane-n-heptane superimposed,

One can see from Figure 32 that the partial molal volume

changes are practically identical for each type of compound

in both solutions and since the systems are almost symme-

trical the partial molal volume changes are nearly equal for

all three components. Since the two systems involving

carbon-tetrachloride were not determined at the same tem-

perature one would not expect the two partial molal volume

change curves to be superimposed.

It was found for these four systems that the total

volume change on mixing increased with increasing tempera-

ture; this type of behavior was also found in the C5F12.-CsEH

C4F10-C4H10 and C6F14-C6H14 systems (2).










34
The coefficient of thermal expansion (ot) as de-
fined by equation 18 was determined from the temperature-
volume data of the pure compounds and the binary mixtures.

o( : 1 fy (18)
v V T/P

Figures 33-36 show that plots of d0 versus composition for
some of the systems exhibit maxim a. The thermal coeffi-
eient of expansion for an ideal mixture (a(o) is a linear
function of the volume fraction as shown below.


0 1V1 l* a2V \1V14 x*V2/ p

0o = XLVl & xi2 l-1f
S XV1 x2V2


Equation 19 is also plotted on Figures 33-36 for
comparative purposes. In order for the total volume change
to increase with temperature it is necessary that the thermal
coefficient of expansion for the mixture be greater than the
coefficient for an ideal solution. This can be shown by dif-
ferentiating equation 17 with respect to temperature

d AM sdV dVo 2 Vo< V VO <
dT _W y 0 0












Since V t Vo

d AVN .

In order for -dAY to be positive Qo( must be greater than
3a?-
(oo; this is in accord with the experimental values of AVN
and (

Since the values of o( plotted on Figures 33-36
were determined in the region of the consolute temperature

the large values of o( might be due to the breaking up of
clusters in the liquid as the temperature increases. The
formation of clusters in systems exhibiting partial misci-
bility has been generally recognized (50). The opalescence
observed Just above the consolute temperature is believed

due to the scattering of light by clusters of molecules.

A molecule in a cluster would have more like-mole-
cules as nearest neighbors than it would have if the mixture
were homogeneous; as the temperature is raised thermal mo-
tion combats the tendency to cluster and the mixture approach-
es homogeneity. If we consider the case where one 1-1 and
one 2.2 pair rearrange to form two 1-2 pairs we find that
the interaction energy of the system containing 1.2 pairs is
2 E12 while the interaction energy of the system containing

1-1 and 2-2 pairs is E -C22 or twice the arithmetic











aean of E11 and E Since E-12 Is approximately the

geometric mean of 6 il and 22 where only dispersion
forces are acting, and since the geometric mean is always
less than the arithmetic mean, the interaction energy of
the system is less when 1-2 pairs are present. These weaker
attractive forces result in a volume expansion and an in-
crease in the enthalpy of the system.

The dispersion of clusters due to thermal agitation
would explain the fact that the volume change on mixing in-
creases with temperature and thus one would also expect the
heat of mixing to increase with temperature. The heats of
mixing in the system perfluoroheptane-iso-octane (26) were
found to increase with temperature as shown by the follow-
ing values; at a mole fraction of one-half, the heats of
fixing were 402, 468, and 616 calories per mole at 300, 50,
and 709 C. respectively. The volume change on nixing for
this system was reported only at 300 C. However, the data
of Taylor and Beed (42) show that the volume change on aix-
ing for this system also increases with temperature.

The volume change on mixing is an important property
in the study of solutions and for this reason it would be
desirable to have a theoretical expression which would pre-
dict this property. Scatchard (38) and Hildebrand (13) have










37
shown that the Gibbs free energy at constant pressure ( AFp)
is related to the Helaholtz free energy at constant volume
( A A) by the following equation

AFp AA I ( AY")2 (20)
2/pV
The correction term involving AV amounts to less than
10 calories per mole as compared to about 350 calories per
mole for AFp, and for this reason it is usually neglected.
Hildebrand used this approximation in deriving an expression
for the volume change on nixing. He started with the ther-
modynamic relation


AV : \ ) T

and by substituting A A for AFp he obtained

Ay Z T
Av ) T 4 'w ( T
By further assuming that the pressure derivative of the
entropy was zero he arrived at

S- p /T "-T Z(Vo T Ti T


(21)



(22)


(23)


His final assumption was that
1 1/z n TV
VDT )T as -V-


(24)


and that n = 1.










38
This assumption is based on the fact that for several non-
polar liquids the internal pressure )T as calculated
from the thermodynamic relation

(1 ), TA ( )z P (25)

can be represented by equation 24 where the coefficient
n varies from 0.9 to 1.1. After making this assumption,
Hildebrand arrived at the following equation for ATV


AVN /a o aW


(26)


Using equation 1 for ABl yields

go22 =(c1 )j 2 41 2 (27)

An alternate theoretical expression for AVM can be obtained
using Reed's (32) correction instead of the geometric mean
assumption, but retaining the condition of constant volume.
Under these conditions NEVN is given by
: (xl1 4 12S2) .l () 2 d'61 S2(lff)12

(28)


311 & 12
: 2(do22/doll)1/2 (34
1 d 2/doll

The ratio d22/d011 can be evaluated from the cube root of


0)










39
the solar volume ratio. Substituting equation 28 into
equation 26 results in

AV /3o(iLVl 4 xa2V2) [(I 2)2 + 2 61S 62(1

fID] +1 2 (31)
Still another expression can be obtained for DVM if it is
assumed that the entropy of mixing at constant volume is the
ideal value, then 4A B in equation 26 can be replaced by
AFIp according to the following:
AFp sAAy AtyV1 TS y
and
Ap ,es A&M TASe

If A y is assumed to have the ideal value then


and

thus
/ Av" : A re (32)

In order to calculate AYV from equations 27, 31,
and 32, it is necessary to know /o, the compressibility
of a solution showing no volume change on mixing. The com-
pressibility is defined by equation 33
/3 : 1 a V) (33)
SV i Pi T

and it can be shown that 3O is a linear function of the











volume fraction as van oo.

1o3 4A + 2 2 (34)
Isothermal compressibility data needed for equations 34,
27, 31, and 32 are available in the literature for per.
fluoroheptane, and carbon tetrachlorlde (20) and n-heptane
(46). Pressure-volume-temperature data for liquid lso-
octane are also available in the literature (3) from which
the isothermal compressibility was determined by graphical

differentiation. eostwater, Frantz, and Hildebrand (46)

have shown that for a pure liquid the quantity a as
defined by equation 35 tois independent of temperature

a = V2T0/3 (35)

Equation 35 can be used to extrapolate compressibility
data from one temperature to another if volume and coef-

ficient of thermal expansion data are also available. The

values of /3 used in equation 34 are tabulated below in

Table III.









41
TABLE III

ISOTHREMAL COMPRESSIBILITIES FOR USE IN EQUATION 34


Compound Temperature OC. /3 Atam1

Cyr7l 30 2.65(10-4)

Cy7Fi 50 3.03(10-4)

C716 60 3.42 (10-4)

n-C7yI6 50 1.82 (10"4)

CCl4 60 1.55(10"4)

1-CsS18 30 1.21(10-4)


Values of 11~v as calculated from equations 27,
31, and 32 are plotted on Figures 37-39 along with the ex-
perimental values for the systems perfluoroheptane-carbon
tetrachloride, perfluoroheptane-n-heptane, and perfluoro.
heptane-iso-octane. Figure 37 reveals that for the
C7F16-CC14 system the agreement between experimental values
of AV* and those calculated from the experimental AFpe is

quite good; the theoretical equation 31 also gives a fair-
ly good estimate of AVY. For the systems C7F16-u-C7H16

and C7F16-i-C8H18, however, all these relations prove to be











42
poor estimates of AVM. It should also be noted that
the theoretical equations 27 and 31 predict values of VIE

which are symmetrical with respect to volume fraction and

therefore should have their maximum values at a volume frac-

tion of 0.5 (about 0.3 0.4 mole fraction of fluorocarbon).

Figures 24-27 reveal that the volume changes for the four

systems of this work and the C7F16-1-CgH18 system are mor-

nearly symmetrical with respect to mole fraction, having

their maxima at a sole fraction of approximately 0.5.

Since equations 27, 31, and 32 failed to predict

reasonable values for &V it might be instructive to ex.
amine critically some of the assumptions and approximations

involved In obtaining equation 26.

The first approximation involved the neglect of the

pressure derivative of the correction term (a V)2 when sub-

stituting for AFpe in equation 21. Although this term is

small and can be neglected in equation 20 its pressure deriv-

ative may not be small enough to be neglected in equation 22.

Another source of error in equation 2# might result from
the assumption that the pressure derivative of the entropy

term in equation 22 is zero. It should be mentioned, how-
ever, that unless these two assumptions are made the ex-

pression for AV* becomes extremely complicated.










43
Another assumption, the effects of which can be
clearly seen, is the assumption that the internal pressure

can be represented by equation 24, where a is equal to
unity. The data are available with which to calculate the
internal pressure of perfluorobeptane (20) from equation

25. This calculation was made and it was found that a

value of n equal to 1.40 was necessary to satisfy equation
24.

If the coefficient n is not assumed equal to unity,
equation 26 would be written

AV a noaIyN (36)

Since n for a fluorocarbon-hydrocarbon mixture would pro.
bably lie between 1.0 and 1.4, equation 36 would predict
values of &VU larger than those predicted by equations

27, 31, and 32, which implicitly assume a value of n equal
to unity. A value of n between 1.0 and 1.4, however,
would still predict low values of aVT for the C7F16-n-C7y16

and C7F16-i-C8H8 systems since a value of n between 2.0

and 3.0 would be required for these systems. Since equa-
tions 31 and 32 closely predict &yV for the C7F16-CC14

system the inclusion of n in equation 36 would impair the
agreement in this case.











44
It is possible that equation 26 is reasonably

correct and that the expressions for AE are in error.

This possibility will be discussed in more detail in

Chapter VII.

It is concluded that there are many assumptions

and approximations involved in the derivation of equation

26 which prevent the accurate prediction of volume changes.













CHAPZU VII


NBTINATICK OF THUF ODYAMIC PROPEBTI B


Heat of Mixing.-It was previously mentioned that
Reed rederived the equations of Scatchard and Hildebrand
omitting the assumptions of no volume change and the geooe-
trio mean, and obtained an expression which predicted heats
of mixing in agreement with experimental values. Reed's
expression for the heat of mixing in a binary mixture is
given below:

AM: = (z 1V xgaV) ( + 22) 2 <1 (1

A I D) 2 1(1 I ) + X2(1 ) (37)
*j VlV2
Where (1/) 2 (38)


The terms fI and tD were defined previously by equations 29

and 30. Although equation 37 predicts values of AZp it can
be shown that the difference between ApRp and AHp is neg.
eligible. In order to use equation 37 it is necessary to know
the ionization potentials and partial molal volumes of coa-
ponents 1 and 2. Reed (34) has presented a method of pre-
dicting the ionization potential of a compound from its po-
larisability and structure which yields good results and can
be used in the absence of experimental data.
Hildebrand (14) has shown that by considering the vol-
45











46
ume change on mixing that the heat of mixing can be calcu-
lated from the following expression.

AHP: &ay (1. OLT) (39)
If the entropy change at constant volume is assumed ideal,
then &I*N can be replaced by AFpe and
&Hp = A p(1. O c T) (40)

Equation 40 can be used to calculate heats of mixing in
fluorocarbon-hydrocarbon systems for which the thermal coef-
ficient of expansion (o ) is known and where AFpe can be
calculated from the binary solubility data as outlined in
Chapter V.
Still another method of estimating the heat of mix-
ing involves the use of the following thermodynamics relation
AHp = arp TASp (41)
In terms of the excess properties, equation 41 can be written

AdRp p A fe TSA S (42)
Since a method of estimating A Fp is available it is only nec-
essary to estimate 6 Sp. The entropy change due to the vol-
ume change on mixing can be determined from the following
Maxwell relation
1-681 = (43)

For a volume change at constant pressure A 8 is given by
/-Vo AM
AS : ( ) dV (44)










47
By assuming that ( .P ) is constant over the small volume
\(T/ V
change, equation 44 results in

A~sf =Y
The 68 in equation 45 represents the change in entropy be.
tween a constant pressure and a constant volume process.
Equation 45 can then be used in equation 42 giving

AHp 1 AFpe 4 TZP ) AV)v T ASYe (46)

If A e is again assumed equal to zero, equation 46 can
be used to calculate heats of mixing where binary solubility
data, volume change on mixing data, and the value of/ Pl

for the pure compounds are available.
Westwater, Frants, and Hildebrand have measured the
quantity (4P) for several pure compounds and equiaolar bins.

ry mixtures and have found that the( Z P term for mixtures
\VT )T V
can be calculated from those of the pure compounds through
the following relation
1/2 1/2 2
amix : (xlal x2a2 ) (47)
where a is defined by equation 35.
The heats of mixing have been calculated from equa-
tions 37, 40, and 46 for the systems C7F16-n-C7118 6 C7F-16-

CC14, 1F6-~IClHi8, CS12-*C5O1I and C4710-C41R0, and are
plotted versus composition on Figures 49-53. The data neces-
sary for these calculations is tabulated in Table XXVII.
The necessary (~P data are not available for the
The nece sary V











48
C512-C5H12 and C4F10-C4H10 systems and therefore equation 46
cannot be used. Figures 51-53 reveal that equations 37 and
40 predict values of the heat of mixing in good agreement
with the reported literature values. The agreement between
equations 37, 40, and 46 is very good in the case of the
C7F16-CC14 system although no experimental values of ABp are
available for comparison. Agreement between equations 37, 40,
and 46 is not too good, however, in the C7yF6-n-C7HI6 system

where again no experimental values of AH are available for
comparison.
Free Energy of Mixing.-.As was mentioned in Chapter
V the excess free energy of mixing can be estimated quite
well from binary solubility data. Equation 28 can also be
used to estimate excess free energy of mixing if it is as-
sumed that the entropy of mixing at constant volume has the
same value as for an ideal system. Figures 18-20 show a com-
parison of AFpe calculated from equation 28 and from binary
solubility data. Reported literature values of AFp are
available for comparison in the CsF12-C5H12, C4F10-C4H10L
and C7F16--C8H18 systems. In the case of C7716-CCI4 no
literature values are available, but agreement between AFp9
calculated from equation 28 and A Fpe calculated from solubil-
ity dr :a is good. In the remaining systems equation 28 always
predicts values of AFdy which are too low.
The excess free energy of nixing can be estimated in
an empirical manner. If it is assumed that equation 28 is










49
the correct expression for A( y* and that the excess entropy
of mixing at constant volume can be represented by equation
48, then it is possible to write equation 49 for ApF .

OSe xiV i 1 1 x2V) *1 ZO 2) 2 t 2 4S 62(1
DI 1 42 (48)
AFpL (1 + zT) (xzl1 V xgV2) (( 1 12)2

2d1JC2(1 f ID) 2 (49)
The term z in equation 49 is merely a correction factor and
can be determined from an empirical correlation of z versus

2)1 e) 2 6l (l fifD)] shown on Figure 58.
Values of z used in establishing this correlation
were obtained from free energy and consolute temperature data
reported in the literature for fifteen fluorocarbon-hydro-
carbon systems. For all these systems the equations of
Scatchard and Hildebrand predict values of the free energy
or consolute temperature which are too low.
The Scatchard-Hildebrand equations for the excess
free energy and consolute temperature can be written
AFe (xIVI x2V2)K 1 2 (50)

RC (i X2V2)3 (51)
where K = (1 + zT) [(d1 d)2 .2& d4(f fD1f (52)
The parameter K represents the effective value of
(1 & 2 )2 d d"2d ( I. f o)]
necessary to fit the Scatchard-Hildebrand equations to the











50
experimental data. The value of z was determined from the
reported free energy and consolute temperature data by
using equations 50, 51, and 52. Values of K and z for the
fifteen systems are tabulated in Table XXVIII along with
the literature reference and the method of obtaining K.

This correlation is only applicable to mixtures
of fluorocarbons and paraffin hydrocarbons. Systems con-
taining benzene, carbon tetrachloride and chloroform could
not be so correlated. A glance at Figure 55 reveals that
the points are widely scattered about the correlation
line and suggests that values of AFpe calculated from

z and equation 49 would be subject to quite a bit of error.
This is not the case because z is a correction factor and
large differences in s result in smaller differences in
the factor 1 + sT. This correlation fits the excess free
energy data with an average deviation of 7 per cent and a
maximum deviation of 20 per cent.

Entropy of Mixing.-The entropy of mixing at con-
stant pressure can be given by equation 45

ASoP an to) o+ the (45)

or in terms of the excess properties

Ap AB (le + Va (45)











51
For the CyF1-i"-CaH18 system values of ASp' and AVf
have been reported (26) and the necessary ( p P data

are available in the literature (20) (3). Values of

TA5Be and TeZl A4 are plotted versus composition

on Figure 56 where it can be seen that the T z Aym

teom is much larger than T ASpW indicating negative

values for A Sye. Negative values of A8e would also

explain the fact that lFe as calculated from equation 28

Are lower than experimental values, since in using equa-
tion 28g ASye was assumed equal to zero, These negative

values of A Sye would also explain the large difference

between experimental values of AH and those calculated by
by equation 46 as shown on Figure 51. The same conclusion
concerning A 8 in the Cjl6en. CH16 system could also be

drawn from Figure 49,
The C7F16-CC14 system however, appears to have a
value of d SyW equal to zero since from Figure 54 it can

be seen that F4 7 calculated from equation 28 is in agree-
sent with AF determined from solubility data. Also values
of AH calculated from equations 37, 40, and 46 are in good
agreement as shown on Figure 50.
Another argument in favor of negative values of
A~ is the fact that the empirical correlation involving










52
z and equation 49 predicts free energies of nixing. This
correlation is based on the assumption that A Sy can be
predicted by equation 483 Since a is a positive number
then ASy* as given by equation 48 will be negative.

If negative values of A8Sy are common to most
fluorocarbon-hydrocarbon solutions, it is surprising that
equation 40 predicts values of AH in agreement with experi-
mental values in the C7116-i-C8H18, C51-Cg512, and

C4o10-C410 systems. In order to understand why equation
40 is successful in this respect it would be well to ex-
amine its derivation. This is done in the following parao,
graphs6
In order to determine the effect of small volume
changes on A By as given by equation I, Hildebrand ex-

panded A Ey about Vo using a Taylor series and obtained

IT "
(53)
By negle,'ting second order and higher terms in AV and
using the thermodynamic relation



he obtained
4Z a & BYv q T7;)V A'V1 T P 'AT1 (54)











53
The relation between AEpO and 4Hp is

aHp s 4XI PaVM (55)

Substituting equation 55 into equation 54 gives

A Up 4- ay \T/ V
We have already seen from equation 26 that the volume change
on mixing is related to the energy of mixing at constant
volume (26)

By substituting equation 26 into equation 56 Hildebrand
obtained
AHS: a E T /3, AyM (57)

If /3 and 30 are assmed equal then equation 39 results
A Hp = A (1 oT) (39)

A possible reason why equation 40 predicts reason-
able values of A H in spite of negative values of ASe is
apparent from equation 56. The substitution of A F for
ARv in equation 56 would result in values of AH which
were too high. This effect is compensated by expressing
AT by equation 26, which we have seen generally predicts
values of AYV which are too low. Thus equation 40 provides
a good estimate of AH, probably due to a fortuitous cancel-
lation of errors.
The fact that it is possible for equation 40 to pre-
dict reasonable values for A H even though A W is not zero










54

and the fact that AFe as calculated by equation 28 is less

than the observed values leads to the conclusion that &8Ve

could also be negative in the C5F12-CH12 and C4F10-C4Hlo

systems.
Negative values of ASVe for fluorocarbon-hydrocarbon

systems are not unreasonable and are consistent with the con-
cept of clustering. In a mixture containing clusters, the

distribution of molecules would not be random and one would

expect the entropy of mixing to be less than the ideal value.
The effect of raising the temperature would be to increase

the random thermal motion of the molecules and decrease the
clustering tendency. Thus the value of A tye should be-
come less negative as the temperature is increased, causing

the value of LSpe to increase with temperature. This effect

was found in the C7H16-i-C8H18 system where the following
values of A8pe were reported for an equimolar mixture.

t AlSpe (cal./mole OK)

30 oC. 0.24
50 OC. 0.46
70 oC. 0.89













CNAP!'U VIII


TERNARY LIQUID-LIQUID O8LUBILITY STUDIES

The ternary liquid-liquid solubility studies were
undertaken to determine whether fluorocarbon mixtures could
be separated by solvent extraction, and whether fluorocarbons
would be good solvents for mixtures of other types of coa-
pounds. Various types of organic compounds were tested as
possible solvents for separating a mixture of perfluoro-
heptane (C7Fi6) and perfluorocyclic oxide (CsFL60).

Mperimental,.-These preliminary studies were per-
formed by vigorously shaking an approximately equiaolar
mixture of the two fluorocarbons with the prospective sol-
vent in a small screv-cap vial and using a Perkin-Klaer
"Vapor Practometer" to analyse the two coexisting liquid
phases. The criterion of a good prospective solvent was tak-
en to be the difference in the C71F6 and C8130O peak height

fractions in the two liquid phases. Of all the organic sol-
vents tested, carbon tetrachloride (CC14) and a-heptane

(n-C7uH16) were found to be the most promising. The ternary

liquid-liquid phase diagrams were determined for the systems

C7Fl6-CSF60-nyHi16 and C7F11-C8Q160-CCl4 at 300 C.
55












56
The methyl ester of perfluoro-octanoic acid
(C7F15COOCH) was tested as a possible solvent for mixtures

of toluene (CgHNCH3) and methyl cyclohexane (COH1ICH3)oince

the consolute temperatures for these two binary systems

containing the eater were quite different. Toluene and

the eater are completely miscible at room temperature where-

as the consolute temperature of the methyloyalohexane-ester

system ts 45 C. The ternary liquid phase diagram was deo

termined for this system at 253 and 100 C.

The isothermal ternary liquid phase diagrams were
determined from chromatographic analysis of the two coex-
isting liquid phases. The liquid mixture was contained in

a screw-cap vial and was vigorously shaken while immersed
in a water bath. After being shaken for some time, samples

of each phase consisting of approximately 0.04 ml. were with-

drawn for analysis by a hypodermic syringe and the mixture

was again shaken. Two or three successive samples were taken

with shaking in between sampling. The hypodermic syringe

was warmed to approximately 100 C. above the temperature of
the mixture prior to sampling in order to prevent any con-

centration changes due to cooling the saturated phases. The
sample was injected into the chromatograph immediately after

sampling so as to prevent formation of a second phase in the
syringe upon cooling.












The water bath used in these determinations was deo
scribed in Chapter VI. The vial was shaken by hand during
the determination et the toluene-methylcyclohexane-ester
system, but it was found that considerable shaking was neces-
sary to effect equilibrium between phases in the two perfluo-
robeptane-perfluorocyclic oxide systems. Therefore, the vial
was shaken by an air-driven mechanism for approximately
thirty minutes before and between sampling. The agreement
between the analyses for successive samples was taken as
the criterion of equilibrium.
Since analyses were performed chromatographically,
it was first necessary to find a suitable partitioning liquid
that would resolve the ternary mixture into three separate
peaks on the chromatograph with no overlapping. After the
proper partitioning liquid had been found, it was then neces-
sary to prepare calibration curves of peak height fraction
against weight fraction for two of the three possible binary
mixtures, since it was found that a ternary mixture could be
analysed from calibration data for only two of the three
possible binary mixtures. This is due to the fact that the
solutes are in very low concentration in the partitioning
liquid and therefore act independently of each other. The
calibration data and curves used for analyses are given in
Tables XVIII and Figures 40-44.










58
The peak height traction for aucoessive samples of
one phase were usually in good agreement and the compoel-
tion was determined from the average peak height fractions.
Where significant differences occurred between peak height
fractions of Successive samples, the compositions of each
sample wer also calculated and are tabulated. The tie l11e
data necessary for construction of the phase diagcrms is taba
lAted in Table XIX sad the phase diagrams are ahown on Figures
45.45'
Conjugate curves are drawn on the phase diagrams
for the purpose of interpolating tie lines; the plait points
for two of the systems were outlasted by extrapolating the
conjugate curve to its intersection with the binodal eurve.
ohese conjugate curves were constructed from points located
by drawing lines through each end of the tie line parallel
to the side of the diagram in such a manner that these two
lines iater eoted inside the diagrams.
Varteressian and renake (44) found that ternary sol m
ability data could be represented by the following relationship

/3 Wl j ,
VI 2 3' X2
The tern /1 is known as the selectivity of the solvent aad
gives a measure of the ease with which a binary mixture can
be separated with a give solvent by solvent extraetion










59
methods. A /3 value of unity would indicate no selectivity
while solvents having higher values of /3 we mare selective.
The seleetivity is amnlogous to the relative volatility
vhi h is need as a measure of the ease with whibh a binary
mixture can be separated by distillation.
Values of the selectivity have been calculated tfro
the tie lie data sad equation 88 tor the four system
studied in this work. inse these values of the selectivity
vary only slightly with composition, their average values
are tabulated below in Table IV.

TABL IV

SOLVUTT LaCTIVITTI8


Mixture to be solvent t c. Average


C1eIo-C77r1 ccI4 so3 1.20

Ce5ru-ce3ls ,C7Ne i300 1.09

C6e5Ca3PC1c4xC3 C71PcscOc3 3sI0 .a16

eaeaCs.Nclncsa ir77cooc3 1o 1.s23


Table IT
tetrashloride is


ahows that neither a-eptaae nor carbon
a good solvent for the fluorocarbon miature











60
but that carbon tetrachloride is the better of the two.
It is also obvious that the ester is not a good solvent

for the hydrocarbon mixture.

From consideration of the Scatchard-Hildebrand the-
ory one would not expect a nonpolar solvent to be very se-

lective for either C7F16 or C87160 since their solubility

parameters (C) are almost equal, being 5.93 and 6.05 re-
spectively. The difference is a measure of the deviation

of a binary system from Raoultt* law as shown by equation 3.

One can see that for a given solvent the S difference be-
tween C7F16 and solvent is practically the same as the Cr

difference between C8F160 and solvent. The high solvent

selectivity found in some reported systems can be attributed

to specific effects such as association, solvation, or hy-
drogen bonding, which are not present in nonpolar systems.
Since the solubility parameters of the fluorocarbons are
almost equal, and since they are nonpolar they cannot exhibit

specific interaction effects with the solvent, It is con-

sidered unlikely that a separation can be effected by sol-
vent extraction.

Theoretical Calculation of Activities in Ternary
Systems.-Hildebrand (15) has extended the treatment of solu-

tions of nonelectrolytes to ternary systems and has arrived










61
at equations 59 for the activity coefficients in terms of
the properties of the pure compounds.

Rt In Y< 1 3 Vi 2 d 2) ( 1 63) 3] 2

(59)
T ]A Vg 2 Z 2
RTlnY3 V3 (3 1S)s f (3- 2) ] 2

Using equations59 the activities in the two conu-.
gate liquid phases can be calculated from the tie line
data. If equations 59 correctly predict activity coeffi-
cients, the calculated activities must satisfy the condition
that the activity of each component be equal in both phases.

Z1 YL x YI

x2) 2 x2'Y2' (60)

3 3 s3 3
Squations 59 were used along with the tie line data
to calculate activities in the coexisting phases for the
systems CF71.-C816O-CCL4 and C716-C810.Oa-CC716. The

solubility parameters were evaluated froa the properties of
the pure components. These calculated activity values are
tabulated in Table XX. From Table XX it is obvious that the
results of equations 59 do not satisfy the conditions of
equations 60. If, however, equations 59 are used with the











solubility parameters evaluated from the binary solubility
data, the activities are found to satisfy equations 60, s
can be sees trom Table XX.
The "etteetive" solubility parameters eaa be found
from the binary solubility data by substituting equations
3 into equations 11 and 12. Two empirical values of each
difference are obtained trom this procedure sinoe there are
two equations (11 and 12) sad only one uaknown (the X ditf
tmenoae) It was found that there was only a slight dif-
ferenee between the two f difference terms sad therefore
aa average value vwa used for substitution into equation 59o
Since the following relation holds
&1 only the difference for two of the binary systems is
needed to evaluate all possible c difterenaes required by
equations g9. Valuea of the O dffttreace evaluated ftro the
binary solubility data are compared with these evaluated
from properties of the pure compounds n Table V.











TAME V

COUPARIS0N OF S DMFFRENCE


S e Difference
System .
Pure Compounds Solubility

C716.-n-CAH16 1.43 2.87

CgF60i-n-C7H16 1.31 2.78

C7r16-cc14 2.52 3.10

C1r6O0-CC14 2.40 2.94


8ince the Van Laar equation has proved useful in

treating binary systems it would be interesting to see if
ternary systems are also amenable to this treatment.
White (47) has applied the Van Laar equation to calculate
equilibrium vapor-liquid compositions in ternary systems
from data obtained from the binary systems. He compared
the calculated results with experimental data for three
ternary systems and found the agreement to be good enough
for engineering purposes. Robinson and Gilliland (36)
have shown that the Van Laar treatment can be extended to
ternary systems where the Van Laar constants for only two
binary systems are needed to calculate activity coefficients
in the ternary system. The ternary Van Laar relations are












'A2 x3A32 vAW/%s


in Y_2 x2A12 All *_ xA_32_ 32
21/12 *, 2 + zx3A32B32]

in Y3 1 | 12 rA31/B12 1' 32
[ /lA Bl: 4+ 2 + Ax3A32/SS
In evaluating the constants in equations 61 the
relations are used


2
(61)

2


following


A12 B21
812 A21
and
A21 B12
Since the square roots of the binary Van Laar con-
stants are needed for equations 61 the question arises as to
whether the positive or negative root should be used. In
This case the binary Van Laar equation is considered similar
in form to equations 3, where the constants can be written

A12 V1 (1 d2) 2
1,f 2 3 ( &2 2)2

22 T
and A12 V1


The square root of A12 is taken to be positive if 6 is


In Y1 =












greater than C2 and negative if the reverse is true. The

relation existing between the constants which allows the
evaluation of all constants from the constants of two bi-

nary systems is

\A \/ ra3X 0

The necessary constants for use in equations 81 were
determined from the binary Van Lar constants by the pro-
cedure described above. The activities for each component
in the two coexisting phases were calculated for the systems
CyF16-C8gF10-CC14 and C7F6CgsF1r60-W-C718.6 These activities

are tabulated in Table ZXX and it can be seen that equations
61 satisfy the conditions of equations 60. Thus we see that
equations 59 or 61 can be used to predict activities in
ternary systems when the constants are evaluated experimen-
tally from two binary systems.
It is also possible to use equations 59 or 61 to
construct the ternary phase diagram from the binary solu-
bility data. This can be done graphically by using equation
59 or 61 to plot contours of constant activity for each com-
ponent on a triangular diagram. The composition of the two
phases in equilibrium can be found by locating two points
at which the activity of each component is equal. An at-
tempt was made to use this method to calculate the phase











66
diagram for the C7716-CF160-CC14 system, but location of

the phase compositions proved very difficult since it was
necessary to interpolate between three sets of activity

contours.













CHAPTER IX


ETRACTIVE DISTILLATION STUDIES

The term extractive distillation refers to the
process of adding a solvent to a Mixture to be separated

by distillation in order to improve the relative volatility.
The solvent is able to improve the relative volatility by
altering the activity coefficients of the various compo-
nents. The relative volatility (0() is defined for a bi-
nary mixture by equation 62

( = y- (62)
i Y2

(In equation 62 the subscript 1 refers to the more volaw
tile compound.) For systems obeying Dalton's law of par-
tial pressures and where deviations from ideal gas behavior
can be neglected the ratio yl/x1 is given by


yl/xI -a

Substituting into equation 62 gives

o1 A1f (63)


From equation 63 it can be seen that by selecting a solvent











63
which increases the ratio of activity coefficients the rela-
tive volatility is increased.
In practice the solvent used is essentially non-
volatile or of a low volatility compared to the original
components and the quantity used is such that the original
components are in low concentrations in the liquid phase and
dc not interact with each other appreciably. This being the
case, the ternary mixture can be treated approximately as
two binary mixtures involving each original component with
the solvent. Since the solvent is essentially nonvolatile
the vapor phase is assumed to consist only of the original
components.
The Scatchard-Hildebrand theory can be used to pre-
dict some properties of a good solvent for extractive
distillation. Assuming two independent binary systems, the
expression for the logarithm of the activity coefficient
ratio as given by equation 3 is

RT lan Y1/ Y2 00 V1 4 3 V2 4 <) 32

(64)
(In equation 64 the subscript 3 refers to the solvent.)
If the molal volumes of components 1 and 2 are ap-
proximately equal then equation 64 becomes


S in [Y/ 2) (,

(65)











69
From equation 65 we see that the logarithm of the activity

coefficient ratio depends upon the square of the volume

fraction of solvent and upon the solubility parameter of the

solvent. From the standpoint of separating power the

properties of a good solvent will be those which increase

the right hand side of equation 64 or 65. This indicates

that the molal volume and the solubility parameter are im-

portant factors in selecting a solvent. It is difficult to

predict the effect of temperature upon the activity coeffi-

cient ratio as given by equation 65 since the molal volume

changes in the same direction as the temperature, and the

difference term is more or less independent of temperature.

One would therefore not expect the activity coefficient ratio

to be a strong function of temperature.

In this work several compounds will be evaluated as
extractive distillation solvents for mixtures of perfluoro.

heptane (CyFl6) and porfluorocyclic oxide (C8F160); also

n-heptane (n-C7H16) and methylcyclohexane (C6gl11C%).

A convenient method of evaluating prospective ex-
tractive distillation solvents is by means of gas-liquid par-

tition chroaatography. Porter, Dual, and Stross (30) have
shown that the activity coefficient of a solute in an in-

finitely dilute solution in the partitioning liquid can be

obtained from the appearance time of the solute peak. The












activity coefficient ratio in equation 63 can be found from
the appearance times of components 1 and 2 when the prospec-
tive solvent is used as the partitioning liquid. The follow-
ing relations were given by Porter et al for determining the
activity coefficient in the infinitely dilute solution.

V R 0 VO+ B av (66)

S : aT/YOpVs (67)

V 0 V (p/ ) ) (68)
R L,3(Pi/ Po)2

The volume occupied by the vapor phase in the column (V0)
is usually mall compared to V0 and can be neglected.
Neglecting V0 and combining equations 66 and 67 we get
o VgRT
VR O (69)
P Vg
If the appearance times, for components 1 and 2 are de-
termined under the same conditions of constant flow rate and
constant pressure drop through the partitioning column then
we can write

S02 R2 02 (70)
.- .- (0

From equitiun 69 the ratio VR2/ v1i can be written

vT = 91 (71)
YR 2 oP










71
Equating equations 70 and 71 gives


(72)
Y20 GlPlO
Substituting equation 72 into equation 63 yields the follow-
ing expression for the relative volatility of components 1
and 2 at infinite dilution in the partitioning liquid.

o0 : e0/ 0e (73)

Since the value of the relative volatility as given by equa-
tion 73 is for an infinitely dilute solution, the ratio of
the appearance times gives the maximum separation that can be
obtained when using the partitioning liquid as an extractive
distillation solvent.

Experimental. -The chromatography columns used in
this work were made from one meter lengths of one-fourth inch
copper tubing; these columns were used in a Perkin-Blmer
"Vapor Fractometer,' model 154.

The stationary phase was Celite C44857 (Johns-
Manville), a diatomaceous earth having rather uniform parti-
cle sime. Before this celite was used the very small parti-
cles were removed by allowing the material to settle in water

and decanting the water containing the suspended fines. After
this the celite was washed several times with concentrated
hydrochloric acid, then washed with distilled water and dried













in an oven.

The prospective solvents were perfluorokerosene,
and three Kel-F oils having the general structure

Cl(CF2CFCl1)Cl. These oils are products of the N. W.
Kellogg Company and were designated Kel-F oils 1, 3, and

10. The N. W. Kellogg Company reports the following vapor
pressures for these oils at 1000 C.

Kel-F Oil 1...17 mm

Kel-F Oil 2... 1 Ma

Kel-F Oil 10..0.1 ma
These four liquids were chosen as partitioning
liquids since their vapor pressures were low enough to

prevent their removal from the packing during operation of

the column at adequate gas flow rates and temperatures.
The ratio of partitioning liquid to Celite used in the
preparation of the partitioning columns was 0.5 to 0.7 ml

of liquid per gram of Celite. The weight of packing required
to fill the column was measured so that the void volume and

the volume of the stationary phase could be computed. The
properties of these columns are tabulated in Table XXII.

The four above mentioned par' zoningg liquids were
evaluated as possible extractive distillation solvents for
the binary systems C7F16 with C8F160, and C7H16 with C6HICE3*.











73
Table XXIII gives the appearance times of C71F8, C8160,

CyH16 and COH11C3 in the partitioning liquids and Table
XXIV gives the values of the relative volatility as cal-
culated from equation 73.

From Table XXIV it can be seen that all four sol.
vents can be rated equally as extractive distillation sol.

vents frr both binary systems. The pronounced effect of team
perature upon the relative volatility is also noted from
Table XXIV.

The C7F16-CsF160 system was investigated by Yen (49)
and was found to obey Raoult's law. Since this system is
ideal the relative volatility is merely the ratio of vapor
pressures. Using the vapor pressures listed in the appendix

for C7716 and C8g160, the calculated relative volatilities

for this system at 350 and 80 C. are 2.34 and 1.96 rela-
tively. Using an average value of the relative volatility
for these compounds in the four solvents it can be seen that
the addition of the solvent changed the relative volatility
from 2.34 to 2.62 at 350 C. and from 1.96 to 2.16 at 800 C.
This change corresponds to a change in Y*/ Y2 from 1.00 to

1.11 at 35 C. and from 1.00 to 1.10 at 800 C. The effect
of temperature upon the activity coefficient ratio is very
slight as was previously suggested.











74
The n-heptane-aethylcyclohexane system was investi-

gated by Bromiley and Quiggle (4), who found the average value

of the relative volatility to be 1.074 in the temperature

range 900 to 101 C. The system obeys Raoult's law and the

relative volatility can be expressed as the ratio of vapor
pressures. Using the vapor pressures calculated from the

Antoine equation given by reference 1 the calculated relative
volatilities for this system are 1.003 and 1.057 at 35 and

800 C. respectively.

Again using the average value of the relative vola-

tility for all solvents it is seen that the relative vola-
tility for these hydrocarbons changed from 1.003 to 1.11 at

350 and from 1.057 to 1.21 at 800 C. The addition of the sol-
vent caused the activity coefficient ratio to change from
1.00 to 1.11 at 35 C. and from 1.00 to 1.14 at 800 C. Again

the effect of temperature on the activity coefficient ratio
is seen to be slight.
Since the physical properties necessary for evalua-

tion of the solubility parameters of the solvents (Cf3) are

not available it is not possible to predict the expected

value of the activity coefficient ratio as given by equation

64 or 65. Equation 64 can be used, however, to evaluate the
solvent solubility parameter ( 63) by using the experimentally

determined activity coefficient ratio and the necessary phys-











75
leal properties of the solutes given in Table XXVI. Values
of S3 were calculated from data for the C7F16-C68018 -
solvent, and C7I16-C6H11CR3 solvent systems at the tem-
peratures of 3U C. sad 80 C. These values of f3 are
tabulated below and it can be seen that 63 ea oentially
the me value when evaluated from experimental data f ra
two different systems.

TABLE VI

CALCULATION OF d0 3 GM EQUATION 64



t (C.) C716-CSgF1O-Solvent C7Hlg-CgNlCC1-solvent

35 7.88 8.05
so8 7.80 7.52


The results in Table VI indicate that the equations
of Seatahard and Nildebrand are applicable to prediction of
solvent properties. From the results of Table VI the average
solvent solubility parameters are 7.98 at 380 C. and 7.51 at
80 C.
These values of the solubility parameter nay seem
somewhat high for chlorofluerocarbon compounds since chloro-.
flueorocarbons for which data are available have solubility

parameters between these of fluorocarbons and hydrocarbons









76
kaviag the Sme boiling points. It should be acted, how..
ever, that the solubility parameter iaereasem with lacreso-
Lag molecular weight within a homologous series a is ob-
vious from the following table of solubility parameters for
the paraffin series as reported by Hildebrand (16).

compound a at 2s c.

!- A%" 7.05

W-C. 14 7.30


_n yCa 7.,.


0% 4 8.0

It right be argued that the large olubility parsme-

ter of the solvets would le4d to imiastellity in the case

of the fluoremarbons, but since the molal volumes of these

solvents are undoubtedly large the entropy effect due to vol-

ame disparity should be considered. The effect of differences

in moIal volumes to to decrease the positive deviatloas from

Raoult'a law and it is possible that the volume disparity is

large *ough to permit miscibility in spite of the large
difference.

In the light of the volume disparity it would be










77
interesting to determine the effect of this factor upon the
activity ooeffieieat ratio of solutes in an extractive
distillation solvent Instead of using equation 3, the
folloviag equatioea as give by Hildebrand (12) will be used
far the activity oeeefieiont since a corretion term for
volume disparity is ieclu4ded
Ia Y11 (c 6) xa 4 i/2 (I ) (74)
T2
If ve again ask the assumption that the volume fraction of
solvent is large enough that component 1 and 2 act ainde
pendeatly of seah other v oea write for the activity 0oef-.
ftlient ratio

In I/ Cs )2 +:2 '12 S2 CF3&2 02s
xL';: Vl/ "" (7$)


V2
When the nolal volumes of the solutes are apprxiaately
equal the last two teras in equation 76 awe eligible and
equation 7T reduces to equation 64. Thus while the volume
eorreetion does affect the ladividmal activity sooefileents,
the relative volatility of the solutes is unaffected. The
success of the Scatehard4ild ebrmad Theory is predicting rel-
ative volatilitte for extractive distillation As then due to
the eamoellation of errors in the individual activity coeffl-
eient expressions when the ratio of activity ooefflieeata are











78
used. hies tact wM rwcogaiad by meed (3s) sad vwa ued by
bin to explala the uneosm of the Scateard "b-il-d raad the-
ory in prediCting asetropes (33) sad relative velatil.tis
in hydrocarbon system.














CHAPTER X


EVALUATION OF METHODS OF SEPARATING FLUOROCARBON MIXTURES

This discussion will deal mainly with possible pro-
cedures for separation of fluorocarbon mixtures since

separation procedures for hydrocarbon mixtures have been

covered quite thoroughly by Rossini et &1a (37).

Distillation.--Several binary systems containing
fluorocarbons have been investigated (5) (24) (49) with

ideal solution behavior reported in all cases. Since fluoro-

carbon-fluorocarbon mixtures can be expected to follow ideal

behavior, the relative volatility or the ease of separation

depends upon the ratio of vapor pressures of the compounds

to be separated.

Yen has shown that when fluorocarbon mixtures are
distilled, laboratory distillation columms are approximately

one-half as efficient as when hydrocarbon mixtures are dis-

tilled. A laboratory distillation column having 100 theoret-

ical plates in a hydrocarbon separation would have approxi-
mately 50 theoretical plates in a fluorocarbon separation.

Aseotropic Distillation.-As would be expected from
the large positive deviations exhibited by fluorocarbon-

hydrocarbon mixtures, aseotropes are formed between fluoro-
79













carbons and hydrocarbons even when differences in normal

boiling points are large. This azeotropic tendency has been

exploited by Mair (23), who used fluorocarbons as azeotrop-

ing agents in separating paraffin and cycloparaffin hydro-

carbons.

The C7F16 and CSF160 used in this work were each

purified by azeotropic distillation with n-C7H16. Since the

addition of a hydrocarbon azeotroping agent to a fluorocarbon

mixture would also increase the efficiency of the distilla-

tion column, it is possible that azeotropic distillation

holds some promise as a means of separating fluorocarbon mix-

tures.

Extractive Distillation.-*It was shown earlier that
some enhancement of the relative volatility of a fluorocarbon

mixture could be obtained by employing a chlorofluorocarbon

solvent for extractive distillation. Yen found chlorofluoro.

carbons to have column efficiencies slightly less than hydro-

carbons, but approximately twice as large as fluorocarbons,

In this case the added solvent would enhance the separation

by increasing the relative volatility and by increasing the

column efficiency.

The effect of the relative volatility and column effi-
ciency upon the separation obtainable by distillation can be

seen from an equation derived by Fenske (8).















X2) D /w (76)
Equation 76 applies for conditions of total reflux and con-
stant o0. The left hand side is a measure of the separation
attainable in a column of N plates; a large value of the
ratio on the left-hand side indicates good separation. The
effect of increasing the coluxa efficiency is to increase the
number of theoretical plates (N); thus if both the relative
volatility and the column efficiency are increased the re-
sulting change in separation can be large.
Liquid Jatraction.-We have seen earlier that separam
tion of fluorocarbons by liquid extraction is not feasible
where specific interactions between one component and the sol-
vent are absent. Where a functional group is present in a
fluorocarbon, there is the possibility that a solvent can be
found which will be selective for this compound. An example
of this type could be found in the system C81F60-C1F35H-

C2H5OH where C8gl60 and C2HsOH are practically immiscible
while C7F15H and C2H50H are miscible even at temperatures as

low as -50 C. In this case there is undoubtedly a hydrogen
bonding effect which would permit the separation of C7F15H
from C81F60 by extraction with C2Hs5O.














CHAPTER XI


COWCLUSIONS

The experimental work and discussion included in
the previous sections of this dissertation provide the

basis for the following conclusions.

1. The simple Scatchard-Rildebrand theory is in-

adequate for predicting excess free energies of mixing,

heats of mixing, and volume changes in fluorocarbon-hydro-

carbon mixtures.
2. The Scatchard-Bildebrand theory with the modi-

fications introduced by Reed provides good estimates of the

heat of mixing in fluorocarbon-hydrocarbon systems.

3. Good estimates of the excess free energy of mix-

ing can be calculated from the Van Laar equation and bi-
nary solubility data.

4. Beats of mixing calculated from the Van Laar

equation and solubility data are unreliable.

5. The excess free energy of mixing fluorocarbons
with paraffin hydrocarbons can be estimated from an empiri-

cal correlation if values of the solubility parameters,
ionization potentials, and molal volumes are available.












6. Comparison of the calculated and observed con-

solute temperature is not a good criterion for testing the

applicability of the Scatchard-Hildebrand theory.

7. Mixtures of fluorocarbons with hydrocarbons

exhibit large volume changes on mixing (in the order of 3

per cent of the total volume at 50 mole per cent). This

volume change on mixing was found to increase with increas-

ing temperature.

8. A negative excess entropy of mixing at constant

volume can be used to explain the disagreement in some

fluorocarbon-hydrocarbon systems between observed thermody-

namic properties and those calculated from the Scatchard-

Hildebrand theory.

9. The concept of clustering can be used to explain

the negative values of the excess entropy of mixing at con-

stant volume.

10. Scatchard-Hildebrand or Van Laar equations may

be used to predict activities in ternary systems if the con-

stants are determined empirically from the solubility data

for two of the binary systems.

11. The Scatchard-Hildebrand equations can be used

to predict relative volatilities in systems containing an

extractive distillation solvent.











84
12. The possibility of separating a mixture of two

fluorocarbons by liquid extraction is slight unless one

fluorocarbon contains a functional group which will permit

some sort of interaction with the solvent.

13. Future work should be directed toward the

measurement and theoretical calculation of the excess entropy

of mixing at constant volume.

14. The problem of theoretically calculating the

volume change attending mixing remains unsolved. Some light

may be shed upon this problem when a theory is developed

which will predict the entropy term.











APPENDIX


I. Purity of Compounds Used

Hydrocarbons.-Most of the hydrocarbons used in this

work were obtainable commercially in a reasonable degree of

purity and were not further purified. The physical proper-

ties of these compounds are listed in Table VII along with

the reported literature values.

Fluorocarbons.-Five fluorocarbon compounds were

used in this work. The physical properties of which are

listed in Table VIII. The physical properties of some of

these fluorocarbons have been reported in the literature;

these values are also included in Table VIII. Since the

supply of some of the fluorocarbon compounds was limited

it was necessary to recover some fluorocarbons from mixtures

with hydrocarbons and repurify then. Where this was done

the physical properties of both batches are recorded in
Table VIII.

1# Perfluorocyclic oxide, C8F160. This material

was the major constituent in "Fluorochemical 0-75"

manufactured by the Minnesota Mining and Manufacturing
Company. It is believed that this fluorocarbon is a

five or six membered, oxygen-containing ring with side
chains. This material was first fractionated in a labo-

ratory distillation column having 60 theoretical plates
85












(when tested with hydrocarbons). The center cut from

this fractionation was further purified by an aseotropic

distillation with n-heptane. The fluorocarbon was then

separated from the hydrocarbon by cooling the azeotrope

to dry ice temperature where liquid phases were found

having very low mutual solubility. The perfluorocyclic

oxide was then freed from the small amount of remaining

n-heptane by redistillation in a 30 theoretical plate

column (when tested with hydrocarbons). A chromatograph
of this purified material revealed only one peak.

2. Perfluoroheptane, C7F16. This material was a
constituent of "Fluorochemical 101" marketed by the Minn-

esota Mining and Manufacturing Company and was purified

by the same procedure as perfluorocyclic oxide. This

purified material also exhibited only one peak when sub-

jected to chromatographic analysis.

3. Perfluorotributyl amine, (C4F9)3N. This material

was the center cut obtained by fractionation of Minne-

sota Mining and Manufacturing Company's "Fluorochemical
N-43" in a 60 theoretical plate column (when tested with

hydrocarbons). Chroastographic analysis indicated that

this material was a mixture of several components, proba-

bly isomers.

4. 1-Hydroperfluoroheptane, C77F15H. This material











87
was prepared in the Fluorine Research Laboratory by

Dr. N. C. Brown by the decarboxylation of the sodium

salt of perfluorooctanoic acid. This material was puri-

fied by simple distillation in a column having 60 theoret-

ical plates (when tested with hydrocarbons).

5. Methyl perfluorooctanoate, C7F15COOCH3. This
material was also prepared by Dr. H. C. Brown from per-

fluorooctanoic acid and was purified by simple distilla-

tion in a 60 theoretical plate column (for hydrocarbons).

II. Thermocouple and Thermometer Calibration

All thermocouples used in this work were the copper-
constantan type. Thermocouple readings were made with a

Leeds and Northrup potentiometer No. 8662 which could be
read to 0.001 millivolt.

1. Thermocouple in two liquid phase still. The

calibration temperatures for this thermocouple were the

ice point and the boiling points of methylcyclohexane at

757.45 and 381.05 pressure. The boiling points of
methylcyclohexane at these pressures were determined from

the Antoine equation given in reference 1. The poten-

tiometer readings (in millivolts) at these temperatures
were used to determine the constants in a three-constant

equation. The calibration data and equation are given

in Table IX.









88
2. Thermocouple in Solubility Cell. This thermo-
couple was calibrated against a thermocouple previously

calibrated by Dr. T. K. Reed of the Fluorine Research

Laboratory having the following calibration equation.

t 0.050 + 24.91e 0.3592.2
The two thermocouples were immersed in a wator bath

and both readings were made at the same temperature.

These millivolt readings are listed in Table IX along

with the bath temperatures calculated from the above

calibration equation. Since the two thermocouple

readings were practically identical, the calibration

equation for the thermocouple in the solubility cell

was taken to be

t Z 0.050 + 24.91e 0.3592e2
3. Thermometer in Temperature Bath. This mercury-

in-glass thermometer was graduated in tenths cf degree

centigrade and could be read to 0.02 C. This ther-

mometer was calibrated against a thermocouple calibrated

by the National Bureau of Standards. The calibration

data are given in Table IX.

Pycnometer Calibration Data and Equations.--The
calibration data for five pycnoneters at several tempera-

tures are tabulated in Table X. The pycnometers were de-

signed by Lipkin (22) and w.wr: essentially U tubes with a











89

bulb in one arm. The arms were capillary tubes provided

with etched graduations.

At a constant temperature each pycnometer was cali-

brated by determining the volumes corresponding to three dif-

ferent liquid heights in the capillary arms. The volume was

related to the total liquid height by the following equation

V = Vo + ah

The constants Vo and a were determined by the method of

least squares.

The volume of a pycnometer at a particular liquid

height was determined from the weight of distilled mercury

occupying the pycnometer and the density of mercury at that

temperature. All weighing were corrected for air buoyancy.

The pycaometers were kept in a constant temperature bath for

approximately thirty minutes before the liquid heights were

read. The constant temperature bath never varied more than

0.050 C. froa the calibration temperature.

Vapor Pressure Measurements.*-The vapor pressures of

all of the pure fluorocarbons were determined over a range of

temperatures by measuring the boiling temperature under various

applied pressures. The still shown on Figure 9 and a boiling

point still similar to that described by Quiggle, Tongberg,

and Fenske (31) were used for these measurements. Calibrated

thermocouples were used for temperature readings. The stills











90

were connected to a closed system containing a mercury
manometer which could be read to 0.10 am by means of a
cathetometer. The experimental data are reported in Table

XI and log p is plotted versus 1/T in Figure 1.











11 A AF 4 A^ A* A
#-A
U A f-IQ 6r4Cf P-4C4 r4 ri) u4<
94 %woe

-M 0 1
M6 "4 m .
1 eg a 0 0 .
0

14 *-t tc o .
j ^' *I ." 8 ft
2 4


^*'B 8^ >^ti <(^ ~ i A
54 4 !M e g 8
+f t % a o
S. *




| 4 11043 8 2 8
^-. H .
00 i 0 "1 0 0


cc0
&r go 5 0 0. 0



m M 0. 0 0.



8 -^ i
00 0 p4 r(0 0
f I
'4"I




i~it.. 0. C'
440 0
sd Owd
i 0r 0 0 S m
i~ 00 3*4 1
j~ --- ff i -dca --- d__-'





____ a & nsa Aug



91




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PAGE 1

PHASE EQUILIBRIUM IN SYSTEMS CONTAINING FLUOROCARBONS By BENJAMIN G. KYLE A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA FEBRUARY 1958

PAGE 2

ACDOWLBDG.llllff The author wishes to thank Dr T. Beed for b1a advice and pidance throughout this investigation. Appreciation is expressed to the supervisory cOllllit 'tee aeabera, Dr. llacJr Tyner, Dr. W. s. Brey, Dr. B. s. Jllachlitz, and Dr. a. B. Beanett for their aid and cooperation. 11

PAGE 3

ACDOWLBDGJIBMT. LIST OF T.ABLBS. TABLJ: OF COIITBRTS Page ii iv LIST OF ILLUSTRATIONS CBAPl'D vi I PUBPOSB . . . . . . 1 2 5 9 I I ll'OIIDCLA TUU III IlffBODUCTION IV BIJUBY SYST:mS FORIIIHG ffO LIQUID PBASBS. Y TOTAL VAPOR PUSSUU OF Blll'ARY MIXTURBS 18 VI VOLtJIIE CBAXGBS IN MIXING FLUOROCARBONS ARD BDBOCAllBOlfS 30 VII BSTIDTIOll OF TBDIIODYNJJIIC PBOPBllTIBS 45 VIII TDlU.llY LIQUID--LIQUID SOLUBILITY STUDIBS 55 IX BXTRACTIVB DISTILLATION STUDIES 67 X EVALUATION OF IIETBODS OF SEPARATING FLUORo-CARBON MIXTURES 79 XI CONCLUSIONS 82 APPENDIX 85 TABLES FIGURES 91 129 183 186 UFERBNCBS BIOORAPHICAL ITEMS iii

PAGE 4

LIST OF TABLES TABLB Page I TBST OF THE COHSOLUTB TBIIPBRATUU CRITDIOH 16 II CHBCK BUB IH TWO LIQUID PHASE STILL. 19 III ISOTIIBIUIAL COJIPUSSIBILITIES FOB VSB 11f EQUATION 34. 41 IV SOLVENT SELBCTIVITIBS V COIIPARISOH OF d DIFFDBNCB VI CALCULATION OF d' 3 FBOII BQUATIOH 64 VII PHYSICAL PROPERTIES OF HYDBOCARBOJIS USED 59 63 75 11' THIS WORK 91 VIII PHYSICAL PBOPDTIBS OF FLUOROCARBOMS USED IM THIS WOU 92 IX THBIUIOCOUPLE AND THDIIOIIBTD CALIBRATIONS 93 X PYClfODTD CALIBUTIOBS XI VAPOR PRBSSUUS OF PUU FLUOROCARBONS XII SOLUBILITY DATA 95 96 101 XIII COIIPARISON OF CALCULATBD AND OBSDVED COHSOLUTB TBIIPDATUUS DD COIIPOSITIONS 107 XIV TOTAL VAPOR PRBSSUU-TBIIPDATURB DATA 108 XV COIIPAJUSON OF VAN Lila ACTIVITIES WITH ACTIVITY RANGE CALCULATED FBOJI BQUATIOH 15& 109 XVI VOLDU OP MlrruaBS OF PEBJ'LUOROIIBPl'AHB AND CARBON TBTBACBLORIDE; PBBl'LUORO CYCLIC OXIDE AHD CAllBOH TBTBACBLORIDB; :fBU'LUOROCYCLIC OXIDE AHD n-HOTAHB; AXD PERFLUOROHBPl'ANB A1fD n=itBPTAHB 111 iY

PAGE 5

TAB.LB XVII TOTAL VOLUJIE CRAKGE AND PARTIAL IIOLAL VOLUIIB CHANGE 01' MIXI1'G XVIII CALIBRATIOlf DATA POB ANALYSIS OF SYSTBIIS: C7P1a-CaP1sO-CCl4; C7P15-CsF150-,!-C7H16; Page 114 A.HD CsB5Cffa-Ce H 11Clfa-C7F15COOCila. 118 XIX TIE LIRE DATA XX ACTIVITIES CALCULATBD FROII EQUATIOB 59 DI ACTIVITIES CALCULATED l'ROII tqUATIOll 61 XXII CHABACTEBISTICS OF CBROlllTOGRAPIIY COWIIRS 120 122 123 use IN EXTRACTIVE DISTILLATION STUDIU 124 DIII APJ'UUCE TIKB 01' C7F1s, CsF160, !,-C7H1s Alm CaH11Clfa II THE VilIOUS PAltTITIORIRG LIQUIDS 124 XXIV llELA.TIVE VOLATILITY OF THE ~F1a-C s F160 SOLVENT AND n-C7H1&-CeH11CJ13 SOLVDT SYSTBIIS 125 UV ACTIVITY COKFFICIBRT RATIOS BAUD OB AVERAGE RELATIVE VOLATIL.ITY MR ALL SOLVENTS DVI PROPERTIES OF PUU COIIPOUllDS FOB US:I IX 125 JQUATIOlf 64 .. 126 XXVII DATA FOR USE IX ~UATIONS 37, 40, AND 46 127 XXVIII DATA USBD IX BSTABLISHIXG BIIPIBICAL coallLATlON FO R EXCESS PUE ENERGY 128 V

PAGE 6

LIST OF FIGURES Figure 1. Vapor Pressure Data for Fluorocarbons 2. Solubility Cell. 3. Binary Solubility curves Systems Containing Page 129 130 C7F16 131 4. Binary Solubility curve Systems Containing CsF1aO 132 5. Binary Solubility curves System Containing (C4F9) 3 N 133 6. Binary Solubility curve System Containing C,F15COOCH3 134 7. Binary Solubility curves Systems Containing C 7 F15B 135 8. Activity Isotherms 9. Two Liquid Phase Still 10. 11. 12. 13. Van Laar Constants Versus Temperature. Total Vapor Pressure Plot System: Per f luorocyclic OXide-.!_-Heptane Total Vapor Pressure Plot System: Per fluorocyclic Oxide-Toluene Total Vapor Pressure Plot System: Perfluorocyclic Oxide-Methylcyclohezane 136 137 138 139 140 141 14. Total Vapor Pressure Plot System: Per fluorocyclic Oxide-Carbon Tetrachloride. 142 15. Total Vapor Preaaure Plot System: Per fluoroheptane-Carbon Tetrachloride 143 Yi

PAGE 7

Figure 16. 17. 18. 19. 20. Total V por Pressure Plot System: fluoroheptane-n-Heptane Per -Activity Coefficient Syatem: T: 262.4 K Exceas Free Energy of Mixing System: CsJ'12-Ct,B12 Bxceaa Free Energy of Mixing System: C4F10-C4B10 Bzcesa Free Energy of Mixing System: c7r16-1_c8 u18 at 30 c 21. Van Laar Activity Coefficient& 22. Van Laar Activity Coefficient Temperature Page 144 145 146 147 148 149 Dependence 150 23. Pycnometer Filling Arrangement 24. 25. 26. 27. 28. 29. 30. 31. Volume Change on Mixing System: c8r16o-cc14 at 50o c ........ Volume Change on Mixing System: C7F1a-C7H16 at 500 c Volume Change on Mixing System: C7P1a-CCl4 at 60 c ... Volume Change on Mixing System: c8r16o-n-e,u16 at 50 c. Partial Molal Volume Change System: 0 C 8 F16o-n..C7 H16 at 50 C Partial llolal Volume Change System: 0 CsF150-CCl4 at 50 c ... Partial Molal Volume Change System: C 7 F16-cc14 at 60 C Partial Molal Volume Change System: C 7 F16-n-C7 H16 at 50o C vii 151 152 153 154 155 156 157 158 159

PAGE 8

Figure 32. Partial Molal Volume Change 33. Thermal Coefficient of Expansion Syatea: C7F16-CCl4 34. Thermal Coefficient of Expansion Systea: C7F 16-n-C7H16 35. Thermal Coefficient of Expansion System: CaF160-CCl4 36. Tberaal Coefficient of Expansion Syatem: CSF160-n-C7Hl6 37. Volume of Mixing System: C7Fl6-CC14 38. Volume of Mixing System: C7Fl6-C7Hl6 39. Volume of Mixing System: C7F16-i-CsB1s 40. Calibration of System c 8 F 16o-c7 F 16 41. Calibration for System CC14-c8 F16o. 42. C a .libration for System c8F 16o-n-C7 B16 43. Calibration for System C5HifB3-CeH5Cffa 44. Calibration for System c 6u11CH3-c7 F15COOCH3 45. Phase Diagram System c 7 F16-c8F 16o-cc14 at 30 c. 46. Pbaae D!agram System: CiF15-C9F150-n-C7H16 at 30 c. . . . . . 47. Phase Diagram System: C6H5CH3-C6HllCH3C7Fl5COOC at 25 c. 48. Pbaae Diagram System: C5H5Cffs-Ca H 11Cffs-C7F15COOC8:3 at 10 c. viii Page 160 161 161 162 162 163 164 165 166 167 168 169 170 171 172 173 174

PAGE 9

Figure Page 49. Heat of Mixing System: C7F 1 6 -n-C7H 16 at 50 c. 175 50. Heat of Mixing System: C7F1a-CCl4 at 60 c. 176 51. Heat of Mixing Syst8ll: CF -i-C H 7 16 8 18 at 30 c. 177 52. Heat of Mixing System: C4Fl0-C4Hl0 178 53. Heat of Mixing System: C5F12-C5Hl2 179 54. Excess Free Energy of Mixing 3yutem~ ~F1a-CCl4 180 55. Free Energy Correlation for Fluorocarbon and Paraffin Hydrocarbons 181 56. Ezceas Entropy of Mixing System: C 7 F 16-1-e8a18 at 30 C. 182 ix

PAGE 10

CBAPl'BR I PCJJUIOSB The purpose of this work is twofold: 1. The detedination of the necessary phase equilibriUII data tor the evaluation of varioua aetboda of separating fluorocarbon mixtures and hydrocarbon mixtures, particular emphasis being given to the methods of liquid extraction, extractive distillation, and azeotropic distillation. 2. The calculation of the thermodynamic properties of soae flurocarbon-hydrocarbon mixtures and the comparison of these calculated properties with properties predicted from various theories of solutions. 1

PAGE 11

CHAPTER II NOMENCLATURE a Activity. standard state taken as pure substance A 'Van Laar constant B Van Laar constant d Distance between centers of nearest-neighbor mole cules H Partition coefficient, defined as the ratio of solute per unit voluae of solvent to solute per unit volume of gas phase I Ionization potential Huaber of theoretical plates pi Inlet pressure in chromatography coluan po Outlet pressure in chr0111&tography colWID p0 Vapor pressure of pure coapound a Gas constant T Absolute teaperature, 0x. V llolal volume, cc Vg Voluae occupied by vapor phase in chroaatography colWIID Vr Retention voluae, defined as the volwae of carrier gas passed through chromatography colwan when aolute peak appears 2

PAGE 12

3 V8 Volume occupied by stationary solvent phase in chromatography colUIID -Vs Kolar volwae of stationary solvent phase, cc w Weight traction x Mole fraction y Mole fraction of a component in vapor phase z Correction factor AE AF as Change Change Change Change Change in Helmholtz Free Energy in Internal Energy in Gibbs Free Energy in Enthalpy in Entropy o<. Coefficient of theriaal expansion 0C. Relative volatility Isothermal compressibility (3 Solvent selectivity Y Activity coefficient, standard state taken as pure substance cf 1T q) e 1/2 1/2 Solubility parameter, (E VfV) (calories/cc) Total vapor pressure Volume fraction Retention time, defined as time for appearance of solute peak

PAGE 13

4 Subscripts :1} Refer to components C D II 0 p V w Refers Refers Refers Refers Refers Refers Refers pot Su2!rscri2ts e Refers II Refers V Refers Refers to consolute properties to distillate composition to mixture properties to ideal solution properties to constant pressure process to constant volume process to composition of aaterial in to excess properties to mixing process to vaporization process to hydrocarbon-rich phase distillation

PAGE 14

CHAPrBR III I N T RODUCTION Before any e quipmeB:t affecting physical separation of two o r more components can be designed, phase equ.ilibrium data must be available. Since the majority of the unit operations involve the contacting of two phases under condi tions approaching equilibriua, the determinat~on, correlation, and prediction of phase equilibrium data play an important role in the field of chemical engineering. A most desirable method of obtaining necessary phase equilibrium data would involve the calculation ot the pro perties o f the mixture from those o f the pure coaponents; however, to be used with confidence, any auch aethod should have some sound theoretical basis. At present there are several approaches to the theory of solutions, most of which have a statistical mechanical basis and require many a&8UJIPtions and approziaations and yield equations which are coaplez and cumbersoae. A simple theory that has achieved considerable suc cess in the treatment of solutions o f nonelectrolytes is one developed independently by Scatchard and by Hildebrand (11). By aaking four simple assumptions, Scatchard and Hildebrand 5

PAGE 15

6 arrived at the following expression for the energy of mix ing in a binary system: A-ii : (x1V1 x2V2) ( cfl 6 2 ) 2 <\)l < 2 (1) The four assumptions were: l 'l'h e energy of a system can be expressed by sum"9 ation o f the int eraction energies of all possible pairs of molecules This interaction energy was assumed to depend only on the distance between the t,ro molecules. 2 The distribution of molecules is r andom ith respect t o position and orientation. 3 There i s no v o lume c hange on mixing at constant pressure. 4 The interaction ner y between 1-2 pairs of I110lecules is the geometric mean of the interaction energy between 1-1 and 2-2 pairs. Strictly speaking this theory applies only to systems containing nonpolar molecules between which only dispersion forces are operating. By further assuming that the entropy of mixing has tbe saae value as that of an ideal solution (a solution obey. ing llaoult's law) it is possible to write for the free energy o f mixing A tabulation of the n011enclature used in this work is given in Chapter II.

PAGE 16

7 llP : (x1V1 X2V2) ( Ol cf 2)2 l

1 2 (3) Froa its inception in 1932 until about 1950 the success of the Scatchard-Bildebrand theory bad been measured by its prediction of the properties of hydrocarbon systeas. Since 1950 aucb work has appeared concerning fluorocarbonhydrocarbon systeaa which were not adequately accounted for by the theory. These systeaa have much larger positive deviations froa Baoults law than are predicted. For som.e syats these positive deviations are large enough so that at rOOII temperature two liquid phases exist. Because of their nonconfonaity to the existing theory, fluorocarbon-hydrocarbon systems have atiJllulated the interest of many investigators. The first comprehensive study of fluorocarbon-hydrocarbon systeas was aacle by Simons and Dunlap (39) followed later by Simons and Mausteller (40); these iueatigators determined the thermodynaaie properties of c5 P12-c5a12 and C4F10-c4a10 systems respectively. Siaons and Dunlap found the Scatcbard-Hildebrand theory to be inadequate in predicting the thermodynamic

PAGE 17

8 properties of their systea, and improved the agreement by rederiving equation 1 omitting the asawaption of no v-olwae change on aixing. Later Beed (32) showed that for tluorocarbon-hydrocarbon mixtures the interaction energy between unlike pairs of aolecules is not the geoaetric aean of like pairs as was also assumed in the derivation of equation 1. Beed also rederived equation 1 oaitting the asaum,ptions of the geoaetric mean and no volume change. Be was alile to calculate values of the heat of mixing which agreed very well with the experimental data of Simons and Dunlap, and Sinlons and ll&uat eller. Since 1110st fluorocarbon-hydrocarbon mixtures do not conform to the present theory, their study should prove useful toward further d evelopment and evolution of the theory and the understanding of solution processes.

PAGE 18

\ CHAPl'ER IV BINARY SYSTEMS FORKING TWO LIQUID PHASES The study of binary system forming two liquid phases was undertaken for two reasons: 1. To determine solubility relationships which might be useful in selecting a solvent for separating fluorocarbon-fluorocarbon mixtures and hydrocarbon-hydrocarbon mixtures. 2. To obtain a measure of the positive deviations from Raoult's law exhibited by binary mixtures of two partially miscible liquids. Experimental.--The properties of the pure compounda used in this study are tabulated in the appendix under Tables VII and VIII. The unmixing temperature of a known binary mixture was determined by heating the mixture until the two liquids were completely miscible, then cooling the solution slowly and observing the temperature at which the second liquid phase appeared. The appearance of the second phase on cooling is marked by cloudiness; this cloudiness is sometimes masked by an opalescence which occurs about 2 or 3 degrees above the consolute temperature. Due to this opalescence, the determination of the unmixing temperature depends to some 9

PAGE 19

10 extent on tbe judgment of the obaerver. Tbe eolubility apparatus shown 1n Figure 2 eonaiated of heavy-walled gl-teet tube clamped tween two etaialeu at 1 flanges by an of four braaa bolta. A Teflon guket plac d between the open end oft e tube and the top flange was uaed to aeal the tube. A tberaocouple, which paaaed through tbe top flange wae uaed to aeaeure tbe tea perature of the rairture. The whole tu U88111bly waa im aeraed ia a.a oil or water bath, which proYided the eeua:ry temperature control. Tbe solubility data are tabulated in Table XII and the solubility curves, which were obtained by plotting the umaixin t perature-cOllpoeitioa data, are abowa on Figure 3 7 Published data are available for the two perfluorobep.. taue eyst a (17); tbeae points are plotted on Figure 3 along with tbe preeent data. The agreeaeat between the two set& of data ta aatiafactory. Du to the preaence o f air in the solubility tube, the values of the umaixing temperatures ao determined per tain to the ixture aaturat d with air and at a preuure in exceas of the equ111briua vapor preuure of the mixture. The difference between tbeae value and thoae of the aisture under its own equilib1ium vapor p:reasure ia generally uauaed to be negligible, but in order to justify tbia aaawnption the un

PAGE 20

11 aizing teaperature was determined for a dep.aaed raizture o f toluene and perf luorocy e l t c o.x1de in a aealed gla.-a tube u nder its own equ 11 1briwa vapor presure. Thia value o f the unai zing tperature ia plotted on Figure 4 along w1tb tboae obtained i n tbe preaence o f a i r and it can be ae n tbat there 1& ao aipificant diff rence. Theoretieal calculation o f Conaolute Teaperature aad Ceapos i tio11. Tbe thermodynaaic eondition oeceuary to def i ne the oonsolute temperature are or Thi e requir ent can be aeen fl"OIII examination of Fipre 8 wh re three isothermal curves of activity ar plotted v raua coapoaition. For illustrative purpoeea tbe activity ia cal culated from the following equation ln al: lD Xl + "Bz.2 2 (S) At T 1 a teaperatur below Te (consalute temperature), tbere exiat two l iquid pbaaea bavina the aaae activity. Tbeae A description of this material 1& given i n the appen d i x

PAGE 21

12 phases correspond to points.& and B. The dashed portion of the curve has no physical significance and corresponds to the Yan der Waals i110thera in the two phaae region on a pressure-volume diagram of a pure substance. As the tem perature is increased, the length of the line .&B decreases until the conaolute teaperature Tc is reached and a point of inflection, C, is observed in the activity curve. At this point the first and second derivatives of the activity are equal to zero. At a teaperature T 2 above Tc, the deviatioas from Raoult's law become aaaller and the activity is a single valued function of com.position. The value of the activity as predicted by the Scatcbard Hildebrand theory is (6) Using equation 6 for the activity and applying the conditions of equation 4, the following expressions result for the consolute teaperature and composition .., :.l 1' cf )2 X1x2V1-Y2 (Ul 2 (X1V1 + X2V2)3 (V12 y22 V1V2)1/2 Y1 V2 Vl (7) (8) BJ using the entropy of aixing for aolecules of different

PAGE 22

13 sizes u calculated frona a lattice odel alon W i t h the energy of ab:in ae given by quation 1, Hildebrand (18) r1v d xp po itlon ions or the consolute t peratur and coadiff :rent froa equations 7 and 1/2 1/2 2 (V1 v2 ) (9) (10) Th consolut te perature and co po it1 have n calcul ted from equatio 7 d d 9 and 10 for the porte in this work nd tabul,at d in Tabl XIII. The vaiue o f the consolut co position in Table III are given only to two figures beca of the unc rtainty in locat-1 the compo 1t1on co~r &pondin g to the mu t perature. Table III it la obviou t t equations 8 and 10 pr diet tbe consolute compos ition quite ell ile quatio 7 and 9 P.l"OVide poor stimates of the consolut for the s y s perfluorocycli c ox1de-tolu ne waa t t perature correctl pr dieted b y equation 7 The tact that equation 8 and 10 predict t conaolute c0111poai t ion would indicate tbat th volume fraction i a useful variable in corr lati solution havior. Thia is borne out by the success ul correlation of xperillental activity

PAGE 23

1, coefficient by tbe Yaa Laar equation, wbich l illll&r 1a fora to eflllatton a, but contalna two acUuatable par ... t.re int ad of coutanta which are tlaed by the phJical proper ti .. of tbe pure ce1aponenta. Tbe failure of 8flll&t1ou 7 and 9 to predict the coneolute temperature is probabl7 due partly to tbe failure of fluoroevboa-hyctrocarbon alxture to conlona to the P(Betric. ao auuaption wbicb ia illlpl:lcit in the" equatlona. Bquatlon 9 preclicu lower taaperaturea tbaD equa.. tion 7 becauae the eaceaa entropy of iaiq dale to different Yoluaea 1a alo,a poaitiYe and th refore the deYiatlc>u froa Raoult'a law due to thia correction are alwa,a neptl 81noe fluorocaa,boa-byclrocarbon alxturea bow auch larpr poa1tiYe deYiatlona than predicted, tile eatropy eorrection 1Jlpaira tbe agreeaeat between tbe obaene4 aad predicted tperaturea. It can not be atatecl, beweYer, that tbe UM of the eatropy tel'II for uae4Ual f'olmaea ia inoo.rrect aince tbe all ettect it contribute la everabaclowed oy the larger effect probably Clue to tbe geeMtrlc aean U8U11lpt~on. It abould be aeationed that, altboup often uaed ta the 11 terature, C011par1aon of tbe calculated aad obaened CODIIOlute teaperatun 1 not a aood eriterion for tetlaa tbe applicability of tile Scatchard-Btldebrand theory_ If

PAGE 24

15 equatioaa 7 and 8 predict the correct teaperature and COJI poaition, thia aeua tbat the ftrat and aecon4 deriYatie of the true activity coefficient w i t h reapect to compoaitioa are equal to the correaponding derivatiYea o f tbe activity coefficient aa giyen by equation 3 Tbi a ia a aece .. ary but not a sufficient condition which muat be fulfilled by equation 3 for it i a conceivable that two different tune tiona could hue equal firat ud .. cond der1Yat1e at a given cOlllpoaition. Tbia reaaoniq cu be aubatutiated by comparinc aetivity coefficient calculated by 941uat ion 3 with experimental value for aome eyateaa which co11fora to the conaolute t911P8rature ~riterion. Thia 1 done below. In a two liqui d phue a;ratem the activity of a component ia equal i n both phaaea and we caa write (11) In aany fluorocarbonhydrocarbon ayatema which fora two liqulcl pbaaes the mole lractloa ot hydrocarbon iD the h,clrocarboaricb pbaae approachea unity at low teaperaturea and the actiYity coefficient alao approacbe unity Thua by aettiDg Y-1 equal to unity, the act1Yity eoetfici at of the hydrocarbon in tbe fluorocarbonrich phaae ( '( 1 ) ls eflUal to the ratto a 1 /x1. Valuea of ln Y1 ao calcu.lated are compared in Table I with Yaluea predicted hy equatioD 3 for

PAGE 25

16 three systems in which the observed and calculated consolute temperatures are in good agreement. TABLE I TEST OF THE CONSOLUTE TEMPERATURE CRITERI O N T K C ln Y' 1 SYSTEII obs. eq. 7 (OC) x1 x 1 eq. eq. an. 11 3 I 323.5 325 26. 3 0 .306 0 .960 1 .14 0 .913 1 9 II 358. 5 360 61.1 0 .320 0.956 1 .09 0 .900 19 III 386 377 69. 0 0 .256 0.981 1.34 0.977 this work I. perfluoromethylcyclohexane and chloroform II. perfluoromethylcyclohexane and benzene I I I perfluorocyc l icoxide and toluene One would expect the same percentage difference be tween the logarithm of the activity coefficients as between the two temperatures in Table I since both Tc and ln Y are directly proportional to the ( 01 02 ) 2 term. Inspection of Table I reveals that the percentage difference between the logarithms of the activity coefficients is much greater than between the consolute temperatures. Since the values of lnY 1

PAGE 26

1 7 d Te in Ta b l I ar coapared at different t penteree, t possi b ility ari that tb aetiTit y coetficie.ota pre d icted by equatio n 3 are &filU&l to t true act1 ty coef-f lcieote at the coaaelute tetQGrature only, and not at other teaperaturee. From coutderatloo of 'the consolute te11pera-ture alo o wo lei rroneousl. -that the thr eyateu in Table I cloaely eonfonaed to tbe tbeor;y.

PAGE 27

TOTAL V CHAP'l' V PRES URE OF BI !!f!rilaeatal.-Total vapor preaeure ersue tpel"a-data re obtairaed tor a1s biaary fluorocarbon-llydr'o-carbon ab:tur The y ioal properties of tbe compouMJa are lieted in Tables YII aad Ylll. The aeuvrementa were aade in the two l ,lqu1d phaee region a1nce liquid com.poaJ. ti.one could be detendned fr the teaperature and the experlaentally eatabliabed aolu b111ty cune. A clynaaic boiling tlll wu uaed tor tbeee measure. aenta, tbe deign detail of which should be otwioua troa eau1nat1on of Fiaure 9. Tbe at111 wu deJll8d ao that igoroua boiling and low liquid lev 1 would preYent auperbeatlng while the tnaulatina Taper epac would prneat any beat lo by the Yapor in the lnaide tube. Durtaa operation of tb atlll under equilibrium eoaclit:lou DO cendenaation wu obaened 1aa1de tbe lmaor tube. A calibrated theraoeouple wu uaed to uuure tbe vapor tperature; the calibration data for this thermocouple 18 reported ia Table IX. Tbe atill waa coADected to a vacuum ayat oonta1aing a -reur1 alUlOl!leter which could be read to the neareat tenth of a ailliaetar 18

PAGE 28

19 by use of a cathetometer. As a check on the performance of the still the total pressure of the system 2 butanone-water was determined at two temperatures. These values compare favorably with the reported literature values (39) as shown in Table II. TABLK II CHBCI RUB Ilf TIO LIQUID PHASB STILL Syatem: 2 butanone-water reference 29 Literature This Work Pressure Teaperature Pressure Temperat\lre -oc -oc 760 73.3 768 73.6 500 62.0 503 62.0 The experillental total vapor pressure versus t-perature data are reported in Table XIY. Calculation of Activity <;:oefficient froa LiquidLiquid Solubility Data.-Tbe following aethod for calculating activity coefficients b&8 been deacribed by Carlson and Colburn (6). In a two liquid phase system the activity of a coaponent is equal in both liquid phases and we can write x1 Y1 = z1' 'f 1 (11) x2 Y 1 = x2' "( 2'

PAGE 29

Tbe mole fraction are known fraa the eolub111ty data aad ,,. ba two 94.uatloas ceatainina tour unkDown cuutltiea. The Dllllber of ullkD.owns cu be reduced to two if it is -SUMd that a two-coutant equation can be towul which correctly expnaNII tbe aetivitJ eoefficlenta u a tunctioa of C011poa1 tion. ODe such equation which hM proYed uaeful 1n correlating eaperillental act1Yity coetflcienta 1 tbe YU Laar equation. (13 ) la 'Y" :--8-2 Bs-e 2 ~ 1) (14) It equation 1 3 and 14 are subatitut d into equationa 11 and 12 written i n logari tbll.1c form, value of tbe conetaota A and B can be f ound. This procedure eaa be repeated t aeveral tperature ao that the temperature dependence o f A and B can be determined. The Van Laar A and B have been calculated for several of the fluorocarbon-hydrocarbon aysteaa for which the aolubillty curves were determi nod and i t waa :found that the conatanta were always l i o ar f u nction o f t perature. Figure 10 abows aeveral o f these linear plots. In order to have contidenee in value of tbe aet1v1t:,

PAGE 30

21 coefficient as calculated from equations 13 and 14, SOile aetbod should be available for deteraining whether the Van Laar equation accurately predicts the activity coefficients. One aetbod of accomplishing this is to COlllpare experillentally deterainecl total vapor pressures with thoat calculated froa equation 15 using the vapor pressures of the pure coapoundll, solubility data, and the Van Laar equation to deteraine the activity coefficients. TT: z1 y-1P10 + x2 "( 2P20 (15) A graphical coaparison of calculated and experillental total vapor pressures is given in Pigurea 11-16, where it is re vealed that the agreement is quite good at lower teapera tures, but becomes poorer as the tperature increase. The fact that calculated and experiaental values of the total vapor pressure agree should not be taken as conclusive proof that the activity coefficients predicted by equations 13 and 14 are correct, however, since there is an infinite nuaber of colllbination of Y 1 and Y 2 which will satisfy equati.on 15. By rearranging equatiun 15 we see that the activity of component two is a linear function of the activity of component one. (15a)

PAGE 31

22 By using equation 15a we can establish limits for the activity of the fluorocarbon (component I) from the limits of the hydrocarbon activity. The upper limit for the activity of the hydrocarbon will be set at unity and since these mixtures all exhibit positive deviations from Raoult's law, the lower limit will be set at the mole fraction of hydrocarbon in the hydrocarbon-rich phase. Table XV shows the activity limits of the fluorocarbon as determined from equation 15a along with the values calculated from the Van Laar equation for all six system s for which the total vapor pressure was determined. Table XV reveals that for most systems the calculated activities fall within the rang e calculated by equation 15a at the low temperatures, but deviate at higher temperatures following a pattern similar to the observed and calculated total vapor pressures. The Van Laar activity coefficients determined from the solubility data of Simons and Dunlap (39) are plotted on Figure 17 along with their activ i t y coefficients determined from partial.pressure data for the system perfluoropentanen-pentane. The value of the total vapor preaaure in the two liquid phase region for this system at 262.4K., calculated from the Van Laar equation, is 214 ma. as compared to the reported value of 216 mm., and the Van Laar activity of 0.766 falls within the 0.718 to 0.855 range calculated from equation 15a. It can be seen from Fig. 17 that the Van Laar

PAGE 32

23 equation with constants determined from solubility data predicts values of the activity coefficients which agree very well with the experilllental ones. The Van Laar equa tion with constants determined from solubility data has successfully predicted excess free energies of mixing in other fluorocarbon.hydrocarbon systems for which the thermodynamic properties have been determined. Figure& 18-20 show that the calculated and experimental excess free energies of mixing for the systems nperfluoropentane and n-pentane (39), n-perfluorobutane and n-butane (40) and ---perfluoroheptane and iso-octane (26) are in good agreement. These experimental values of the excess free energy of mixing were determined from partial pressure data. The solubility data for the syatem perfluoroheP tane and isooctane were taken from reference (17); calculated values of fl Fe for this system were made from the solubility data and the Van Laar equation at 17 c. while the reported data are at 30 c. The excess free energy data of Simons and Dunlap and Simons and Mausteller are the averages of several temperatures in the ranges 262 to 293 K. and 233 to 260 K., respectively, while those calculated from solubility data are at 262.4 and 220 K respectively. The small difference in temperature between c .alculated and observed free energies is negligible since

PAGE 33

2, the teaperature derivative of the excess free eneray of aizing is the excess entropy of mixing at constant preaaure. Values of excess entropy of aixing are tabulated below for several systems. ASp8 System at x: 0.5, cal./aole ox Reference C4F10 -C4H10 1.00 40 C5F12 -C5H12 0.43 39 C7F16 -!,-Ca81s 0.24 26 This entropy term does not usually exceed one entropy unit and a change of ten degrees would result in le than a 10 calories per mole change in the free energy term. The partial aolal beat of aix1ng can also be cal culated froa the Van Laar equation and the teaperature derivatiYe& of its constants (16) l 2

PAGE 34

25 Heats of mixing calculated from the Van Laar equation are approxiaately twice as large as those determined experimentally in the three fluorocarbon-hydrocarbon systems cited above. ood (48) has calculated the thermodJDaaic properties for the systera cyclohexane-methanol from solubility data alone, but using a two-constant Scatehard equation instead of the Van Laar equation to repreaent activity coefficients. He found that bis calculated excess free energies of mixing were in line i t t ose reported for the methanol-benzene and aetbanol-carbon tetrachloride systems, but his calculated heat of mixing values were bout twice as large as those for the two reported methanol systems. Besides the Van Laar equation, two-constant llargules and Sca-tchard equations were used in this work for aubeti tution into equations 11 and 12, but these equations predicted total vapor pressures that did not agree with the obsened vapor pressures as well as did those predicted froa the Van Laar equation. These two types of equation also predicted heats of mixing which were in poorer aareement with the experimental values than those predicted by the Van Laar equation. Since the temperature derivative of the free energr is nee rl for calculation of the heat of mixing, amall errors in the free energy will produce larger errors in the beat of

PAGE 35

26 ixing. The disagreement between experimental heats of ixing and those calculated from the Van Laar equation could be attributed to small errors in the free energy as pre icted by the Van Laar equation. However, these error are not of a random nature since the calculated value is always about two ti.Jiles as large as the experillental values. In order to det rmine why the Van Laar equation fails we should consider in detail the proce s by which the Van Laar constants are determined. Figure 21 illustrates graphically the conditions required to obtain the Van Laar conatants. F,quations 11 and 12 can be rearranged to (lla) (12a) The differences ln Y 1 ln Y 1' and ln l 2 -ln Y 2 are rep.. resented on Figure 21 by ab and cd respectively. Using equa ti.ona 11, 12, 13, and 14 is equivalent to findi.ng the constants A and B such that at z1 and z 1 the differences ln Y 1 -ln Y 1 and ln Y 2 -ln Y 2 given by the Van Laar equation are equal to the corresponding differences between the true activity coefficients. This does not mean that the actual values of the Van Laar activity coefficients are correct or that the Van Laar curve is identical with the true

PAGE 36

27 activity coefficient versus composition curve. At lower temperatures the composition of the con jugate phases approaches that of the pure compounds and the true activity coefficient and Van La&r actiYity coefficient both approach unity. This aeans that at lower teaperaturea the actiYi ty coefficients Y 1 and Y-2 corresponding to points a and con Figure 21 can be predicted by the van Laar equation. Since the Van Laar activity coefficients and true activity coefficients approach each other at a and c, and since ab and cd as given by the Van Laar equation are equal to ab and cd corresponding to the true values of ln Y-1 ln Y1' and ln Y 2 ln Y 2, the Van Laar and true actiYity coefficients also approach each other at band d. Tbia is manifested by the Yery good agreement between obsened and calculated total Yapor pressures at lower taaperaturea. As the teaperature increases the concentration of the aajor C011ponent in each phue decreases causing the ac. tiYity coetficienta to differ from unity and it is possible that differences occur between the Van Laar and true actiYity coefficients at a and c. Tbis would result in differences at band d and would cause the values of the obsened and calculated total yapor pressures to diYerge. ODe reason why the Van Laar equation doea not correct ly predict beats of aixin1 can be seen fr011 ezination of

PAGE 37

28 Figure 22. Curves 1 and 2 on Figure 22 represent the Van Laar equation at two temperatures, curve 1 being at the lower teaperature. Curves 3 and 4 represent the true activity coefficient curves, where curve 3 and l, and 2 and 4 are at the saae teaperatures. Only the curves for one component are shown for the sake of aiJllplicity. The shape of the two types of curves is greatly exaggerated for illustrative purposes. At the temperature T 1 the Van Laar equation (1) predicts correct values of the activity coefficient at a and b even though its form is different fr011 the true activity coefficient curve (3) at that temperature. Increasing the teaperature to T 2 causes only a slight change in the true activity coefficient curve (4), but due to the difference in fora the Van Laar curve (2) must change by a greater amount in order that it may predict the activity coefficients at c and d. Since the heat of aixing ia deterained froa the teaperature derivative of the logarithm of the activity coefficient at constant coapoaition, it can be aeen that larger heats of aixing would be obtained by the Van Laar equation. We aee that the inability of the Van Laar equation to predict heat of aixing could be due to a difference in fora between the calculated and true activity coefficient curve. Thia difference is undoubtedly all since the

PAGE 38

29 excess free energy of mixing curve calculated from the solubility data using the Van Laar equation agree in magnitude and in shape with experiaentally determined excess free energy. curv es. Based on the preceding considerations it is con cluded that the Van Laar equation can be used to estimate free energies in systems which fora t1t0 liquid phases if the constants are determined at temperatures where the coa positions of the two coexisting phases approach the pure compound&. Of course more confidence can be placed in the Van Laar equation if total pressure data are aYailable. Since the teaperature derivative of the free energy ia -all, these eatiaated free energies can be uaed without appreciable error at other temperatures within 20 or 30 c. of the t8Dlperature at which the estiraate was made. It is further concluded that the heats of mixing predicted by the Van Laar equation are unreliable.

PAGE 39

CHAPl'BR VI VOLUIIE CHANGES IN MIXING FLUOROCARBONS AND HYDROCARBONS Experillental.-The molal volumes as a function of coapoaition were determined for four fluorocarbon-hydro. carbon systems. The physical properties of the pure com pounds are given in Tables VII and VIII. Pycnometers described by Lipkin (22) and having a n<>lllinal capacity of 5 milliliters were used to eaaure the voluaes of mix tures of known composition. These pycnometera were calibrated with distilled mercury at 40, 45, 50, and 60 c.; the calibration data are given in Table X. The molal volumes of the fluorocarbon-hydrocarbon solutions were meuured over the entire cc:apoaition range at a temperature slightly above the consolute temperature of each system. The molal volumes were also measured over the limited composition range at two other temperatures s0 and 10 c. below the complete isotherm. For the systems perfluorocyclic oxide-!_heptane, perfluorocyclic oxidecarbon tetrachloride, and perfluoroheptane-n-heptane the isothermal volume measurements were made at 40, 45, and 50 c. while for the system perfluoroheptane-carbon tetra-30

PAGE 40

31 chloride they were made at 50, 55, and 60 c. Tbe thermal coefficient of expansion of the materials limited the tperature range to ten degree for one filling of the pycaoa eter. Since aoae of the mixtures were two liquid phaaea at roOD1 temperature it was neceaaary to fill the pycD011eter at a temperature above the conaolute teaperature. Figure 23 abon the arrangement for filling the pyenoaeter. The desired mixture was weighed out into the transfer tube, which was then closed off by aeans of a ground glua atopper and placed in the water bath at a temperature above the con110lute temperature of the ayatea. After remaining in the water bath aeveral minutes the tube wu shaken until mixing was complete and the ground glaaa topper was replaced by the ayph o n tube, which had been heated to the bath temperature. The pycnoaeter waa connected to the transfer tube by a small section ot Tygon tubing and wu filled by applying auction to the other arm. The pycnoaeter was al ways filled at the higheat temperature of each aeries. The pycnometer reading waa taken after approximately fifteen ainutea at the bath temperature, then the bath temperature was lowered five degrees to the next temperature. The water bath temperature was controlled manually

PAGE 41

32 by aeaaa of an electrical heating element connected through a Variac. The aercury-in-glass theraoaeter aeasuring the bath teaperature could be read to!: 0.02 c. and was checked against a theraocouple calibrated by the Kational Bureau of Staaclards. The temperature of the bath never varied aore than o.os0 c. from the desired t .. perature while the pyc aoaeter wu approaching tbenaal equilibrium. After the pycDC>11eter reading was made at the three temperatures the pfc D01Hter was removed from the bath and allowed to cool to rooa temperature. The pycnometer was then weighed, emptied, and weighed eapty; all weights were corrected to weights in vacuo. Knowing the weight of material in the pycDOll8ter, the composition of the material, and the pycnoaeter r..,._ inga, it is a siJllple matter to find the molal volumes of the mixture at the three temperatures. The molal volume-composition data is tabulated in Table XVI. The volume change on mixing was calculated by equation 17 (17) The partial aolal voluae change on aixing was deteriained by plotting the total y pluae change versus aole fraction ot hydrocarbon, graphically taking the tangent to the curve at tbe deired composition, and determining the value of the

PAGE 42

33 intercepts of the tangent line at x 1 : 0 and x 1 : 1. These values of the intercepts are the partial aolal voluae changes of mixing of components 2 and l respectively. Plot& of the total volwae change on mixing ( v1') versus mole traction of hydrocarbon are shown on Figures 24-27. Values of t h e partial molal volume changes on mixing are tabulated in Ta ble XVII and plotted versus composition on Figures 28-31. Figure 32 shows the plots o f partial molal volUDle changes ver sus composition fort e systems perfluorocyclic oxi de-.e_-heptan e and perfluoroheptane-,!!-heptane superimposed. One can see fro Figure 32 that the partial molal v o lume changes are practically ident ical for each type of compound in both solutions and since the syst s are almost symme trical the partial molal volume changes are nearly equal for all three components. Since the two syst a s involving carbon-tetrac loride were not determined at the same tem perature one would not expect t e two par t ial molal v o lume change curves to be superimposed. It was f o und for tbe&e four systems t hat the total volume change on mixin g increased with increasing t empera ture; this type of behavior was also fou

PAGE 43

1,' 34 Tbe coefficient of theraal e:apansion (a..) as de fined by equation 18 was detentined fr0111 the teaperatureToluae data of the pure C011pounds and the binary ai:atures. o( : (ov) V p (18) Figures 33-36 show tbat plots of rA versus eoapoait1on for aoae of the systems emibi t au1a a. The thenaal coeffi cient of e:apansion for an ideal at:xture ( o( 0 ) is a linear function of the voluae fraction aa &boWD below. o( 0 : :al V10( 1 :a2'f2 CX. 2 :alfl s2V2 o( o : ~l 1 + ~2 2 (19) Kquation 19 la alao plotted on Figures 33-36 for eoaparative purposes. In order for the total voluae change to increase with teaperature it is necessary that the theraal coefficient of e:apansion for tbe ai:ature be greater than the coefficient for an ideal solution. This can be &hoYD by differentiating equation 17 with respect to temperature : dYM d'Yo " o< V o( elf cfr" 0 0

PAGE 44

Since Va~V0 In order for d Av at 35 to be positive a( must be 1reater than ~ 0 ; thia is in accord with the ezperiaental values of AV8 and ' Since the Yalues of o< plotted on Figures 33-36 were determined in the re1ion of the consolute temperature the large yaluea of o( might be due to the breaking up of clutera in tbe liquid u the temperature increaaea. The foraation of clusters in systems exhibiting partial aiaci bility bu been generally recognized (50). Tb.e opalescence obaened just above the conaolute temperature ia belined due to the scattering of light by cluster ot aoleculea. A aolecule in a cluster would haye aore like .. ole culea aa nearest neigblM>rs than it would haye if tbe mixture were hoaogeneous; as the temper a ture ia raised tberaal ao tion coabats the tendency to cluste r and the mixture approaches boaogeneit7. If we conaider the cue where one 1-1 and one 2--2 pair rearrange to fora two 1-2 pair we find that the interaction energy of the ayatea containing 1.2 pairs ia 2 E 12 while the interaction energy of the ayet-containing 1-1 and 2-2 pa irs 1a E:ll 22 or twice the art tbaet1c

PAGE 45

36 mean of E; 11 and E 22 Since E:.12 ia approximately the geometric mean of E. 11 and E. 22 where only diapers ion force are acting, and aince the geometric mean 1a always leas than the aritbaetic mean, the interaction energy of the aystem ia leas when 1-2 pairs are preNnt. Theae weaker attractive force result in a volume expanaion and an in creaee in the enthalpy of the ayatem. The diaperaion of cluster due to tberaal qitation would explain the fact that the voluae change on mixing increaeea with teaperature and thus one would also expect tile beat of aixing to increase with temperature. The heat of aixing in the ayatem perfluoroheptane-iao-octane (26) were found to increase with temperature u shown by the followina valuea; at a mole fraction of one-half, the heats of mixing nre 402, "68, and 616 calorie& per mole at 308 sd', and 10 c. reapectively. The voluae chanp on mixing for this syatea wu reported only at 30 c. However, the data of Taylor a.ad Beed (42) show that the voluae change on aixing for tbia ayatem also increaaea with teaperature. The voluae ebange on aixing ia aa illportant ~pert:, in the atudy of aolutiona and for thia reaaon it would be desirable to have a theoretical expresaion which would predict tbia property. Scatcbard (38) and Hildebrand (13) have

PAGE 46

37 sboWD that the Gibbs :free energy at constant pressure ( AFp) -is related to the Hellllboltz tree energy at constant wluae ( A Ay) by the following equation (20) The correction tera involving ~yH aaount to leas than 10 calories per aole as copa.red to about 350 calories per aole for 8 Pp, and tor this reason it is usually neglected. Hildebrand used this approxlaation in deriving an expresaion for the voluae change on aixing. He started with the ther aodynaaic relation f';.V :: ( ~:F ) T (21) and by substituting AAy for llFp he obtained 6V :(; ) T -T~A;v ) T By further usuaing that the pressure derivative of the entropy was zero be arrived at (22) / 'ol.lB,) /oA&y) ( 'cV0 (oABy' llV: ~/T =\~ T\75.J T -Yo/3o\ 15vo /T (23) His final assuaption was that (~) D 'oV T (24) and that n: 1.

PAGE 47

-----------------------38 Thi ... uaption is baaed on the fact that for several non.polar liquids the internal preuure,(~)T, u calculated from tbe thermodynamic relation can be represented by equation 24 where the coefficient n varies from 0.9 to 1.1. After making this U8Ulllption, Hildebrand arrived at the foll<,wing equation for 8 vi' Using equation 1 for ll&y yields (25) (26) vii= /30(z1 V1 x2v2 } ( i, [< dl 02>2 2 01 cf2(l-f rf ~J+i~ 2 (28) (29) ( 30) 0 0 The ratio d 22/d 11 can be evaluated from the cube root of

PAGE 48

39 the aolar Tolwae ratio. Substituting equation 28 into equation 26 results in Av= /30(x1V1 x2V2) [ ( d1 -62 ) 2 + 2 &1 cf 2c1 f1fo~ +1 ~2 (31) Still another expression can be obtained for AV if it is assuaed that the entropy of mixing at constant wlwae is the ideal value, then OBy in equation 26 can be replaced by AFp8 according to the following: A-,p :My : ~Byll T D Sy and APp8 : AByll TASy8 If ASy is U8Ulled to have the ideal value then ASye: O and thus / (32) In order to calculate ~v frGIII equations 27, ll, and 32, it is necessary to know (30 the coapreasibility of a solution showing no voluae change on aixing. The com pressibility is defined by equation 33 13 : ( ; ) T (33) and it can be shown that {3o is a linear function of the

PAGE 49

40 volume fraction u was b /30
PAGE 50

,1 TABLB III ISOTHDIIAL COIIPUSSIBILITIBS FOR USE IN .BQUATION 34 Compound Temperature 0c. /3 Ata-1 Cr1"16 30 2.65(10-') C71"16 50 3.03(10-') C71"15 60 3.42(10', ~-C., H 16 50 1.82(10-') cc14 60 1.55(10-') !-CaB1s 30 1.21(10-4 ) Values of AV11 u calculated frOII equation 27, 31, and 32 are plotted on Figure 37-39 along with the experiaental values for the ayetems perfluoroheptane-carbon tetrachloride, perfluoroheptane-~-heptane, and perfluoroheptane-iao-octane. Figure 37 reyeals that for the c7 F 16-cc14 ayetem the agreement between ezperillental values of Av and those calculated from the experimental AFp8 is quite good; the theoretical equation 31 al110 give a fair ly good estimate of Av. For the systems c7 F16-n-c7u16

PAGE 51

42 poor estimates of ~v. It should also be noted that the theoretical equations 27 and 31 predict values of Av which are BjDUletrical with respect to voluae fraction and therefore should have their aaximum values at a volunae frac tion of 0.5 (about 0.3 0.4 mole fraction of fluorocarbon). Figures 24-27 reveal that the volwae changes for the four systellll of this work and the C,F1s-!-CsB1a system are mor a nearly &Jllllletrical with respect to lllOle fraction, having their maxima at a aole fraction of approximately 0.5. Since equations 27, 31, and 32 failed to predict reasonable values for Av it might be instructive to examine critically soae of the assumptions and approxillations involved in obtaining equation 26. The first approxiaation involved the neglect of the ( 2 pressure deriYative of the correction term llV ) when sub-2jv sti tu ting for /l Fp 8 in equation 21. Al though this tel'Bl is small and can be neglected in equation 20 its pressure deriv ative may not be small enou g h to be neglected in equation 21. Another source of error in equation 2f might result from the assumption that the pressure derivative of the entropy term in equation 22 is zero. It should be mentioned, however, that unless these two assumptions are aade the ex pression for Av becomes extremely complicated.

PAGE 52

43 Another USU11ption, the effects of which can be clearly aeen, ia the aaawaption that the internal preuure can be repreaented by equation 24, where n 1 equal to unity. The data are ayailable with which to calculate the internal preaaure of perfluoroheptane (20) from equation 25. Thia calculation waa aade and it waa found that a yalue of n equal to 1.40 wu neceaaary to aat1afy equation 24. If tbe coefficient n is not ua1aed equal to unity, equation 26 would be written (36) Since n for a fluorocarbon-hydrocarbon mixture would pro bably lie between 1.0 and 1.4, equation 36 would predict yalue of A vii larger than those predicted by equationa 27, 31, and 32, which illplicitly uauae a Yalue of n equal to unity. A value of n between 1.0 and 1.4, howeyer, would still predict low Yalue of Av for the CrFi&-!,-C,B1a and c7 F16-.!,-C8 B18 systems since a Yalue of n between 2.0 and 3.0 would be l'equired for theae ayatema. Siaee equa tions 31 and 32 closely predict 6r' for the c7 F16-cc14 system the incluaion of n in equation 36 would illpair the agreement in thi case.

PAGE 53

44 It is possible that equation 26 ta reasonably correct and that the ezpreeaiona for 6Ey are in error. This possibility will be discussed in more detail in Chapter YI I. It is concluded that there are many assumptions and approximations involved in the der1Tation of equation 26 which prevent the accurate prediction of volU111e changes.

PAGE 54

CBAPTD VII B8TIIIATI01' or THBIUIODD.AJIJC PaOPDTIBS Beat of x1a1.-It was preYiously aentioned that Reed rederived the euations of Scatchard and Hildebrand oaitting the asauaptions of no vol\Jlle change and the geoae tric aean, and obtained an expression whleh predicted heats of aixing in acreent with experillental values. Beed' expression tor the heat of aixing in a binary aixture is 1iYen below: l).'&p: 2 2 t If~ t1 i> 2 + B1 V (1 -!!. ) V1 Where 1/2 = (i )cl cf l cf 2 (1 + ~v <1 !!> (37) V2 (38) The tel'lls :fx and t0 were defined previously by equations 29 and 30. Although equation 37 predicts values of AEp8 it cu be shown that the difference between O.Bp and 8p ia negligible. In order to use equation 37 it is necessary to know the ionization potentials and partial aolal Yoluae of coaponenta 1 and 2. Beed (34) bu presented a aetbod of pre dicting the ionization potential of a coapound fr011 ita po larizability and structure which yields good reaulta and can be uaed in the absence of experiaental data. Hildebrand (14) bas shown that by conaidering the vol-45

PAGE 55

46 Wile change on mixing that the heat of mixing can be calculated from the following expression. (39) If the entropy change at constant voluae is aaauaed ideal, then ABf1I can be replaced by A Ppe and 6Bp : A Ppe(l ()( T) (40) Equation 40 can be used to calculate heata of aixing in tluoroearbon-bydrocarbon ayatellS for which the tberaal coef ficient of expansion ( 0( ) is known and where ll Fpe can be calculated from the binary solubility data as outlined in Chapter V. Still another aethod of estillating the beat of mix ing involve the use of the following theraodynuaic relation ABp: AJ'p TA Sp (41) In teras of the excess properties, equation 41 can be written (42) Since a method of estimating AFpe la available it la only n easary to estimate {)a Sp8 The entropy change due t o the vol uae change on mixing can be deterained fro11 the following Maxwell relation (43) For a volume change at constant pressure fl 8 is given by (r, V0 AVM ~8: _j({';;'op) dV (44) V 'oT V 0

PAGE 56

47 By usuaing that f 'o P ) is constant over the small volume \'oT V change, equation 44 results in AS :f 'sT V ry aixtures and have found that the ( 'o P) tera for mixture a \lc)T V can be calculated from tboae of the pure coapound& through the following relation 1/2 1/2 2 -.1x: (x1a1 + z2a2 ) (47) where a is defined by equation 35. The heats of mixing have been calculated fro equa tions 37, 40, and 46 for the systems c7 F16-!.-c7u16, ~F15 CCl4, '7F1e-!-CsH1s, CsJ'12-C5B11 and C4P10-C4H10, and are plotted versus compos ition on Figure s 49-53. The data neces-sary for these calculations The necessary~~~ }v is tabulated in Table XXVII. data are not available for the

PAGE 57

4 8 CsJ'1rCsH12 and C4F1 0-C4 H 10 systems and therefore equation 48 cannot 'be used. Figures 51-53 reveal that equatiou 37 and 40 predict values of t h e heat of mixing in good agreeaent with the reported literature values. The qreement between equations 3 7 40, and 46 is very good in the cue of the c7 F1 6 -cc14 system although no ezperillental values of A H p are available I.or coaparison. Agreement between equation 37, 40, and 46 is not too good, however, in he CfF1&-~-C,H16 system where again no experimental values of AH are available tor comparison. Pree Bnergy of Kizin&.-As was mentioned in Chapter V the excesa free energy of mixing can be eatlaated quite well from binary solubility data. F.quation 28 can also be uaed to eatiaate ezcess free energy of mixing if it is assuaed that the entropy of aixing at constant volume bas the aaae value as for an ideal systea. Figures 18-20 show a comparison of fl Ppe calculated :from equation 28 and from binary solubility data. Reported 11 terature values of A Fpe are available for coaparilSOn in the c5 P 1 2-C5B 12, C4F1g-C4B10 and c7 F 1 6-!-C8 B 1 8 systeas. In the case of C,P16-cc14 no 11 terature values are available but agreeaent between A Fpe calculated frOlll e q uation 28 and A Fpe calculated from solubil i ty dr : ; a is good. In the remaining systems equation 28 always preclicts alues of a Fpe which are too low. The excess free energ y of aixing can be eatillated in an eapirical maaner. If it is asswaed that equation 28 is

PAGE 58

49 the correct expression for AEv and that the excess entropy of aixing at constant voluae can be represented by equation "8, then it is possible to write equation 49 for AFpe. Ally8 : z(x1V1 s:aV:a) [< cf 1 d':a)2 + 2 d'1 02(1 -f1fD~ t~2 (48) Mpe : (l tzT) (z1V1 x2V2) I ( cf 1 02)2 + 2 i_ 'P2 (49) The term z in equation 49 is merely a correction factor and can be determined from an empirical correlation of z versus [< d'l d2> 2 2 di, cf 2(1 t1f0ij s hown on Figure 55. Values of z used in establishing thia correlation were obtained from free energy and consolute temperature data reported in the literature for fifteen fluorocarbon-hydrocarbon systems. J'or all these systems the equations of Scatchard and Hildebrand predict values of the free energy or consolute temperature which are too low. The Scatchard-Hildebrand equations for the excess free energy and consolute temperature can be written /lF8 : (x1V1 x2V2)K 11 t2 (50) BT 2z1zav 1 2v2 2 K (51) C -(x1V1 + x2V2)3 where K : (1 + zT) [< cf1 ~)2 + 2 61 02(1 fifD~ (52) The parameter K represents the effective value of 01 02)2 2 cfl d2(l fifD8 necessary to fit the Scatchard-Hildebrand equations to the

PAGE 59

50 ezperiaental data. The value of z was deteralned fr0111 the reported tree ener1y and consolute temperature data by using equations 50, 51, and 52. Values of I'. and z for the fifteen syste11a are tabulated in Table XXVIII along with the literature reterenee and the method of obtaining I'.. This correlation is only applicable to aixturea of fluorocarbons and paraffin hydrocarbons. 81steas con taining benzene, carbon tetrachloride and chlorofora could not be ao correlated. A glance at Pigure 55 reveals that the points are widely scattered about tbe correlation line and suggests that values of 6 Pp e calculated froa z and equation 49 would be subject to quite a bit of error. This is not the case because z is a correction factor and large differences in z result in aller differences in the factor 1 + zT. Thia correlation fits the excess free energy data with an average deviation of 7 per cent and a aasilllua deviation of 20 per cent. JCDtropy of llizina.-The entropy of ai.Jting at constant pressure can be given by equation 45 or in terms of the excess properties ~Spe : ASye + (~) V Av1' (45) (45)

PAGE 60

51 For the CrF16-!-c8u18 systea values of llSp8 and ov haye been reported (26) and the necessary /'c) ) data \;'>ot y are available in the literature (20) (3). Values of TA Sp8 and T (;g; )v AyM &re plotted versus compesi tion on Pigure 56 where it can be seen that tbe T(;g;)v ov tera is much larger than T llBp9 indicating negative values tor A Sy9 Negative values of Aly e would also explain the fact that a 1'8 as calculated troa equation 28 ue lower than ezperiaental values, since in using equa tion 28; ASy8 was assuaed equal to zero. 'flleae negative values of A Sy e would also explain the large difference between ezperillental values of AB and those calculated by by equation 46 as shown on Figure 51. The eaae conclusion concerninc A s.,e in the C7F1a-.!""CrH1& aystea could also be drawn fr011 Figure 49, Tbe C7l'1s-CCl,t systea however, appears to hae a Y&lue of '1 5ve equal to zero aince froa l'igure 54 it can be seen that Ll -,e calculated froa equation 28 is in agree aent with a-,8 determined froa solubility data. Alao values of AH calculated from equations 37, 40, and 46 are in good agreement as shown on Figure 50. Another arguaent in favor of negatiYe Yalues of e ASy is the fact that the empirical correlation inYolving

PAGE 61

52 z and equation 49 predicts free energies of aixing. This correlation is based on the assumption that A 5ve can be predicted by equation 48. Since z is a poaitiYe nuaber then A Sy8 as given by equation 48 will be nep.tiYe. If negative values of A 8v e are coaaon to moat tluorocarbon-byclrocarbon solutions, it is aurpriaing that equation 40 predict valuea of AH in agreeaent with experimental values in the C,F1e!..CaH1s, CsJ'1rCsJ112, and C4"10-C4B10 systems. In order to understand why equation 48 is successful in this respect it would be well to ex amine its derivation. This is done in the following paragraphs. In order to determine the effect of aaall volU!lle changes OD A av as given b}' equation 1, Hildebrand ex-p~ded AEy about V0 using a Taylor series and o b tained tu,/ ,: l!.BJR + ( ,~: ~l A.,. .r ?J21!.~) ( 6 v8)2 1 T \. fo V 2 T 2 By Dflglec~iag aeconcl order and hisher terms in Av and usin1 the thermodynamic relation (J:~)T T~]:) V -p (53) he obtained 11....,;, : A&r, II. T(~ ;)v av -P A... (54)

PAGE 62

The relation between ABpll and a P is L\Hp : LlEJ/' P yK (55) Substituting equation 55 into equation 54 gives l\ Bp : 6Byl' ,J 'o P} ov11 (56) A\'oT V We have already seen from equation 26 that the vol\llle change on aixing is related to the energy of mixing at constant voluae By substituting equation 26 into equation 56 Hildebrand obtained ABp: llEyK T fo /3g l\Byl( If (3 and /30 are assuaed equal then equation 39 results ~ Hp= ruy (1 + at. T) (26) (57) (39) A possible reason why equation 40 predicts reason~ able values of AH in spite of negative values of A 8v e ts apparent from equation 56. The substitution o:t A F8 for Aly in equation 56 would result in values of AB which were too high. Thia effect is coapensated by expressing 61' by equation 26, which we have seen generally predicts values of Avl' which are too low. Thus eciuation 40 provides a good estimate of .0 B, probably due to a fortuitous cancellation of errors. The fact that it ia possible for equation 40 to pre dict reasonable values for A H even though O 9ye is not zero

PAGE 63

54 and the fact that AF8 a s calculated by equation 28 ta leas than the observed values leads to the conclusion that A 9ve could also be negative in the c5 F12-c5B12 and C4F10-C4H10 systeas. Negative values of A aye for fluorocarbon-hydrocarbon aysteras are not unreasonable and are consistent with the concept of clustering. In a aizture containing clusters, the distribution of molecules would not be randoa and one would expect the entropy of aixing to be less than the ideal value. The effect of raising the temperature would be to increase the random thermal motion of the molecules and decrease the clustering tendency. Thus t h e value of 4 5ye should be-coae less negative as the temperature i s increased, causing the value of A Sp8 to increase with temperature. This effect was found i n the C,H 16-,!-Ca H18 syste where the following values of A Sp8 were reported for an equilllolar mixture. t 30 c. 50 c. 10 c. A Spe (cal. /mole 01:.) 0.24 0.46 0.89

PAGE 64

CJIAPTE YIII TBBHABY LIQUID--LIQUID SOLUBILITY STUDIES The ternary liquid-liquid solubility atudiea were undertaken to deteraine whether fluorocarbon aixturea could be separated by solvent extraction, and whether fluorocarbons would be &00d aolventa for mixtures of other types of coapouncta. Various types of organic coapounda were tested as possible solvents for separating a aixture of perfluorobeptane (<>,:r1e) and perfluorocyclic oxide (Ca:r1eo). Bxperiaental.-These preliainary studies were perfOftlecl by vigorously &baking an approzillately equilllolar airture of tbe two fluorocarbGns witb the proapective sol vent in a all screw-cap vial and using a Perkin-:&llller "Vapor l'ract0111eter" to analyze tbe two eoeziating liquid phases. The criterion of a good prospective solvent was taken to be the difference in the c7 P16 and C9P1sO peak height fractions in the two liquid phases. Of all the organic sol vents tested, carbon tetrachloride (CCl4) and a-heptane (_!~His> were found to be the aost pr011is1Dg. The ternary liquid-liquid pbaae diagrua were deterained for tbe syats O,P1s-ca:r1e O _!-O,B16 and C7P1e-CaP190-CCl4 at ao0 c. 55

PAGE 65

56 The aethyl ester of perfluoro-oetanoic acid (C,P15COOCB3) waa tested aa a possible solvent for aizturea of toluene (C6B5CH3 ) and aethyl cyeloheme (CeB11CH3)since tile conaolute teaperatures for these two binary ayets containing the eater were quite different. Toluene and the ester are coapletely aiacible at room teaperature whereas the consolute tperature of the aetbylcyclohesaae-eater systea is 45 c. The ternary liQuid phase diagr wu d.e terained for this systea at 2So and 100 C. The isothel'llal ternary liquid phase diagrs were deterained frOlll ehrcmatographic analysis of the two coezisting 11Quid phases. The liquid aizture was contained in a screw-cap vial and was vigorously shaken while illlaersed in a water bath. After being shaken for aoae tiae, plea of each phase consist1q of approximately 0.04 al. were with drawn tor analysis by a hypoderaic syringe and the aizture waa again shaken. Two or three successive plea were taken with shaking in between spling. The h)'J)Odermic syringe was wanaed to approxilllately 10 c. above the temperature of the mixture prior to aaapling in order to prevent any concentration changes clue to cooling the saturated phases. The auaple was injected into the chrOJ11atograph illllediately after pllng 110 as to preTent tonaation of a second phase ln the syria1e upon cooling.

PAGE 66

57 Tbe water bath used in these deterainationa waa described ln Chapter VI. Tbe vial was ahaken by band during tbe determination <1 the toluene-aethylcyclohexane-eater t; but it was found that considerable shaking was neceasary to e:f:fect equilibriua between phasea in the two perfluorolleptan-per:tluorocyclic oxide ayateaa. Tberefore, the vial was ah*ken by an air-clriven aechani for approxiaately thirty ainutes before and between spllng. The agreem.ent between the analyaes tor nccesaive plea was taken as the criterion of equilibriua. Since analyses were perforaed cbrollatop-aphically, it na first necessary to find a suitable partitioning liquid that would resolve the ternary alxture into three aeparate peaka on the cbroaatocrapb with no overlapping. After the proper partitioning liquid bad been found, it waa then neceasary to prepare calibration cunea of peak height fraction ac&inst weight fraction for two of the three poaaible binary alzture, aince it waa found that a ternary aixture could be analyzed froa calibration data for only two of the three pesaible binary aixtures. Tbia 1 due to the fact that the solutes are in very low concentration in the partitioning liquid and therefore act independently of each other. Tbe calibration data and curves used for analyses are given in Tables DIII and ~igurea 40-44.

PAGE 67

58 ft peak ipt fraction for aucceuiye -plea of one phalle w re uauallJ in aood ap-eaaent &Dd th CG11poai tion wu rained frea th ayerase pe&k heqbt fractiou. r aipificant differ nee occurr tw en peak h i1bt fractioas of succe-1 saapl ; COIIQ)Oaltlona ot eaob ple wer &lao calculated and ar tabulat d, The tie llae data necesaary tor comatruction ot the pbaae dlacz,mu ie tabu-lated in Table a and t pbaae diap9 46-48. &re ISbo,m OD l'lprN CoDJuaate cun ar dra on the pha.e dta,:rama for th purpo of inter latin tie 11 e; t plait polllte for two of th yst s we.re st ted by extrapolating tile ooDJuaat cun to its interaeetion with the nodal cu.ne. Tbeae COQJupte cunea were constructed tram pointa located bJ clrniag 11n a tbrouab each e d of tile tie line parallel to tbe alclea ot t e dlagr in ch a saner that tbeae two line iateraected inside the dlagr Yartereasian and l'enae (44) found tbat 'ternary aolobility datil could be rep.l'eseated y the followiq relatioaahip A z1 s2 I"" :: w l - II.' Tile tent (3 la known as the selectiYitJ of tu aolffat and 11YN a aeuure of tile .... wltb wbicb a billUJ atatv eu be -,.rated with a 11Yea aolyent by 110lYm1t auaotion

PAGE 68

59 .. tbode. A f3 -.awe of ual ty would l.Ucate ao Nlect1Y1 ty while aelentll h&Tiq laigber T&luea of (3 are aore ... lecti The aelectiYlt11a aaaloaou to the relatle YOlatllity whioll la aNd u a aeU\lre ot tbe -with which a biD&l'J' aixture can be .. ,.,ated by dlatillation. Yaluea of tbe ae1eot1Yity h&Te bMD calculated fNIII the tie 11ae data and equation 18 for the four a,ateaa tuclled la th1 'IIOl'k. line theae Taluea of the Mleetlylty TN'7 oaly allghtly with 0011poaitlon, tJaeir race Yaluea are tabulated below la Table IT. TABU ff SOLYDT IBLIICTfflTJg Klature to be S.lTeat t
PAGE 69

0 but that carbon tetrachloride is the better of the two. It la alao obTious that the ester is not a good solvent for the h)'drocarbon aizture. Proa consideration of the Beatchard-Bildebrand the ory o ne would not expect a nonpolar solvent to be Yery aelect1Ye for either C7F16 or Csl'1&0 sin.ce their solubility paraaeter (d) are alaost equal, being 5.93 and 6.05 respectiYely. The cf difference is a aeasure of the deviation of a binary systea froa &aoult's law as shown by equation 3. One can aee that for a given solvent the O difference be tween C,1'15 and solvent ia practically the aae as the cf difference between C9F1sO and solvent. The high aolvent selectiYity found in sou reported syst cu be attributed to specific effects such as association, solvation, or hydrogen bonding which are not present in nonpolar systeas. Since the aolubility paraaeters of the fluorocarbona are alllost equal, and aince they are nonpolar they cannot exhibit apecific interaction effects with the solvent. It ia con sidered unlikely that a separtion can be effected by solvent extraction. Theoretical Calculation of Activitiea in Ternary Syateas.-Bildebrand (15) has extended the treatment of solu tiona of nonelectrolytea to ternary aysts and has arriyed

PAGE 70

61 at equations 59 for the activity coefficients in terms of the properties of the pure compounds. BT ln Y 1 : V1 [< 01 d'2> ~2 ( cf 1 03) ;~ 2 (59) BT ln Y.2: 'f2 [<02 01> <\>1. <02 d'3) '~ 2 &T 1n : \'3 [< 03 01> + l ( cf 3 02) '1>2] 2 Using equatioma59 the actiYitiea in the two conjugate liquid phases cu be calculated froa the tie line data. It equations 59 correctly predict actiYity coefficients, the calculated actiYities must aatiafy the condition that the activity of each component be equal in both phasea. X y 1 : Xl )" 1 t x r = s r 3 3 3 3 (60) Kquatlons 59 were used along with the tie line data to calculate actiYitiea in the coexisting phases for the solubility pareters were evaluated fr011 the properties of the pure eoaponenta. These calculated actiYity Y&luea are tabulated in Table n. Froa Table XX it is ohYious that the results of equations 59 do not satisfy the conditions of equations 60. If, bowner, equations 59 are used with the

PAGE 71

62 solubility paruetws evaluated tr011 tbe blaary aolub111ty data, tbe actlwitiea are fouacl to aatlaty equatiou 60,. aa can be seen fl'OII Table D. Tile "effectlwe'-' aolubilitJ par_t_.. cu be found froa tbe biaary aolubtlity data b:, aubetitutiq equatlou a in'tO cauatlona ll. ad 12. Two filllP.irlc&l -.alue of eacb 41tiereac are obtailled fNII tbis procedure alnce there are two equatlou (11 u4 12) and onl7 oae uon.on (the cf di1 f re11e ). It wu found that there was 0111:, a all&bt dif fereue between the two cf difference tenaa and therefore u race yaJ.ue was used for 11\lbstitutioa into equation 89. Biace tbe following relation boldll 01 02 < 01 6s> -< 01 d3> only tbe cf diffweao tor two of tile binar:, rt-la aeedecl to ewaluate all poaaibl cf differeaoea ~uired by equatiou SI. Yaluea of ine d cliffereDCe ff&luated il"Gll the binary aolubillty data are compared with tboae naluated fl'OII propertlea of tbe pure coapoUDda in Table Y.

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Syst911 C7F1e-~-C7H16 Csl'160-~-C,H16 C7J'1s-CCl4 CaF1eO-CCl4 T.dlE V COMPARISON OF O DI F F ERENCE cf Difference Pure Coapouncls 1.43 1.31 2.52 2.40 Solubility 2.87 2.78 3.10 2.94 Since the Yan Laar equation has proyed useful in treating binary systeas it would be interesting to see if ternary systems are also aaenable to thia treataent. White (47) has applied the Yan Laar equation to calculate equilibriWll vapor-liquid coapositions in ternary ayatema froa data obtained froa the binary syateaa. Be coapared the calculated results with ezperiaental data for three ternary systems and found tbe agreeaent to be good enough for engineering purposes. Robinson and Gilliland (36) haye shown that the Van Laar treataent can be extended to ternary systeas where the Van Laar constants for only two binary systems are needed to calculate actiYity coefficients in the ternary systea. The ternary Van Laar relations are

PAGE 73

6 ln Y 1 : I x2 ~2 X3A32 J,:;_3l8s2 l 2 ~1A1:af812 + X2 X3A32f8:3~ 1n y 2 : I ":r'12 JA;l X3'32 Ji;:s!Bs;\ ~1A12/812 x2 + x3l32/Bs2] ln y 3 : I x1A12 /i;1IB12 x2 I 2 ~1A12"812 + X2 + X3A32/B:i2] 2 (61) In naluating the constants ia equations 61 the following relations are used and Since the square roots of the binary Van Laar constants are needed for equations 61 the question arises as to whether the positive or negative root should be used. In This case the binary Van Laar equation is considered similar in form to equations 3, where the constants can be written and A V1 12 -RT 812: !! R T A12 V1 812 vi' ( 01 0. )2 2 (62 d' )2 1 The square root of A 12 is taken to be positive if d 1 is

PAGE 74

65 greater than O 2 and nega ti Ye if the reYerse ia true. The relation existing bstwee n t e constants which allows the e-valuation o f all constants from the constant of two bi nary aysteas is VAi.2 -;;:;,3 The necesaary contants for use in equations 61 were deter11ined from the binary van Laar constants by tbe procedure described above. The act1Y1t1ea fer each coaponent in th two ceezisting phaaea were calculated for the ayateaa c7 F 16-c8 16o-cc1, and c,r16-c8 F16o-!.-cru16 The aetiYitie.s are tabulated in Table UI and it can be aeen that equationa 61 satisfy the conditions of equations 60. Thus we see that equations 59 o.r 61 can be uaed to predict act1Y1ties in ternary systeas when the constants are naluated experimen tally from two binary ayst-. It 1& also poaaible to use equations 59 or 61 to construct the ternary phase diagram from the binary solubility data. This can be done graphically by uaing equation 59 or 61 to plot contours of constant actiYity fer each component on a triangular diagram. The composition of tbe two pb.aaes in equilibriua can be found by locating two points at wbicb the actiYity of each coapone.nt ls equal. An at tempt was made to use this aethod to calculate the pbue

PAGE 75

6 diagram for the c7 F 1 6-c F 160-cc14system, but location of the phase compositions proYed v ery difficult since it was necessary to interpolate between three sets of activity contours.

PAGE 76

CHAPl'ER IX EXTRACTIVE DI8TILLATIOK 8'1'UDIB8 The tera extractiTe cliatillation r efers to the proces of adding a solvent to a aixture to be separated by diatillation in order to illprOTe the relative volatility. The solvent is able to illproTe the relative Tolatility by altering the actiTity eoef:ficients of the various c011ponents The relative volatility (0() is defined for a binary aixture by equation 62 Y1 Xi (62) ex.:. Xl Y 2 (In equation 6 2 the subscript 1 refers to the a.ore Tola. tile coapound.) For systems obeying Dalton's law of par tial pressures and where deviations from ideal gas behavior can be neglected the ratio y1;x1 is g1Yen by Substituting into equation 62 g ives 0 P1 11 --o( = (63) P20 Y2 Prom equation 63 it can be seen that by selecting a solvent 67

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68 which increas s the ratio of activity coefficients the relative Yolatility is increased. In practice the solv n t used i s essentially nonvolatile or of a low volatility compared to the original components and the quantity used is such that the original components are in low concentrations in the liquid phase and de not interact with each other appreciably. This being the case, the ternary mixture can be treated approximately as two binary mixtures involving each original component with the solvent. Since the solvent is essentially nonvolatile t he vapor phase is assumed to consist only of the original components. The Scatchard-Bildebrand theory can be used. to predict some properties of a good solvent for extractive distillation. Assuming two independent binary ayatems, the expression for the logarithm of the activity coefficient ratio as given by equation 3 1s RT ln YJ.1 Y2:: V1(03 01)2 ~32 V2Cd3 d2)2 ~32 (64) (In equation 64 the subscript 3 refers to the solvent.) If the aolal volwaes of components 1 and 2 are ap proxiaately equal then equation 64 becO!Jles (65)

PAGE 78

69 From equation 65 we see that the logaritha of the activity coefficient ratio depends upon the square oft e volua :fraction of solvent and upon the solubility parameter of the solvent. From the standpoint of separating power the properties of a good solvent will bet oae which increase the right hand side of equatio n 64 or 65. This indicates that the molal volume and the solubility parameter are important factors in selecting a solvent. It is difficult to predict the effect o te perature upo the activity coefficient ratio as given by equation 65 since the molal volume c anges in th same direction as the t m p e rature, and the difference term is more or less i dependent of temperature. One would therefore not exp ct the activity coeLfic i e t ratio to be a stron function of temper a t u r In this w rk s everal compo unds will be evaluated as extractive distillation solvents for ixtures of perfluoro d perfluoroc c l i c oxi d (C F1 6o ) ; also n-eptane (!!,-C, H16) and methylcyclohe:zane (C6 11 C Is). A convenient method of evaluating prospective extractive distillation solvents i y means o gas-liquid partition chro ato raphy. Porter, Deal, aud Stro&s (30) have shown that the activity coefficient of a solute in an infinitely dilute solution in the paiti tio ing .1.iquid can be obtained fr011 the appearance time of the solute peak. The

PAGE 79

70 activity coefficient ratio in equation 63 can be found froa the appearance times of coaponents 1 aad 2 when the prospec tive solvent is used as the partitioning liquid. The follow ing relations were given by Porter et al for determining the --activity coefficient in the infinitely dilute solution. a0 : o BVs B: rr/Y0pvl 'f o : 'f I / (P1 / P 0 ) 3 ... 11 R a; ~(P1/ Po> 2 .. !1 (86) (67) (68) The vol1111e occupied by the vapor phase in the coluan (v0 ) is usually small compared to v8 and can be neelected. Beglecting v0 and COlllbining equations 66 and 67 we get Vo. VsBT R -yo O"' P Vs (69) If the appearance tiaes, e for cc:aponents 1 and 2 are detel'llined under the same conditions of constant flow rate an~ / constant pressure drop through the partitioning colwan then we can write 0 Va 2 va01 ":a2 ---Va1 Fro equatiun 69 the ratio Vu/ VRl can be Yritten vu= Y1op10 Vai f2op7,0 (70) (71)

PAGE 80

Equating equations 70 and 71 gives (72) Substituting equation 72 into equation 63 yields the following expression for the relative volatility of coaponents 1 and 2 at infinite dilution in the partitioning liquid. (73) Since the yalue of the relative volatility as given by equa tion 73 is for an infinitely dilute solution, the ratio of the appearance times gives the maxilllua separation that can be obtained when using the partitioning liquid as an extractive distillation solvent. Experimental.-The chromatography coluans used in tbia work were made from one meter lengths of one-fourth inch copper tubing; these columns were used in a Perkin-Blaer nyapor Fractoaeter," model 154. The stationary phase was Celite C44857 (JohnaManville), a diatoaaceous earth having rather unifol"lll parti cle size. Before thie celite was used the very all parti cles were removed by allowing the material to -ttle in water and decanting the water containing the suspended fines. After this the celite was washed several tiaes with concentrated hydrochloric acid, then washed with distilled water and dried

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72 in an oven. The prospective solvents were perfluorokerosene, and three Kel-F oils having the general structure Cl{CF 3 CFCl)xCl. These oils are products of the w. Kellogg Coapany and were designated Jtel-F oils 1, 3 and 10. The Kellogg Company reports the following vapor pressures tor these oils at 100 c. Kel-F Oil 1 17 U1 Kel-F 011 2 1 DUil Kel-F Oil 10 0.l mm These four liquids were chosen as partitioning liquids since their vapor pressures were low enough to .prevent their removal from the packing during operation of the coluan t adequate gas flow rates and temperatures. The ratio of partitioning liquid to Celite used in the preparation of tbe partitioning coluans was 0.5 to 0.7 al of liquid per gram of Celite. The weight of paeking reQ.uiJ'ed to fill the colwm was measured so that the void volume and the volWlle of the stationary phase could be computed. Tbe properties of these columns are tabulated in Table XXII. The four above mentioned par: ~ioning liquids were evaluated as possible extractive distillation solvents tor the binary systeas ~P16 with C9F16o, and C,B1s with ct;H11CH3.

PAGE 82

73 Table XXIII gives the appearance times of c7 F16, c8 P16o, C7H1 6 and c6 H11CBa in the partitioning liquids and Table XXIV gives the values of the relative volatility as calculated from equation 73. From Table DIV it can be seen that all four sol vent can be rated equally as extractive distillation sol vents frr both binary syateas. The pronounced effect of temperature upon the relative volatility is alao noted fro Table llIV. The C,F1aCsl'1sO system was investigated by Yen (49) and was found to obey Raoult's 1 w. Since this system is ideal the relative volatility is erely the ratio of vapor pressures. Using the vapor pressures listed in the appendix for C7Fl6 and CgP1sO, the calculated relative volatilities for this system at 35 and ao0 c. are 2.34 and 1.96 rela tively. Using an average value of the relative volatility for these compounds in the four solvents it can be seen that the addition of the solvent changed the relative volatility from 2.34 to 2.62 at 35 c. and from 1.96 to 2.16 at so0 c. This change corresponds to a change in V-1 ; Y-2 fro 1.00 to 0 0 1.11 at 35 c. and froa 1.00 to 1.10 at 80 c. The effect of temperature upon the activity coefficient ratio is very slight as was previously suggested.

PAGE 83

74 The n-heptane-aethylcyclohexane system was investigated by Broailey and Quiggle (4), who found the average value of the relative volatility to be 1.074 in the temperature ranee 90 to 101 C. The syatem obeys Raoult'a law and the relative volatility ean be expressed as the ratio of vapor preaaures. Using the vapor pressures calculated froa the Antoine equation given by reference 1 the calculated relative volatilities for this system are 1.003 and 1.057 at 35 and so0 c. respectively. Again using the average value of the relative vola tility for all solvents it is seen that the relative volatility for these hydrocarbons changed fr011 1.003 to 1.11 at 35 and frOlll 1.057 to 1.21 at ao C. The addition of the solvent cauaed the activity coefficient ratio to ~hange fr0111 1.00 to 1.11 at 35 c. and from 1.00 to 1.14 at so0 c. Again the effect of temperature on the activity coefficient ratio is seen to be slight. Since the physical properties necessary tor evalua tion of the solubility paraaeters of the solvents (d3 ) are not available it is not possible to predict the expected value of the activity coefficient ratio as given by equation 64 or 65. Equation 64 can be used, however, to evaluate the solvent solubility parameter (03 ) by using the experiaentally deteJ"lllined activity coefficient ratio and the necessary phys-

PAGE 84

75 1eal pJtOi,e,-ti of the solutes giYen in Table DVI. Values ot c:S 3 ,rere calculated f:NJ11t data for the c7 16-c8 u o ... aolent1 and C,Hu;-ceu11cn3 solv nt syst. t the tea pe,:ature of a a0 c. and 8-0 c Th8" valuea of cf 3 are tabulated below and it can be ea that o 3 ball eueatiulr the ... Yalue when evaluated froa experilleotal data :frOJI two different ayatems. 80 TA LE I CALCUUTIOI( er O 3 FIOII 7 .88 7 .IO ATION &, The r eulta in Table YI indicat that the ecauatiou of 8eatellar4 and Jl1lclebran4 _. applicable to precltotion of aolent properties. l'roa th result of Table Yl the ~race Mlftat aolubUi't,y par._.tera are 7.98 at 3rl' c. aad 7.51 at ao c TbeN ..iuea of tbe ao.lubili'ty Ptr aay -IIOllewbat high for chlorofluorocarbon cc.pol1ada ataee dllorofluorocarbona for which data ar Pailable Jaoe 11elubtltt1 par-ten between tboae of tluorooarbou aad bydrooarbou

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16 ll&Y1aa tbe nae boiltng poiDta. It Should be ted, ovever, that tile aolub111ty par-ter increaae wtt .increaatq aolecular wei. t within a h lop.us eerie aa a obvtoua froa tbe foll,,,.lna table of aolubilit:, p.r ... ten f .OJ' the ~fin sori s u repe>rt d by lde aad (16). COllf!'!. cf at 2cf' c,. !:-C~11 7.81 !.-C&B14 ~ 818 !.-Ca81a ,!-Cgll20 !:1. 8 o It ldglat be uped tllat tbe J.ar1 aolublllty parter ot tba lnu would lead to iaa1ac1W..lltJ 111 tbe c ... o tbe fluorocarbou, but eiuee the molal wlaea of the eoaai r d ffect of cliff re oea 1A molal Y<>lUla io to deer ue t poa ti elev a ioas froa ult' ln aod lt a poe 1 l e that . olume clispa:rit7 i large e-,uch to perai t aiaolbili tJ la apl t-a of ta.. l&r d iff r DO Int light of tile voluae iapari y it would be

PAGE 86

71 later .. tlq to clet.,.lae the effect of th.la taotor 11,oa tbe aottlt1 ooef'f1oleat ratio of aolut.ea 11a u traot1Ye cllat1llatlo.a lMat. Instead of uat .. e411at1on 31 tile tolJ.owtac ..,attoa u al bf H114ebrud (11) will be uMd for tbe utlYity ooel!lcieau lace a oorreotloa tena for W>l-clJ.Jtparlty la 111eludM, la 'f 1 :~ (d'1"' 011>11~ ... 111 ~1/i (1~)~11 (74) If aaa1a aue tu U8Ullptioa tbat tile Yoluae traction of aolYeDt ia lup eaoup tllat coapoaeat l aad I act indepeadeatly ot eacb other..,. can write for tba actiYlt:, coe1-11etent ratio la '( l / y II:~ ( cfl .. tf3)2 f s I (01 d'3)3 ~a2 + (" ) 1D tbe iDtilal aotlYltJ O
PAGE 87

78 used. nua fact waa noopiud by Beed (35) aad wu UNd bJ hill to uplaU the 8UCC8811 of the loa~ldebraad 1,-. ory in predictl azeotropea (33) aad relative volat1U1il.ea io h)'4rocarboa apteu.

PAGE 88

CHAPT E R X EVALUATION OF IIETHODS OF SEPARATING FLUOROCAllBON IIIXTURES This discussion will deal mainly with poasible procedures for separation of fluorocarbon aixture since separation procedures for hydrocarbon aizture have been covered quite thoroughly by Rossini et al (37). Distillation.-Several binary systs containing fluorocarbons have been investigated (5) (24) (49) with ideal solution behavior reported in all cases. Since fluorocarbon-fluorocarbon aixturea can be expected to follow ideal behavior, the relative volatility or the ease of aeparation depends upon the ratio of vapor pressures of the coapounds to be Hparated. Yen has shoWD that when fluorocarbon aixturea are distilled, laboratory distillation coluans are approxiaately one-half as efficient u when hydrocarbon aixturea are dis tilled. A laboratory distillation coluan having 100 theoret ica l pl~tes in a hydrocarbon separation would have approxi mately 50 theoretical plates in a fluorocarbon separation. Azeotropic Distillation.-Aa would be expected froa the large poaitive deviations exhibited by fluorocarbon hydrocarbon mixtures, azeotropes are fol'lled between fluoro79

PAGE 89

80 carbons and hydrocarbons even when differences in normal boiling points are large. This azeotropic tendency has been e xploited by air (23), who used fluorocarbons as azeotroping agents in separating paraffin and cycloparaffin hydrocarbons. The C 7Fl6 and C 8 F1 6 0 used in this work were each purified by azeotropic distillation with ,!-CrH16 Since the addition of a hydrocarbon azeotroping agent to a fluorocarbon mixture would also increase the efficiency of the distilla tion column, i t is possible that azeotropic distillation holds some promise as a means of separating fluorocarbon mix tures. Extractive Distillation.-It was shcnrn earlier that some enhancement of the relative volatility of a fluorocarbon mixture could be obtained by employing a chlorofluorocarbon solvent for extractive distillation. Yen found chlorofluorocarbons to have eol\ltlln efficiencies slightly leas than hydro carbons, but approximately twice as large as fluorocarbons, In this case the added solvent would enhance the separation y i ncr asing the relative volatility and by increasing the column efficiency. The e ffect of the relatiye volatility and coluan effi ciency upon the separation obtainable by distillation can be seen from an equation derived by Fenske (8).

PAGE 90

81 (i) D/ ( ~). : o(B (76) Equation 76 applies for conditions of total reflux and constant ex. The left hand side is a measure of the aeparation attainable in a coluan of N plates; a large value of the ratio on the left-hand side indicates good separation. The effect of increasing the col~ efficiency is to increase the : number of theoretical plates (N); thus if both the relative Yolatility and the col'uan efficiency are increased the re sulting change in separation can be large. Liquid BKtraction.-We haYe seen earlier that separa tion of fluorocarbons by liquid extraction is not feasible where specific interactions between one component and the aolYent are absent. Where a functional group is present in a fluorocarbon, there is the possibility that a aolYent can be found which will be selectiye for this compound. An exaaple of thia type could be found in the syatea c8 F 160-C,F15s-c2a50H where c8 F 16o and c2a5oB are practically 1.maiscible while C.,F15B and C:,B5oa are miscible eyen at teaperatures as low as -so0 c. In this case there is undoubtedly a hydrogen bonding effect which would pel'lllit the separation of c7 F15B froa cai&O by extraction with c~5 0H.

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CBAPTBll XI COBCLUSIONS The experimental work and discussion included in the previous sections of this dissertation pro v ide the basis for the following conclusions. 1. Th e s imple Scatchard-Bildeb r&lld theory is inadequate for predicting excess free energies of mixing heats of mixing, and volwae changes i n fluorocarbon-hydro carbon aixturea. 2 The Scatchard-Hi ldebrand theory with the aodi fications introduce d b y Beed p rovi d e s good estimates of t h e heat of mixing in fluorocarbon-hydrocarbon systems. 3. Good e stimate s of the excess free Anergy of mixing can be calculated from t h e Van Laar equation and bi nary solubility data. 4. Beats o f a ixing calculated from the Van Laar quation and solubility data are unreliab l e 5. The exoe s free energy of mixing fluorocarbons with paraffin hydrocarbons can be estimated from an empiri cal correlation if values of the solubility parameters, ionization potentials, and molal volumes are available. 82

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83 6. Comparison of the calculated and obaerved con solute teaperature is not a good criterion for testing the applicability of the lcatchard-Hildebrand theory. 7. Kixtures of fluorocarbons with hydrocarbon exhibit large vol\11118 changes on mi.zing (in the order of 3 per cent of the total voluae at 50 mole per cent). This Yoluae change on aixing was found to increase with increas ing teaperature. 8. A negative excess entropy of aixing at conatant voluae can be used to explain the disagreeDlent in some fluorocarbon-hydrocarbon systems between obsened theraodynamic properties and those calculated fro the ScatchardHildebrand theory. 9. The concept of clustering can be used to explain the negatiye values of the excess entropy of mixing at con stant voluae. 10. Scatchard-Bildebrand or Van Laar equations may be used to predict actiYities in ternary systeaa if the constants are determined empirically froa the solubility data for two of the binary systeas. 11. The Scatchard-Hildebrand equations can be used to predict relatiYe volatilities in systems containing an extractive distillation solYent.

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8 4 12.. The possib111 ty of separating a mixture of two fluorocarbons by liquid extraction is slight unless one fluorocarbon contains a functional group whieh will permit soae sort of interaction with the solvent. 13. Future work should be directed toward the measurement and theoretical calculation of the excess entropy of mixing at constant volume. 14. The problea of theoretically calculating the volume change attending mixing remains unsolved. Some light may be shed upon this problem when a theory is developed which will predict the entropy tena.

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APPDDIX I. Purity of Compounds Used Rydrocarbona.-llost of the hydrocarbou used in this work were obtainable c01111ercially in a reasonable degree of purity and were not further purified. The phyaical proper ties of theae coapounda are listed in Table VII along with the reported literature values. l'luorocarbou.-l'iTe fluorocarbon c011pounds were used in this work. The physical properties of which are liated in Table VIII. The physical properties of aoae of theae fluorocarbons have been reported in the literature; these values are also included in Ta ble VIII. Since the supply of SOiie of the fluorocarbon coapounda was liaited it was necessary to recover fJOlle fluorocarbons frOlll aistures with hydrocarbons and repurify them. Where this was done the physical properties of both batches are recorded in Table VIII. 1, Perfluorocyclic oside, c8 F 16o. This material was the aajor constituent in np1uorocheaical 0-75" aanufactured by tb.e tnneaota Mining and llanufacturing Collpany. It ia believed that this fluorocarbon is a five or sis aeabered, osysen-containing ring with aide chains. Thia material was first fractionated in a laboratory distillation colUIID having 60 theoretical plate 85

PAGE 95

86 (when tested with hydrocarbons). The center cut from this fractionation was further purified by an azeotropic distillation with n-heptane. The fluorocarbon was then -separated frOlll the hydrocarbon by cooling the azeotrope to dry ice temperature where liquid phases were found haTing Yery low autual solubility. The perfluorocyclie oxide was then freed from the small aaount of remaining ,!-heptane by redistillation in a 30 theoretical plate colWlln (when tested with hydrocarbons). A chroaatograph of this purified material revealed only one peak. 2. Perfluoroheptane, C,F16 This material was a constituent of "Fluorocheaical 101" aarketed by the Minnesota Mining and anufacturing Coapany and was purified by the same procedure as perfluorocyclic oxide. This purified material also exhibited only one peak when sub jected to chromatographic analysis. 3. Perfluorotributyl aaine, (C4 F 9 ) 3x. This material was the center cut obtained by fractionation of Minnesota tning and Manufacturing Coapanys "Fluorochemical R-43" in a 60 theoretical plate colWllD (when tested with hydrocarbons). Cbroaatographic analysis indicated that this aaterial was a mixture of several coaponenta, probably iaomers. 4. 1-Hydroperfluorobeptane, C,F15s. This material

PAGE 96

87 was prepared in the Fluorine Research Laboratory by Dr. H. C. Brown by the decarboxylat1on of the sodiUDl salt of perfluorooctanoic acid. This material was purified by simple distillation in a colWllD having 68 theoretical plates (when tested with hydrocarbons). 5. Methyl perfluorooctauoate, C,F15coocu3 This material was also prepared by Dr. H C. Bro,rn from per fluorooctanoic acid and was purified by simple distillation in a 60 theoretical plate column (for hydrocarlx>ns). II. Thermocouple and Thermometer Calibration J All thermocouples used i1;1 this work were the copperconatantan type. Thermocouple readings were made with a Leeds and Northrup potentiometer No. 8662 which could be reAd to 0.001 millivolt. -1. Thermocouple in two liquid phase still. The caU.bration temperatures for this thenraocouple were the ice point and the boiling points of methylcyclohexane at 757.45 and 381.05 pressure. The boiling points of aethylcyclobexane at these pressures were determined froa the Antoine equation given in reference 1. The poten tioaeter readings (in aillivolts) at these temperatures were used to deteraine the constants in a three-constant equation. Tbe calibration data and equation are given in Table IX.

PAGE 97

88 2. Thermocouple in Solubility Cell. Thia thermocouple was calibrated against a theraocouple previously calibrated by Dr. T. Beed of the Fluorine Research Laboratory having the following calibration equation. t = 0.050 + 24.9le 0.359282 The two thermocouples were iuaersed in a wate r bath and both readin g s were mad e at the same temperature. These millivolt reading s are listed in Table IX along with the bath teaperaturea calculated froa the above calibration equation. Since the two thermocouple readings were practically identical, the calibration equation for the theraocouple in the aolubility cell was taken to be t : 0.050 + 24.9le 0.3592e2 3. Thermometer in Temperature Bath. Thie mercury in-glass thermometer was graduate d in tenths of degree centi rade and could be rea d to 0.02 c. This ther-aometer was calibrated against a thermocouple calibrated b y the National Bureau of Standards. The calibration data are g iven 1n T able IX. Pycnometer Calibration Data and Equations.-The calibration d t a for f i v e p ycnoneter s at several temperatures are tabulated in Table X. The pycnOllleters were designed by Lipkin (22) a n wor u essentially U tubes with a

PAGE 98

89 bulb in one arm. The arms were capillary tubes provided with etched graduations. At a constant temperature each pycnometer was cali brated by deter ining the volumes corresponding to three dif ferent liquid heights in the capillary arms. The voluae was related to the tot 1 liquid height by the following equation V: V0 + ah The constants V0 and a were determined by the method of least squares. The volW1e of a pycnometer at a particular liquid height was deter. insd from the eight of distilled mercury occupying the pycnometer and the density of mercury at that temperature All weighings were corrected for air buoyancy. The pycnometers were k ept in a constant temperature bath for approximately thirty minutes before the liquid heights were read. The constant temperature bath ne-ver varied more than o.os0 c. fro~ the calibration t emperatur. Vapor Pressure Measurements.--The vapor pressures of all of the pur fluorocarbons were determined over a range of temperatures by measuring the boiling temperature under varioua applied pressures. The still shown on Figure 9 and a boiling point still similar to that described by ~iggle, Tongberg, and Fenske (31) were used for these meaS\Jrements. Calibrated thermocouples were used for temperature readings. The atills

PAGE 99

90 were connected to a closed syatea containing a aercury aaaoaeter which could be read to 0.10 -by aeaas of a cathetoaeter. flle ezperilleatal data are reported in T able XI and 101 pis plotted -versus 1/T in l'igure 1.

PAGE 100

U) ... Compound n-Heptane Methyl Cyclohexane Toluene Carbon Tetra,chloride Ethanol 2-Butanone TABLE VII PHYSICAL PROPERTIES OP HYDROCARBONS USBD IN THIS WORK Source Refractive Index Denaity BoiliDK Point at 25 c. gm/al at 25 C. 0 c. -ri-Literature BzperiLiterature BxperiLiteramental mental -ntal ture (1) (1) (1) Dow 1.-3852 1 38511 0.6798 0.67951 98.4 98.427 latheaon, 1 4206 l.42~ll 0.76511 (1) 0.78506 100.9 (1) 100.934 Coleman, and Bell Baker and 1.49.1 0.8623 2 o.86~!A 110.7 110.~ll ldamaon Laboratory 1.4567 ,43) 1 73 1.5844 1.Jg> 76~r> Supply [.aboratory 1.3596 1 35~ 0.79089 (1) o. 78506 78.2 (1) 78.33 Supply (1) (1) (1) latheaon, l.3761 1.37643 0.7995 0.79970 79.6 79.59 ~leaan, IUld Bell

PAGE 101

co N TABLE VIII PHYSICAL PROPBRTIBS OF FLUOROCARBONS USED IN THIS WORIC Compound Befract1Ye Inde Deaaity Boiling Point at 25 c. p/al 0 c. bperiLiterature ExperiLiterature ExperiLiterature mental mental mental Perfluoroheptane 1.2594 1.7258 O,F16 1.2!1!A 1.1!18~ 82.1 ,28) 1.2603 1.7276 82. Perfluorocyclic 1.2770 1.7633 OXide ---102.8 C9F160 1.2768 1.7634 1-Bydroperfluro1.2700 l.,,,i 1.723 3 95.4 94-9,25) heptane C,F15H ._rfluorotribu-1.2906 -1.8772 -177.6 tyl-iae (C4P9)3H (41) (41) (41) tbylperfluoro1.3033 1.304 1.6967 1.684 160.8 158 octanoate C,P15COOCH3

PAGE 102

TABLE IX THERMOCOUPLE AND THERM ER CALIBBATIONS A. Therm ocouple i n Two Liquid Phase Still Substance Ice Jlethylcyclohezane M ethylcyclohezane Vapor Pressure BUil --757.45 381.05 t 0 c. o.oo 1 00.82 713.16 Calibration equation: t = 25.40e 0.4672e2 B Thermocouple i n Solubility Cell Solubility Cell PreYiously Calibrated Thenaocouple Theraocouple Millivolts Millivolts 1.724 1. '128 2.340 2.340 2 .844 2.844 3.273 3.26 6 3.353 3.353 3.140 3.146 3.016 3.016 volts 0.000 4.311 3.274 Bath Temperature 0 c. 42.0 56.4 68.0 7 7 6 79.5 74.9 71.9 Calibration operation: t: 0.050 + 24.9le 0.3592e2 93

PAGE 103

TABLE IX (Continued) TIIBIIIOCOUPLB AND THBIUIODTD CALIBRATIOHS c. Tellperature Bath Thermometer Tberaoaeter Beading Standard Tberaocouple Beading 0 c. . v. 0 c 0.04 o.o o.o 20.00 1.023 19.90 24.96 1.289 25.00 30.57 1.580 30.56 37.73 1.964 37.86 47.23 2.471 47.'4 94

PAGE 104

s:I Q) k Ok G> ~! 8 j s..u Bi0 u t 100 25 101 25 51 25 1 40 1 45 1 50 1 55 1 60 2 40 2 4 5 2 50 TABLE X PYCNOllETER CALIBRATION S CM ... o,c~ .. CM >-i r-i u 0 0 k .... .s:I .... .... Jji ::, tiO k +) ... s C,...t .... .jj Qi i I A 136.6083 10.0937 12.-71 V: 9.-9948 0_.007782h 136.2601 l0.0680 9.4'0 135.5923 10.0186 3.06 136.4716 10.0836 13.31 V 9.9787 0.007883h 135.9787 10.0472 8.70 135.3102 9.9978 2.42 65.9762 4.8748 13.10 V: 4.7724 0.007823h 65.4239 -t.8340 7.84 6-t.8817 4.7940 2.78 68.7939 5 .0969 10.15 V: 5.0161 0.007960h 68.5161 5.0760 7.52 68.1134 5.0"62 3.78 68.7901 5.1012 10.72 V: 5.0170 0.-00786lh 68.5123 5.0806 8.08 68.1097 5.0507 4.30 68.7901 5.1058 11.28 V: 5.017 6 0.007818h 68.5123 5.0852 8.64 68.1097 5.0553 4.82 68.8410 5.1142 12.32 V = 5 .0168 0 .007919h 68.2914 5.0734 7.11 67.6230 5-.0237 0.89 68.8410 5.1188 12 .90 V 5.0174 0.007877h 68 2914 5 .0780 7 6 5 67.6230 5.0283 1.40 69.7673 5.1690 12.26 V: 5.-0706 0.008010h 69.2219 5 1286 7.28 68.7600 5.094" 2.94 69.7673 5.1737 12.78 V: 5.0699 0.008113h 69.2219 5.1332 7.85 68.7600 5.0990 3.57 69.7673 5.1783 13.32 V: 5.0701 + 0.008111h 69.2219 5.1379 8.38 68.7600 5.1036 4.10 9 5

PAGE 105

TABLE XI VAPOR PRESSURES 01' PURE FLUOROCABBOBS Substance Temperature Pressure log P 1/T (103 ) 0 c. mm. T in o K. Perfluoro-82.8 767.3 2.88497 2.8090 heptane C7F15 82.4 759.0 2.88024 2.8121 82.3 758.3 3.87984 2.8130 81.8 745.8 2.87262 2.8169 81.5 739.8 2.86911 2.8193 79.7 698.7 2.84429 2.8337 79.5 688.5 2.83790 2.8353 77.6 650.1 2.81298 2.8506 76.1 619.5 2.79204 2.8629 75.9 616.4 2.78986 2.8645 73.2 560.6 2.74865 2.8869 71.2 522.4 2.71800 2.9036 70.0 503.9 2.70234 2.9137 65.0 419.5 2.62273 2.9569 61.4 367.3 2.56502 2.9886 56.8 310.0 2.49138 3.0303 53.2 267.6 2.42749 3.0637 49.2 226.5 2.35526 3.1017 46.4 202.3 2.30814 3.1289 96

PAGE 106

TABLE XI (Continued) YAPOR PUSSUUS 01' POU FLUOROCARBOBS Substance 'l'elllgerature Pressure log P c. mm. 42.5 171.1 2.23325 38.2 142.2 2.15290 33.5 115.5 2.06258 Perfluoro102.8 761.4 2.8816 1 cyclic OZide 97.3 6 39.1 2.80557 CsF150 92.7 551.6 2.74162 6.5 4"8. 7 2.65196 79.9 357.4 2.55315 74.0 288.8 2.46060 66.2 214.5 2.33143 60.4 1 69.5 2.22917 55.3 136.3 2.13450 52.5 121.1 2.08314 46.9 94.3 1.97451 39.3 66.5 1.8226 9 34.7 52.l l.71642 30.5 42.4 1.62737 Perfluorotri-177. 6 762. 6 2.88230 butylaaine (C4P9)3R 173.4 6 75.6 2.82969 97 1/T (103) Tino K. 3.1676 3.2123 3.2605 2.6596 2.6191 2.7330 2.7878 2.8321 2.8802 2.9464 2.9976 3.0441 3.0703 3.1240 3.2000 3.2478 3.2927 2.2183 2.2391

PAGE 107

TABLE XI (Continued) VAPOR PUSSURES OP PURE PLUOBOCARBOMS Substance Teagerature Pressure log P c. 170.2 620.0 2.79239 165.4 539.1 2.73167 159.5 450.6 2.6S379 154.8 390.3 2.59140 1'8.8 335.1 2.52517 139.4 229.9 2.36154 Perf luorotri bu131.1 172.4 2.2365' tylaa ine (C4F9)3lf 126.1 122.7 2.10072 115.2 94.0 1.97313 104.4 58.8 1.76960 95.0 40.6 1.60831 90.3 31.1 1.49248 85.3 23.5 1.37070 82.: 19.2 1.27217 Methyl-per-158.5 716.3 2.85510 fluorooctanoate 160.6 756.4 2.87877 C7F15CC>OClfa 159.8 739.4 2.86886 158.2 705.7 2.84862 155.4 650.7 2.81336 98 1/T (103) T in o I. 2.2553 2.2800 2.3111 2.3364 2.3685 2.4237 2.4734 2.5259 2.6123 2.6484 2.7160 2.7510 2.7893 2.8139 2.3164 2.3052 2.3095 2.3180 2.3332

PAGE 108

TABLE XI (Continued) VAPOR PUSSUKBS OF PUU FLUOROCARBONS Subataace Telllperature Pressure log P 152.6 601.0 2.-77890 146.0 494.7 2.69430 138.2 387.2 2.58789 132.4 322.5 2.S0856 124.8 249.3 2.39674 116.6 184.3 2.26548 110.8 146.9 2.16687 104.8 116.7 2.06700 99.2 94.4 1.97025 91.3 66.7 1.82380 Methyl-per-86.0 52.8 1.72280 fluoro79.4 38.6 1.58629 octenoate C7F15COOC83 72.3 27.3 1.43584 68.8 22.1 1.34361 65.0 18.3 1.26293 1-hyclroper-98.5 840.5 2.92454 fluoroheptane 97.2 807.0 2.90687 C7F15B 95.8 77 3.3 2.88835 95.1 753.4 2.87703 99 1/T (103 ) T in o X. 2.3485 2.3855 2.4307 2.4655 2.5126 2.5654 2.6042 2.645 5 2.6853 2.7435 2.7840 2.8361 2.8944 2.9240 2.9557 2.6903 2.6997 2.7100 2.7151

PAGE 109

TABLE XI (Continued) VAPOR PU8SUllXS 01' PUJlB FLUOROCABBOJIS Substance Temperature Pressure log P 0 c. 95.0 751.6 2.87S99 94.9 750.8 2.87552 93.8 726.3 2.86112 90.6 655.3 2.81644 88.7 618.3 2.79130 85.2 543.9 2.73552 82.0 493.9 2.69364 100 1/T (103 ) T in o K. 2.7159 2.7173 2.7255 2.7495 2.7631 2.7901 2.8155

PAGE 110

TABLE XII SOLUBILITY DATA Systems with Perfluorobeptane (C7F1&) ole Fraction Unaizlng Jlole Fraction Umaizing Carbon Temperature n-heptane Temperature Tetrachloride 0 c. 0 c. O .305 25.3 O .153 16.5 .349 31.7 .236 31.3 .393 37.7 .324 40.5 .436 42.6 .387 44.8 .480 46.9 .485 48.2 .586 54.2 582 49.4 .672 57.0 .684 49.5 .737 57.5 .803 47 .l .835 57.0 .865 42.1 .897 52.9 .904 34.2 .933 45.2 .924 28.3 .963 3~.9 0 .948 17.6 o.975 19.9 101

PAGE 111

TABLB XII (Continued) SOLUBI LIT Y DAT.A S ystems with Perfluorocyeli ~ OXid e (C8 F 1 6o) x : llole traction o f other coaponent I UDllli :ing teaperatur e O c ,I G> .... = ... 0 G M 0 Cl,) i ,d "A = QU +' ~o G> +' .8: Qi .cs" :: i j +' C) .-4 ~+' ii~ u'4 I d X t X t X t X t X t 3 8 1 ~5.7 .123 5.8 ~130 8.2 .098 25.6 066 14.0 .440 32.4 .229 2 6.1 .228 31.5 .140 59.1 ,090 33.4 5 1 5 39.4 .28 9 33.2 290 41.0 .278 77. 5 ~137 38. 5 .575 42.8 .359 39.8 387 52.1 .361 8 9 3 ~206 54.5 .679 46.8 .440 43.8 .488 59.8 .491 103 1 ~269 65.8 733 47.3 4 8 0 45.,6 ,592 63.5 ,594 109.4 .331 73 6 794 47.4 .54 7 45.8 6 4 5 65.0 .696 114.0 .409 82.6 818 47.4 .642 "6.9 7 00 65.2 .802 1 13.2 1 501 89. 0 .872 "6.2 .686 46.7 .759 65.1 .899 105.2 .580 92.6 890 44.9 .694 46.0 .800 65.2 .945 9 4.0 7 3 3 96.0 .916 41.4 .763 4 5 3 8 4 9 61. 6 9 6 8 76. 2 795 9 5 4 .93 2 38. 0 .835 42. 0 .900 55.9 .978 62.8 .862 93.0 .948 32. 2 .906 31. 0 .955 37.0 "i990 3 9 0 -.917 86-..6 .957 27.3 .950 14.8 974 20-.8 -.749 114.<>' .959 '71.0 Sealed tube determina tion-. 101 I I I I ,d X t .004 31.3 0 1 7 42.6 021 46.0 ,028 58.6 .039 61.1 .052 65.0 .117 81.4 .201 98.6 .268 109.4 .372 121.2 .975 109.0 9 9 3 65.5 .998 12. 5

PAGE 112

TAB L E XII (Continued) SOLUB ILITY DATA Systems with Perfluorecyclic OXide (CaP160) x = Mole fraction of other component t: Unmixing temperature O c Q) k s:I G) 0 Q) Q ,... IS i ,Cl ... J G> s:lj d ,8 Jot 0. g ~ Q) .... Cl) ::, i = ,-f, c., I! I :it J s:I X t X t X t X t X t .978 55.,1 .990 Z6.9 .992 14.8 Syateu with Perfluorobutylamine (C4"9)3B !,-heptane toluene X t X t 0.109 9.8 o.06 3 7.3 .215 40.5 .161 53.6 .312 58.3 .288 87 .. 0 .409 69.2 .396 105.2 o.50 7 75.9 O .. 550 125.3 103 ,... g .d X t

PAGE 113

a-heptane X t 0 .607 80.0 .765 82.6 .818 82.0 .902 77.4 ,.949 66.0 0 ,.990 22.0 T.&.BLB XII (Continued) SOLUBILITY DATA toluene z O .767 .888 .951 .981 O 995 t 140.4 140 6 132.0 110 1 71.0 Syat Containing aethJl Perfluoro-octanoate (Ci1'15COOCJ1a) n-beptane htbylcyclobezane Toluene z t z t z t O .249 11.0 0 .197 2.8 0.100 6.0 347 20.5 .310 21.8 .463 27.8 .428 33.8 .545 30.2 577 42.4 o .626 32.8 0 .666 44.8 104

PAGE 114

TABLE XII (Contin u ed) SOLUBILITY DATA Systeaa Containing ethyl Perfluoro-octanoate (C7 P15COOC1fa) n-beptane lletbylcyclobexane Toluene t t t 0.702 32.5 o.741 44,5 .817 30.6 .. 824 43.5 11898 23.3 .908 42.2 o.949 12.5 .938 36.5 O .972 21.8 Syateas Containing lBydroperfluorobeptane (C7F15B) n-heptane llethylcyclohexane Toluene X t X t X t 0.210 12.3 o.193 1 7.8 0 .408 12.8 .307 23.0 .323 37.0 .456 18.8 .405 2 8 6 .417 44.3 .511 24.5 11496 31.0 .504 48.0 .597 30.4 .628 32.5 610 51.3 .672 34.0 704 31.0 .705 52.5 .760 36.0 o.794 2 7.5 O .805 48.6 o .798 34.5 105

PAGE 115

TABLE XII (Continued) SOLUBILITY DATA Syatems Containing 1-Hydroperfluorobeptane (c7r-15B) n-heptane X t o.903 14.0 llethylcyclohexane X O .888 .940 o .e11 106 t 41.3 26.8 6.0 o.8"4 .897 0 .951 Toluene t 32.0 27.5 11.0

PAGE 116

TABLE XIII COMPARISON OF CALCULATED AND OBSERVED CONSOLUTE TEIIPERATUllES AND COMPOSITIONS System Conaolute ( K.) Coapoaition Temperature t-0) co A ,:, c:I c:I ,:, = = Q) 0 0 G) 0 0 .. .... .... t .... .... k +a +a +a j .. J .. i i i i 0 CH3C6H5-CsF1&0 386 377 324 0.73 0.77 0.18 CH3C6H5-(C4F9)3N 415 660 460 .82 .86 .87 CH3C6H5-C7F15COOCH3 279 256 220 CH3C&B5-C,F1sli 309 266 236 .75 .74 .74 D-C7H1a-CsF1a 0 320 130 123 .63 .67 .67 D-C7B16-C1F15COOCH3 306 84 76 .67 .69 .69 n_C7H1a-C7F15H 305 99 95 .61 .63 .63 D-C7H16-(C4F9)3N 355 286 240 .79 .78 .79 CH3CaB11-CsF150 338 189 173 .74 .71 .71 CH3C5H11-C7F15COOCH3 318 124 111 .75 .73 .73 CH3CaH11-C7F15H 325 140 132 .69 .68 .68 C1faCOC2H5-CsF160 369 500 408 .75 .81 .82 CCl4-CsF1aO 321 292 242 .so .78 .79 CCl4-C 7 F1 6 331 310 252 .75 .78 .78 n-C7H1s-C,F1a 323 98 94 0.63 0.66 0.66 107

PAGE 117

TABL.6 XI V T O'l'AL VAPOR PB.ESSURE-TEMPERATUR DATA t ( C.) Pro~ure t < o c.> Pressure t ( C. ) Preg~re m m Sys-Perfluorocyclic Perfluorocyclic Perfluorocyclic t: Qxide-Toluene Qxide-n-Heptane OSide-Metbyl-cyclohexan 37.4 106.9 24.0 67.4 22.4 64.1 42.2 132.9 25.5 73.8 2 .9 83.9 47 2 168.6 29.4 88.6 34.8 116.4 51.0 197.3 32.3 100.8 41.4 154.9 61.8 304.1 34.4 111.9 '8.5 209.9 67.S 393.3 35.6 118.3 55.2 271.8 76.0 513.9 36.5 122.6 a1.a 344.8 80.6 800.1 39.7 143.0 64.4 381.9 86.7 730.6 43.0 165.4 85.4 758.2 ss.o 761.9 45.8 185.6 46.2 187.8 46.9 196.4 SysPerfluorocyclic PerfluoroheptanePerfluoroheptane-tea: OXide-Carbon n-Heptane Carbon Tetra-Tetrachloride chloride 2 7 3 147.S 26.2 1 17.6 27.8 194.8 28.6 157.1 28.8 130.9 so.o 216.1 30.0 167.8 31.5 151.0 32.7 24'2.9 31.3 180.2 33.9 169.1 36.8 287.0 33 .. 0 191.7 34.0 166.8 40.6 336.2 37.2 227.8 36.4 187.0 43.3 373.9 41.5 268.9 36.6 189.0 "6.9 427.2 43.5 290.9 3 8.7 207.4 49.7 469.4 45.0 308.4 41.1 228.9 52.3 517.7 48.2 324.0 44.7 264.2 54.6 562.1 46.2 321.7 46.6 286.1 57.1 613.4' 4 8.4 307.8 63.5 760.0 49.5 320.5 108 \

PAGE 118

co TABLE XV COIIPABISON OF VAN LA.AR ACTIVITIES WITH ACTIVITY RANGE CALCULATED FBOII EQU.ATIOB 15a .. , 10 ,..., ,..., .-4 .-4 .-4 0 CJ u j a J a j II 0 0 0 0 0 0 .... "'4 "'4 ~ .. .... +a .. .. :I i : g. :I i p .. Perfluorocyclic Oxide-Perfluorocyciic Oxid&-Perfluorocyclic Oxide-n-Heptane Toluene lletbycyelobexane 25 0.782-0.880 0.849 40 0.925-0.934 0.892 30 o.sso-o.aea 0.834 30 o.775-0.903 0.827 50 0.916-0.928 0.865 35 0.828-0.886 o.s1a 35 o.769-0.926 0.810 60 0.869-0.885 0.858 40 0.814-0.879 D.786 40 0.763-0.959 0.782 70 0.836-0.857 o.s.22 so 0.111-0.865 D.7M 45 0.761-1.0 0.762 80 o.s1s-o.a,1 0.784 60 0.760-0.916 0,701 Pertluorocyclic OxidePerfluoroheptanePertluoroheptane-Carbon Tetrachloride n-Heptane Carbon Tetrachloride 30 0 .. 666-0.724 0.705 25 0.824-0.862 0.855 30 0.756-0.808 0.760 35 0.652-0.843 0.675 30 0.828-0.875 0.-844 35 o.1as-o.s2& 0.736 40 0.619-0.861 0.643 35 0.827-0.887 0 .. 828 40 0.781-0.834 0.709 45 0. 569-0. 903 0.606 40 0.810-0.883 0.805 45 0.729-0.819 0.684 45 0.793-0.890 0.780 50 0.698-0.811 0.655

PAGE 119

TABLE XVI VOLtJIII OF KIXTURES OF PERFLUOROHEPTANE AND CARBON TETRACHLORIDE; PDFLUOROCYCLIC OXIDE AND CARBON TETRACHLORIDE; PERFLUOROCYCLIC OXIDE AND n-HEPl'ANE; AND PERFLUOROHEPTANE -AND n-HEPl'ANK Kole Fraction Volume of Mixture (cc/mole) Syatea: Perf luoroheptane-Carbon Tetrach_loride Carbon 50 c. 55 c. 60 c. Tetrachloride 1.00 100.22 100.96 101.65 0.950 107.98 108.72 109.51 0.903 115.70 116.60 0.817 129.59 0.701 145.97 0.583 161.26 162.76 0.504 170.73 172.24 173.75 0.377 187. 56 189.23 191.00 0.335 192.89 194.60 196.43 0.236 205.62 207.44 208.98 0.123 219.73 221.67 223.77 0 234.43 236.50 238.74 Syatem: Perfluorocyclic OXide-Carbon Tetrachloride Carbon "o C. 45 c. 50 c. Tetrachloride 1.00 98.97 99.57 100.22 0.969 104.09 104.79 105.48 0.936 109.21 110.12 110.82 110

PAGE 120

TABLE XVI (Continued) VOLUJIE OF MIXTURES OF P LUOROHEPl'ANE AND CARBON TETRACHLORIDE; PERFLUOROCYCLIC OXIDE AND CARBON TET Clll,ORIDE; PERFLUOROCYCLIC OXIDE AND n-B EPl'ANE; AND PERFLUOROHEPl'ANE -AND n-HEF.t'A.~E Kole Fraction Volume of ixture (cc/mole) Carbon 40 c. 45 c. 50o c. Tetrachloride 0.905 114.90 115.72 0.845 125.11 0.768 136.62 0.701 146.80 0.631 157.30 0.553 167.30 168.66 0.469 177.96 179.36 181.13 0.397 188.19 189.66 191.18 0.329 197.54 199.09 200.70 0.253 208.07 209.68 211.37 0.161 220.36 222.07 223.85 0.087 230.15 231.92 233.77 0 241.30 243.18 245.08 System: Perfluorocyclic Oxide-_!-Heptane n-Heptane 40 c 45 c. 50 c. -1.00 150.15 151.14 152.14 0.972 153.40 154.43 155.48 111

PAGE 121

TABLE XVI (Continued) VOLUIIB OF MIXTURES OF PERFLUOROHIPTANE AND CARBON TBTU.CBLORIDE; PBRFLUOBOCYCLIC OXIDE AND CARBON TETRACHLORIDE; PEllFLUOROCYCLIC OXIDE AND nHEPTANE; AND PBRFLUOROHEPTANE -AND n-HEPTANE Jlole Fraction Voluae of llixture (cc/mole) _!Heptane 40 c. 45 c. 50 c. 0.943 156. 7 9 157.84 158.94 0.925 158.89 160.00 161.14 0.898 162.06 163.22 164.40 0.867 165.28 166.50 167.74 0.825 170.88 1 72.20 0.801 175.72 177.11 0.706 184.33 0.596 195.16 0.502 204.09 0.418 210.10 211.91 0.349 214.34 216.12 217.96 0.287 219.53 221.32 233.16 0.213 225.93 227.31 229.61 0.146 230.95 232.77 234.68 0.07 3 236.23 238.09 240.00 0 241.27 2'3.12 245.04 112

PAGE 122

TABLE XVI (Continued) VOLUIIE OF MIXTURES OF PDFLUOROHEPTANE AND CARBON TETRACHLORIDE; PERFLUOROCYCLIC OXIDE AND CARBON TETRACHLORIDE; PERFLUOROCYCLIC OXIDE AND n-HEPl'ANE; AND PERFLUOBOHEPl'ANB -AND n-HEPTANE Mole Fraction VolUlle of Mixture (cc/nole) S:,stem: Per:fluoroheptane-.!!,-Heptane !,-Heptane 1.0 0.942 o.9oo 0.803 0.799 0.715 0.614 o.579 0.500 0.393 0.299 0.227 0.147 0.092 0 40 c. 150.29 211.37 216.48 221.69 225.90 230.29 113 45 c. 151.27 157.72 162.73 213.25 218.36 223.63 227.84 232.28 50 c. 152.30 158.83 163.92 172.67 173.24 180.61 189.58 192.68 198.93 208.19 215.20 220.31 225.62 229.88 234.30

PAGE 123

Xl 0.087 0.161 0.253 0.329 0.397 0.469 0,553 0.631 0.701 0.768 0.845 0.905 0.936 0.96 9 T A BL E XVII TOT.AL YOLUJIB CBAJl'GB A1ID PARTIAL IIOLA.L YOLUD CIIAMGB O N M IXI N G 6V11 xl OV1 ov2 cc/aole cc/mole ee/aole Systea: c 8 F160-cc14 at so0 c. Subscript 1 refers to CC14 1.23 o.o 14.1 o.o 2.05 0.1 12.0 0,19 2.87 0.2 9.67 0.62 3.31 0.3 7.17 1.46 3.55 0.4 5.58 2.27 3.96 o.s 3.99 3.52 3.75 0.6 2.65 5.22 3.55 0.7 1.62 7.04 3.21 o.a 1.17 8.81 2.75 0.9 0.22 15.0 2.72 1.0 o.o 20.0 1.77 1.27 0.77 114

PAGE 124

xl 0.092 0.147 0.227 0.299 0.393 0.500 0.579 0.614 0.7lfi 0.800 Q.803 0.900 0.942 TABLE XVI I (Continued) TOTAL VOLUME C G AND PARTIAL MOLAL VOLU)fE CHANGE H M IXI N G l\.VM Xl AV1 AV2 cc/mole cc/mole cc/mole System: C7F16~7H16 at 50 Subscript 1 refers to _!!-C7H16 3.12 o.o 29.4 0 3.37 0.1 22.4 0.31 4.62 0.2 15.2 1.54 5.42 0.3 10.7 2.96 5.97 0.4 7 .20 4.81 5.63 0.5 5.51 5.93 5.69 0.6 4.,2 7.43 5.63 0.7 3.12 10.0 ,.94 o.s 2.19 13.2 ,.54 0.9 0.83 20.6 ,.06 1.0 0 32. 7 3.42 1.77 115

PAGE 125

xl 0.073 0.146 0.213 0.287 0.349 0.418 0.502 0.596 0.706 0.825 0.867 0.898 0.925 0.943 0.972 TABLK XVII (Continued) TOTAL VOLUD CBABGB A1ID PARTIAL IIOLAL VOLUO: CBAKGB OR MIXIRG ov Xl l\Vl ~V2 cc/aole cc/aole Systea: C8Fl60-!,-C7Hl6 at 500 C. Subscript 1 refers to _!-C 7 H16 1.78 o.o 28.1 o.o 3.17 0.1 20.9 0.26 4.35 0.2 15.1 1.16 4.80 0.3 9.64 2.95 5.30 0.4 7.66 4.34 5.70 0.5 5.74 5.74 5.68 0.6 3.94 7.94 5.53 0.7 2.78 10.3 4.91 0.8 1.70 14.0 3.84 0.9 0.46 22.1 3.25 1.0 o.o 29.0 2.80 2.00 1.53 0.77 111

PAGE 126

i I xl 0.123 0.236 0.335 0.37 7 0.504 0.583 0.701 0.815 0.903 0.950 TABLB XVII (Continued) TOTAL VOLUD CIWl'QE AKI> PARTIAL MOLAL VOLUIIB CHANGI ON KIXINO 6V11 Xl 6V1 lli2 cc/mole cc/mole System: c 7 r16-cc14 at 60 C. Subscript l refers to CC14 1.84 o.o 15.5 o.o 2.65 0.1 12., 0.18 3.66 0.2 10.7 0.49 3.93 0.3 8.23 1.34 4.05 0.4 6.05 2.52 3 .90 0.5 3.86 4.24 3.36 0.6 1.98 5.74 2.52 0.1 1.63 7.55 1.62 o.8 0.83 10.1 0.94 0.9 0.21 14.4 1.0 o.o 18.S 117

PAGE 127

TABLE XVIII CALIBRATION DATA FOR ANALYSIS OF SYST S: C7P1 6-Cs F1aOCCl4; C,F15-CgF150-_-C-1 16; AND C 6 B5CH3-C6 11 CH3-C7F15COOCffs Peak. Height Fraction CsF160 0.829 0.77 4 0.450 0.718 0.922 0.170 0.115 0.07 8 0.046 Peak Height Fraction C5F160 0.861 0.074 0.029 0.048 0.778 0.319 0.154 System: C,F16-CsF160-CCl4 Partitioning Liquid: Kel-F Acid Ester Cl(CJ'2Cl'Cl)3CF2COOC2B5 Heliua Plow: 30 cc/min. ColWJn Temperature: so C. Weight Fraction C9F1eO 0.840 0.775 0."38 0.702 0.918 0.161 0.119 0.077 0.044 Peak Height Fraction C8!'1 6 0 0.634 0.846 0.404 0.242 0.124 0.637 0.403 0.236 Weight Fraction CsF1eO 0.760 0.910 0.527 0.338 0.179 0.760 0.527 0.338 Systea: c7 F16-c8 F16o-n-c7e16 Partitioning Liquid: kel-'J Acta Ester Cl(CF2CFCl)3CF2COOC3B5 Beliua Flow: 30 cc/min. Col1111n Tellperature: 800 C. 0.933 0.134 0.060 0.084 0.883 0.467 0.243 118

PAGE 128

TA L B XVIII (Continued) CALIBRATION DATA FOR ALYSI 0 SYST S: C 7 F1 6 CsF1sOCCl4; C,F1 ~ c F150-_-C 7 1 ; A N D CsH5 C H3-C5B11C H3-~F15COOCH3 S ystem: C 6H 5CH3-<;; H11CH 3-C7 F15COOCH3 Partit o 1 g Liquid: S i l i c o DC 5 50 and Stearic Acid on Celite Peak Height c .,, F15COOCH3 0.752 0.404 0.152 0.326 0.440 0.328 0.578 0.362 0.575 0 7 ':; 6 '1.423 0.185 0.676 0.286 0.545 0.350 0.257 0.6 8 Kitrogen Flow: 3 0 cc/min. Column Te perature: 95 C. Weight Fraction Cr,F15COOCH 3 0.886 0.466 0.132 0.361 0.522 0.36 1 0.712 0.224 0.712 0.886 0.466 0.132 0.783 0 .. 2 9 0.636 0.361 0.22, 0.7 8 3 119 Binary Syste m c6u5cH3-c6 u 1 1 c n 3 Peak Right Weight Fraction C6H11Cii3 CsH11C H 3 0.660 0.537 0.926 0.781 0.635 0.7 2 7 0.935 0 49 3 0.795 0.49 2 0.6 5 5 0.590 0.929 0 3 6 3 0.47 0 0.424 0.110 0.792 0.362 0.6 0 0.5 2-8 0.938 0.790 0.618 0.7 0 3 0.939 0.3 44 0.807 o. 4 4 0.630 0 5 2 8 0.938 0.282 0.396 o. 3 4 0.703 0.807 0.282

PAGE 129

TABLE XIX TIE LINE DATA Top Phase Bottom Phase "l W2 W3 wl w2 w3 Sys tem C,F16-c8 F 16o-c7u16 at so0 c. 0.245 o .755 0 .930 --0.010 -0 .297 0.703 o.e2s 0.075 0.179 0.142 0.679 0.530 0.395 0.01s 0.200 0.119 0.68 1 o 593 o.333 0.074 0.236 o .oso 0 683 0 700 0 .221 0.073 0.262 0 .046 0 .692 0.784 0 .140 0.076 0.043 0 .280 0 6 77 0.146 0.77 5 0.079 0.096 0 220 0 .684 0 .304 0.619 0.077 0.176 0.142 0 .682 o.528 0.400 0.072 Syste C,F16-CsF160-CCl4 a t 30 c --0 12 8 0.872 --0 777 0.223 0.084 -0 .916 o 0 0 --0.200 0.084 -0 .916 0 .836 -0.164 0.008 0.11 8 0.87 4 0 .056 0 724 0 220 0.01s 0.10 6 0.87 6 0.12 8 0.655 0 .217 0.025 0.100 0 .875 0.18 2 0 615 0 203 0.05 7 0 078 0 864 0 276 0.514 0.210 0.031 0.07 6 0 .893 0.276 0.514 0.210 0.047 0.062 0.891 0 389 0.414 0.19 7 0.082 0.018 o.90o 0.698 0.123 0.180 0.053 0.025 0.922 0 5 7 5 0,.232 0 4 193 0.074 0.032 o.894 0.586 0.231 0.183 0.058 0.045 0.897 0.477 0.336 0 .187 0.058 0.045 0.897 0 .472 0 .321 0 20 6 0.091 0.010 0.900 0 .769 0.073 0.15 7 0.091 0.010 0.900 0.7 53 0.07 1 0.180 0.088 0.018 0.893 0 .710 0.132 0.159 0.088 0.018 0.893 0 .100 0.131 0.170 0 0 7 7 0 .024 0.900 0.645 0.175 0.182 0.077 0.024 0.900 0.648 0.182 0.168 120

PAGE 130

""1 0 .025 0 .052 0.081 0.106 0 .146 0 .115 -0 .286 0 371 0 .401 0 .415 0 .242 0.131 0 .242 0 .402 0 .308 Top Phase W2 TABLE X I X (Continued ) TIE LINE D A T A "3 wl Bottom Phase "2 System CaH5CH3-C6H11CH3-C,F15COOCH3 at 25 c 0 .782 0 .218 -0 .096 0 .727 0 .248 0 .005 0.111 0.685 0 26 3 0 .010 0.116 0 619 0 300 0 .019 0 .118 0 551 0 .343 0 .031 0 1 3 1 0 427 0 427 0 0 6 0 0.162 0 23 7 0 .648 0 .115 0 237 System CaH5CH3-Cti811CHs -C1F15COOC83 at 10 c o .950 0 .050 --0 .055 0 .534 0 .180 0 .05 0 .077 8 .346 0 283 0 .128 0 .092 0 .235 0 .364 0 .196 0 .094 0 23 3 0 .352 0 .192 0 .091 0 .606 0 .152 0 .024 0 076 0 755 0 .112 0 .017 0 077 0 596 0.162 0 .040 0 0 8 2 0 218 0 3 7 4 0 266 0 .101 0.114 0.578 0.308 0 .114 121 "'a 0 .904 0 .883 0 .875 0 .864 0 .838 0 .778 0 .648 0 .945 0 870 0 .780 0 710 0 7 1 7 0 .900 0 .906 0 .878 0 .673 0 .578

PAGE 131

a1 0.68 0 .10 0 -.. 74 0 .72 0.,73 0 1 1 0 7 1 0 .34 0 .33 0 .33 0.34 0 .35 0 .35 0 .33 Note: TABLE ll ACTIVITIE S CALCULATED FROK EQUATION 59 ds Eva luated from Pure Com unds a 1 a2 2' &3 a3 a 1 System: C7F16-CsF1aO-CCl4 at .96 0 .23 .54 0 .QS .16 .97 .96 .95 0 .16 .38 0 .15 3 1 .97 .96 .95 o .o5 .12 0 2 6 .54 .97 .99 .95 0 0 7 1 7 0 .24 .50 .97 .96 .96 0 .10 .25 0 .20 .42 .97 .98 .96 0.14 .35 0 .16 .33 .97 .97 .96 0 1 7 .42 0 .11 .26 .97 I .98 System : C7F16CsF100-!_-C7H16 .90 0 .10 0 .46 0 .07 3 1 .94 .95 .90 .12 0 .51 0 .06 .26 .94 0 .94 .90 0 .l4 .60 O Q4 .18 .94 9 5 .90 0 .15 .67 0 .02 .11 .94 0 .96 .90 .03 .13 O .l5 6 2 .94 ~ -97 .. 90 0 .06 .27 0.11 .49 .94 .96 .90 0 .10 .46 0 0.7 .32 .94 0 .95 Subscript 2 refers to C 7 F 1 6 Subscript 3 refers to CaF1aO 122 30 c 58 57 41 .40 .13 .13 .17 .18 .24, .27 .35 .37 .43 .45 at 30 c 55 .50 .61 .55 .72 .64 8 1 .71 .14 .14 .31. .29 .55, .50 ~ 1 from s .39 0 .33 .33 0 .28 .22 0 .19 .12 0 .12 .79 0 .68 .63 0 .53 .39 0 .34

PAGE 132

TABLB XXI ACTIVITIES CALCULATED FROII ~UATIOlf 61 0.63 0.44 0.14 0,19 0.26 0.37 0 .48 0.54 0.61 0 .72 0,79 0,13 0.30 0.54 a 1 o 5 7 0 41 0 .13 0 1 8 0 2 7 0 .37 0 .45 0.49 0.55 0.64 0.72 0.14 0.29 0.49 0 .97 0.97 0.97 0.96 0.97 0.91 0.97 0.94 0,94 0 .94 o.94 0.94 0.94 0.94 a 2 o .98 0.98 0.99 0.9 0.99 o .99 1 .00 0 9 5 0.96 0 .95 0.95 0 .95 0.95 o.9 5 Note: Subscript 1 refers to C7F16 Subscript 3 refers to c8 F16o 123 0.17 0.33 0.56 0.52 0.43 0.35 0.26 0.37 0.32 0.21 0.12 0.7 4 0.58 0.37 a 3 0.17 0.32 0.57 0.52 0.44 0.35 0.27 0.34 0.29 0.19 0.12 0.69 0.54 0.35

PAGE 133

TABLE :UII CHARACTDISTICS OF CffBOU.TOGRAPBY COLUIINS USED IR BXTUCTIVB DISTILLATIOB STUDIBS 505-112 el-P Oil l 505-136 el-P Oil 3 505-137 el-F Oil 10 505-135 rfluoro17 ma at 100 c. 1 at 100 c. 0.1 at 100 c. Boilin1 Point 170-2300 c. TABLK DIII 9 8 5 22 APPUUKCJ: TIU OP CiPl6' C9P160, !,~Hl6 ilD Ct;H11CIJaIB THE YABIOUS P.DTITIOJfilfG LIQUIDS Partitioning t carrier Gas Appearance Tille (llin.) Liquid 0 C. Flow Bate cc/ain. ~Fl6 I ~aF1a0 ~-C,816 r:aB11CJla KelF Oil 1 35 60 11.5 29.9 37.8 42.5 Kel-F Oil 3 35 60 12.3 32.3 -Kel-F Oil 3 80 25 7.08 14.8 22.7 27.6 Jtel-:r Oil 10 35 57 6.75 18.3 26.5 29.5 1'.el-F 011 10 80 25 5.08 10.9 16.8 20.2 Perfluoro3 5 3 0 18.7 48.2 --kerosene 124

PAGE 134

TABLB XXIV UL&TIVE VOLATILITY o:r THE C,F16-Cal'1sO-SOL'YDT AlfD .!!,-C,B16-C5H11 CBa-SOLV:IRT SYSTBIIS Solvent t O c. Relative Volitility C7F 1 6-CsF u,0 .!!,-C7H16-C6H11C8:J Jlo 35 2.34 1.003 solvent 80 1.96 1.057 Kel F 0111 35 2.60 1.12 JCel P 0113 35 2.62 -80 2.12 1.22 Itel F 35 2.10 1.11 Oil 10 80 2.20 1.21 Pertluoro35 2.58 -kerosene TABLB XXV ACTIVITY COEl'FICIDT RATIOS B&SBD ON AVERAGE am..ATIVB VOLATILITY FOR ALL SOLVBNTS System t O c. P10/P20 r11 r2 C,F16-c8:r16o-Solvent 35 2.34 1.11 80 1.96 1.10 .!!,-C7H1s-cH3C;B11~lvent 35 1.003 1.11 80 1.057 1.1, 125

PAGE 135

TABLE XX'fI PROPDTIBS o:r PUll COIIPOmmB FOR USE Ilf IQUATI01' 64' Coapound t, O c. 0 1/2 (cal./cc) V (cc/aole) 35 5.93a 228 80 5.41a 248d 35 a.osa 2-&0c 80 s.s2a 2598 35 7.31b 149f 80 6.10b 159f 35 7.70b 130f 80 7.20b 137f 8Determined froa vapor pressure and density data ot this work. work. bT. K. Reed private communication. cTbis "ork. d Bztrapolated frODl density teaperature data of this e Kinnesota Kining and llaDufacturing Coapany data. f Reference 1. 126

PAGE 136

TABLE XDII DATA FOR USB IH BQUATIOHS 37, 40, ARD 46 Partial molal volumes: Table XVII Coefficient of Tberaal Bspansion, oJ... : Figures 32-35 Excess free energy of mixing, AF8: Figures 17-19 and from Van Laar equation using constants frOlll Figure 9 Voluae change on a izing, A'f: F igures 2 3-26 ,, s:I ::, 8. ~Fl6 C7P16 C71'16 n-C,Hl6 I-cs81s CCl4 I>. ~. s:I Iii-a ... ...~ ., O..t !o ~., ....... ~... G a &s:ai G) ., ... ..., &; .a 11, ... 0 .. o, Ns:I ~" :s ... .... '" CD~ IB raQ +J,-f s:I..., ... j OU
PAGE 137

... ti,) GD TABLE XXVIII DATA USED IR BSTABLISBIHG BIIPI&ICAL CORREieA"t'IOH FOR UCBSS l'UB BMDGY Syatea Type of Data Telllpera-Kin []. ture Equations o K. 50 and 51 C7F16 .. ,!-C9B18 Free Bnergy 303 1.00 3.95 C7P163..C8a~H15 Solubility 343 7.67 5.31 C7F16-.!!,-C8 81s Solubility 341 6.50 5.86 C7F16.!!,-~B1& Solubility 328 7.02 5.63 ~P1e-.!!,-CSB14 Solubility 302 8.18 4.94 C7P1s-3-CB3C5B11 Solubility 292 8.12 4.32 C7F15-2,2(CB3)2C4B9 Solubility 273 6.20 4.34 C7P1&-2,3(CB3)~4Ba Solubility 283 6.35 4.87 CsP1r.!-C5H14 Solubility 288 7.45 5.82 CsJ'12-2-clf3CsB11 Solubility 273 7.24 4.15 C5"1~BaC51f11 Solubility 278 7.34 3.63 CsP12-2,2(Clf3)2C4Bs Solubility 257 6.92 3.35 CsJ'12-2,3(Cll3)2C4Ba Solubility 269 7.18 3.H C5"1rn.,.c51112 Pree Energy 266 7.51 4.43 C4F10-.!!,-C4B10 Pree Bnerg7 246 7.72 5.44 [] = d'l 02)2 2 d'l cf 2(1 flfD~ Z(l03 ) Reference 2.M 26 1.28 27 0.32 9 0.76 Thia work 2.18 10 3.01 10 1.57 10 1.06 10 0.97 7 2.71 7 3.67 7 4.12 7 3.05 7 2.63 39 1.70 40

PAGE 138

... N q) LOG P 3.0 ....--------.-----.----r-----.----,----, 2 5 2 0 I-C1F1 6 1.5 II C7F15H ill-C8F160 IS[ -C7 F15COOCH3 (C4F9)3N I m TI[ I. 0 .....__ __ __,__ ___ ___ ...___ __ __._ ___ __.._ __ ___. 2 2 2.4 2.6 2.8 3 0 3 2 3.4 1000/T FIGURE I. VAPOR PRESSURE DATA FOR FLUOROCARBONS 1

PAGE 139

STEEL TUBING I I GASKET THERMOCOUPLE FLANGES GLASS TUBE I I '-. / I I FIGURE 2 SOLUBILITY CELL 130

PAGE 140

... w ... T (C) 60r-----i---.---.-----.--.---r--.----.---.----. 50 4 0 3 0 20 o C 7 F16-CCl4 THIS WORK C7F16-CCl4 REF. 17 D C7F16-C~16 THIS WORK C1F,6-C7H16 REF. 17 IO 0.5 1.0 MOLE FRACTIO N OF HYDROC A R BON FIGURE 3 BINARY SOLUBILITY CURVES SYSTEMS CONTAINING C1F1s

PAGE 141

120 ~ ------.----~-~----.-------, 100 80 60 40 20 0 ETHANOL C A RBON TETRACHLORIDE 50 MOLE PERCENT OF HYDROCARBON FIGURE 4 BINARY SOLUBILITY CURVES SYSTEMS CONTAINING C8 F16 0 132 100

PAGE 142

i I 140 120 80 T(C) 60 40 20 0 TOLUENE 0 5 MOLE FRACTION OF HYDROCARBON FIGURE 5. BINARY SOLUBILITY CURVES SYSTEMS CONTAINING (C4 F9)3 N 133 1.0

PAGE 143

.... w .. T{C) 501------.-------.-----,---~ 40 30 20 10 0 METHYLCYCLOHEXANE 0.5 Q ~e-T_QLUENE / / "' I \ MOLE FRACTION OF HYDROCARBON FIGURE 6. BINARY SOLUBILITY CURVES SYSTEMS CONTAINING C1F1~00CH3 1.0 1 I I

PAGE 144

6 0---------y-------r------.------, 50 METHYLCYCLOHEXANE 40 30 20 10 0 0.5 MOLE FRACTION OF HYDROCARBON FIGURE 7 BINARY SOLUBILITY CURVES SYSTEMS CONTAINI N G C7F15H 135 1.0

PAGE 145

1.0 0.5 0 Tc 0.5 x,-FIGURE 8. ACTIVITY ISOTHERMS 136 1.0

PAGE 146

GROUND GLASS JOINT LIQUID LEVELS \ 0 CONDENSER THERMOCOUPLE WELL HEATERS FIGURE 9 TWO LIQUID PHASE STlLL 137

PAGE 147

Cf) z Cf) z 0 (.) a:: <( <( _J z <( > / 5.0 o C7F1s-C1H1s o C7F16-CCl4 4.0 6. C8F160-CCl4 'v C8F160-C7H16 1.0 20 30 40 50 T (C) FIGURE 10. VAN LAAR CONSTANTS VERSUS TEMPERATURE 138 B A 60

PAGE 148

LOG 1T 2.4r------r----,----~----2.2 2.0 1.8 o OBSERVED a CALCULATED BY EQUATIONS 13, 14 a 15 l.6---~--~---~--3.0 3.1 3.2 1000/T 3.3 3.4 FIGURE 11. TOTAL VAPOR PRESSURE PLOT SYSTEM: PERFLUOROCYCLIC OXIDEN-HEPTANE 139

PAGE 149

3 Q r-----,-----,---------r------.----.---, 2 8 2 6 LOG TT 2.4 2.2 2.0 o OBSERVED 0 o CALCULATED BY EQUATIONS 13, 14 a 15 2 8 2.9 3 0 3.1 3.2 1000/T FIGURE 12. TOTAL VAPOR PRESSURE PLOT SYSTEM: PERFLUOROCYCLIC OXIDE TOLUENE 140

PAGE 150

2 .6~--.-----.------,---~-----, 2.4 2 2 LOG TT 2 0 0 o OBSERVED a CALCULATED BY EQUATIONS 13, 14 8 15 1.8'------'---------'----------'~------'----~ 3.0 3.1 3 2 3 3 3.4 1000/ T FIGURE 13. TOTAL VAPOR PRESSURE PLOT SYSTEM: PERFLUOROCYCLIC OXIDEMETHYLCYCLOHEXANE 1 4 1

PAGE 151

2 .6-~---....-----~----, 2.4 LOG TT 2 2 o OBSERVED D CALCULATED BY EQUATIONS 13, 14 S 15 2.0..______.__ ___ ....____ __ ____.___ __ 3.1 3.2 3.3 3.4 1000/T FIGURE 14. TOTAL VAPOR PRESSURE PLOT SYSTEM: PERFLUOROCYCLIC OXIDE -CARBON TETRACHLORIDE

PAGE 152

2,8,---..,~--r-----r-----r------, 2.6 LOG 1T a 2.4 o OBSERVED o CALCULATED BY EQUATIONS 13, 14 8 15 2.2~ _ __._ ___ .....__ _ __._ _, 3.0 3.1 3.2 3.3 1000/T FIGURE 15. TOTAL VAPOR PRESSURE PLOT SYSTEM: PERFLUOROHEPTANE CARBON TETRACHLORIDE 1 4 3

PAGE 153

LOG1T 2 Gt------r----,-----___,----, 2.4 2 2 o OBS E R VED o CALCULATED BY EQUATIONS 13, 14 815 2 .0 ~ --'-----L--------L--_____;_-----1 3 1 3.2 3.3 3.4 1000/T FIGURE 16. TOTAL VAPOR PRESSURE PLOT SYSTEM: PERFLUOROHEPTANE -N-HEPTANE 1 4 4

PAGE 154

2.5 VAN LAAR EQU ATION FROM SOLUBILITY DATA D EXPERIMENTAL DATA R EF 39 2 0 o RT I n t, = 7.69 V1 cp~ } REF 39 RT In ~2 =7.69 V 2 cp2 I 2 LIQUID D PHASES 1.5 0 D \r, 0 0 1.0 a 0.5 0 0 D 0 0 5 MOLE FRACTION C5H12 FIGURE 17. ACTIVITY COEFFICIENTS SYSTEM: C5 H12 -C 5 F12 T= 262.4 K 141 1.0

PAGE 155

400.------r------r-----r-------, o CALCULATED BY VAN LAAR EQUATION o EXPERIMENTAL DATA REF. 39 300 6 CALCULATED BY EQUATION 28 w ....J 0 ":-200 ....J <{ u -QJ LL
PAGE 156

400r------.-----.-----~----, o EXPERIMENTAL DATA REF. 40 300 o CALCULATED BY VAN LAAR EQUATION 6. CALCULATED BY EQ U ATION 28 w ...J 0 200 ...J <( u 100
PAGE 157

400.------,------r---,-----, o EXPERIMENTAL DATA REF. 26 o CALCULATED BY VAN LAAR EQUATION fl CALCULATED B Y EQUATION 28 300 0 -w _J 0 200 '>-'
PAGE 158

2 LIQ UID PHASE REGION t / / / / C / ,, / \J ......__ / '----.1 / / ' r(j / -------/ ---0 1.0 FIGURE 21. VAN LAAR ACT I VITY COEFFICIENTS

PAGE 159

I .c 2 LIQUID PHASE REGION AT T1 2 LIQUID PHASE REGION AT T2 X -FIGURE 22. VAN LAAR ACTIVITY COEFFICIENTS TEMPERATURE DEPENDENCE 150

PAGE 160

WATER LEVEL HEATING WIRE GROUND GLASS JOINT -CAPILLARY TUBING TRANSFER TUBE SUCTION t PYCNOMETER FIGURE 23. PYCNOMETER FILLING ARRANGEMENT 151

PAGE 161

5 4 3 --u u ~2 >
PAGE 162

' -I -------------------6.0 0 0 0 5.0 0 4 0 0 -8 3.0 0 -E >
PAGE 163

5.0 4 0 G 3.0 u -E 2.0 1.0 0 0 0.5 MOLE FRACTION CCl4 FIGURE 26. VOLUME CHANGE ON MIXING SYSTEM: C7F16-CCl4 AT 60C. 154 1.0

PAGE 164

6.0 5.0 4.0 c33.0 u >2.0
PAGE 165

\ \ 25 I I \ 20 15 -10 u u I>
PAGE 166

20,---------,-----y 15 10 0 0 0.5 MOLE FRACTION CCl4 FIGURE 29. PARTIAL MOLAL VOLUME CHANGE SYSTEM: CaF,EP -CCl4 AT 50C. 157 1.0

PAGE 167

-----------------------20r-------,------,-------r------, 15 _10 u u t>
PAGE 168

-(...) (...) -30 20 10 0 0.5 MOLE FRACTION NC7H1s FIGURE 31. PARTIAL MOLAL VOLUME CHANGE SYSTEM: C1F16-NC1H16 AT 50C 1 1.0

PAGE 169

I I I 35~, ----,-----,------.-------. i 30L C) \ 25 20 15 u i 1> IQ <] 5 0 0 C1F,s -NC7H1s AT 50C. C] Ce F1sO-NC7 H,s AT 50C. \ I 0.5 MOLE FRACTION C7H1s FIG URE 3 2 PARTIAL MOLAL V O L UME CHANGE 160 1.0

PAGE 170

-IQ 0 '6 -If) 0 c$ 2.0------.----------r-----r------, 0 0 1.5 o<0 EQUATION 19 o EXPERIMENTAL 1.0 0 0.5 1.0 2 0 1.8 1.6 1.4 1.2 MOLE FRACTION CCl4 FIGURE 33. THERMAL COEFFICIENT OF EXPANSION SYSTEM: C 7 F16-CCl4 --------......_ .....__ ......... -..... O\o EQUATION o EXPERIMENTAL 0 0.5 1.0 MOLE FRACTION NC7H1s FIGURE 3 4 THERMAL COEFFICIENT OF EXPANSION SYSTEM: C 7F,s-NC7 H,s l 1

PAGE 171

1.s ~----~----o o EXPERIMENTAL 1.2 ..__ 0 0 5 MOLE FRACTION CCl4 ---FIGURE 35. THERMAL COEFFICIENT OF EXPANSION SYSTEM: C8Fu;O-CCl4 1.0 1,9.-------.,....-------.--------r-------, 1 .8 1.7 ----/ / \ / \ \ \ \ '; 1.5o
PAGE 172

5.o..------~--------,--------;~------, 4.0 3.0 <32.0 u E >
PAGE 173

EXPERIMENTAL I 7.0r o EQU ATION 27 I 6.0 5.0 4.0 3.0 -(.) (.) E> 2.0
PAGE 174

70 6.0 5.0 4.0 3.0 u u ---DATA OF MUELLER 8 LEWIS (26) Cl EQUATION 27 o EQUATION 32 V EQUATION 31 0 0 0 f. >2. 0
PAGE 175

1.0 ,--.------r------r----------,------,) '?o lL CD (.) z 0 (.)
PAGE 176

1.0....-----,,-------.-----~----9o l-' u..-a) u I STATIO N ARY PHA SE: KEL-F ACID ESTER Cl(CF 2 CFCI )3 CF 2 COOC2 H~ HELI U M FLOW : 30 CC/MIN COLUMN TEMPERATUE: 80 C. r I u c::i: 0 51 0: u.. r I w I
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0(0 I.L..-CD (.) z 0 t-10,--------,-----~-------.------, STATIONARY PHASE = KELF ACID ESTER Cl(CF2 CFClhCF2COOC2 H5 HELIUM FLOW: 30 CC/MIN. COLUMN TEMPERATURE: 80C. 0 5 er. LL.. rI (!) w I
PAGE 178

fC') I u I U> u z 0 1-1.0.----------r------.------""T""---------,, ~0.5 a:: LL. I I (.!) w :c
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1.0.-------~-----.----~---rf') I 0 0 0 u.-r--0 z 0 ..... ~0. 5 a::: u.. ..... I <.!) w :I: :::.::
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... -.J ... FIGURE 45 PHASE DIAGRAM SYSTEM C7F16-C8 ~ 6O-CCl4 AT 30C NOTE": COMPOSITIONS ARE IN WEIGHT FRACTIONS 40\ 0 --------~ -------,~ I ~--,--CONJUGATE CURVE 40 60

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N FIGURE 46 PHASE DIAGRAM SYSTEM: C7Fi6-C8Fi60-NC7H16 AT 30C. NOTE: COMPOSITIONS ARE I N WEIGHT FRACTIONS I CONJUGATE CURVE CaF1sO / L v v v ---1 v ~C1H,s 0 20 40 60 80 100

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.... C4 ,_ ----:9' -FIGURE 47 / ~6H5CH3 PHASE DIAGRAM SYSTEM: C6H~CH3-C6H11CH3 -~Fj5COOCH3 AT 25C. NOTE: COMPOSITIONS ARE IN WEIGHT FRACTIONS 60 CONJUGATE CURVEl PLAIT POINT C6H11CH3 C7F,~COOC H3 0 20 40 60 eo 100

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... -l -------FIGURE 48 PHASE DIAGRAM SYSTEM : C6H5CH3-C6H11CH3 C,Fj5COOCH3 AT 10 C. NOTE: COMPOSITIONS ARE IN WEIGHT FRACTIONS 0 20 .,., PLAIT PO INT 40 60 80 100

PAGE 184

--------------------~ ~ 8 0 0--------,,-----.-,-----.-,-----, 6 6. 6 0 0 -6 6 -D (] 6 D 0 -0 0 w 0 0 6400 6. 0 8 :E D 0 ..J 6
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I I I 600 I I I e 0 6 a 0 D w 0 6. 5400 ._ 6. D D 0 0 ....J A 6 ~' u 0 D ......,. I200 -
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I I I -EXPERIMENTAL DATA REF 26 800 o EQUATION 37 6 EQUATION 46 o EQUATION 40 .6. 6 600 0 D D W4QQ ...J 0 0 I:::. 0 _J 0
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600---------.-------.------.------~ j400 0 .....J <1 u ;;200 <1 0 X X >( X g B g ~ 0 >< EXPERIMENTAL DATA REF. 40 o EQUATION 37 o Q U A TION 40 0 --~---~----0. 5 MOLE FRACTION C4H10 FIGURE 52. HEAT OF M IXING SYSTEM: C4F,o-C4H10 178 1.0

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600.------------~----,---w _.J 400 0 _.J
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I I I 600r-------.------r------.-------, w ...J 0400 ........ ...J
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i I I I 0 4.0 0 \ \ 3.0 ~ \ 0 \ 0 \ -2 0 If) 0 --0 N 0 I 1.0 0 I o~ __._ _ ___.__ __ _.__ __ .l-.-_----J 20 3 0 4.0 5 0 6 0 [ ( cf 1 cf2 ) 2 -t-2 cf. d;_ ( I fr f O 7 0 FIGURE 55. FREE ENERGY COR REL A TION FOR FLUOROCARBONS AND PAR AFFIN HYDROCARBONS 181

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400 w300 _J 0 ........ ....J t3 200 -(lJ Q. en
PAGE 192

I I I BD'BURCBS 1. American Petroleua Institute, Research Project 44, "Selected Values of Properties of Hydrocarbons," Bational Bureau ot Standards, Washington, D. c. (1950). 2. Bedford, D. and Dunlap, a. Article to be published in J. All. Chea. Soc. (1958). 3. Bridpan, P. w., Ja. Acad. Arts Sci., Yol. 67, Bo. 1 (1932). 4. Bromiley, I. c., and Quiggle, D., Ind. Bng. Chem., 25, 1136 (1933). s. Cady, G. H., J. All. Ch811. Soc., 78, 5216 (1956). 6. Carlaon, H. C., and Colburn, A. P., Ind. Eng. Chea., 3-t, 581 (1942). 7. Dunlap, B., Digman, B., and Vreeland, J., Abstracts 0 Papers; 124th Meeting Alllericaa Chical Society, Chtcaao, Septeaber 1953. 8. Fenske, M. B., Ind. Eng. Chem., 24, 482 (1932). 9. Hickman, J.B., J. Am. Chea. Soc., 75, 2879 (1953). 10. Hickman, J.B., J .Am. Chea. Soc., 77, 6154 (1955). 11. Hildebrand, J. H., and Scott, B. L., ''Solubility of lfonelectrolytea," 3rd ed., Reinhold Publishing Corporation, Bew York, B. Y., p. 123. 12. Ibid. p. 131 13. Ibid. p. 138. 14. Ibid. p. 139. 15. Ibid. p. 200. 16. Ibid. p. 436. 183

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17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 2 7 28. 29. 30. 31. 32. 33. ]84 Hildebrand, J. H., Fisher, B. B., and Benezi, H. A., J. Aa. Chem. Soc., 72, 4 348 (1950) Hildebrand, J. H., Cbeaical Engineerinf Pror.es SymposiUJ1, Series, lo. 3, vol. 48 l952. Hildebrand, J. H., and Cochran, D. a. F., J. Am. Chem.. Soc., 71, 22 (1949). -Hildebrand, J. H., J. Chem. Phys.,~. 1060 (1954). Honig, a. E., J. Chea. Phys.,!!., 105 (1948). Lipkin, 11. a., Ind. Eng. Chea., Anal. Ed.,_!!, 55 (1944). llair, B. J., Anal. Chem., 28, 53 (1946). llarshall, w. a. "Liquid-Vapor Bqu.111bria in Fluoro carbon Systems," Ph.D. Thesis, University of Washington (1954). llcLa.ughlin, B. P., and Scott, a. L., J. Phys. Chea., 60, 674 (1956). heller, c. a., and Lewis, J.E., J. Chem. Phys., 26, 286 (1957). Neff, ,J. A., and Hickman, J. B. J. Phys. Chem., 59, 42 (1955). -OliYer, G.D., Bluakin, s., and CUnningh, c. w., J. All. Chem. Soc., ,!!, 5722 (1951). Othmer, D. P., and Benenati, a. F., Ind. Eng. Chem., 37, 299 (1945). Porter, P. E., Deal, c. H., and Stroas, F. B., J. All. Chem. Soc., 78, 2999 (1956). Quiggle, D., Tongberg, C. o., and Penske, K. a., Ind. Eng. Chem. Anal. Bel., !, 466 (1934). Beed, T. K., III, J. Phys. Chea., 59, 425 (1955). Beed, T. K., III, J. Phys. Chea., 61, 1213 (1957).

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185 34. Beed, T. M., III, J. Phys. Chea., 59, 428 (1955). 35. Reed, T. a., III, Subaitted for publication J. Phya. Chem. (1958). 36. Robinson, c. s., and Gilliland, B. a., "Elements of Fractional Distillation," 4th ed. llcGrawHill Book Co., Kew York, B. Y., p. 72. 3 7 Bossini, F. D., Mair, B. J., and Streiff, A. J., "Hydrocarbons from Petroleua," Reinbold, Bew York, H. Y. 38. Scatchard, G., Trans. Faraday Soc., !!, 160 (1937). 39. Simons, J. H., and Dunlap, J. Chem. Phys.,!!,, 335 (1950). 40. Simons, J. :e., and llausteller, J. Chem. Phys., 20, 1516 (1952). 41. Sillons, J.B., "Fluorine Chemistry," vol. II, Acadeaic Press, Inc., Kew York, x. Y. 42. Taylor, T. B., and Reed, T. M., III, aulaitted for publication J. PhJ&. Chea. (1958). 43. Tillaeraans, J., "Physio-Cheaical Constants of Pure Organic Coapounds," Elsevier Publishing Co., Hew York, X. Y. 44. Varteressian, K. A., and Fenske, M. a., Ind. Eng. Chea. 29, 270 (1937). 45. Watanabe, K., J. Chea. Phys, 26 542 (1957). ------~-46. Westwater, w., Frantz, H. w., and Hildebrand, J. H., Phys. Bev., !!,, 135 (1928). 47. White, a. a., Trana. All. Inst. Chea. Bngra., 41, 539 (1945). -48. Wood, s .I., J. Am. Chea. Soc., 68, 1963 (1946). 49. Yen, L. c., "The Efficiency of a Laboratory Fractiona tion ColWllll Distilling Fluorocarbon Coapounda, n aster's Thesis, University of Florida (1957). 50. Zilllll, B. H., J. Pbys. Coll. Chem., 54, 1306 (1950).

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I BIOGIIAPBICAL IDE BeaJaaiD G. l)'le wu born 1D Atlanta, Georgia on Decellber 4, 1927. lie graduated froa DruidBilla Bigh School 1D Atlanta and entered The Georgia IDatitute of TechDolou in .Jane, 194&. a. graduated in June, 1910, with the deg:r-of Bachelor of Chemcal ~ineeriag after eenlng one year in the Aray (1948-1947). SiDce grac:hlation froa the Georgia Institute of TechDolou he hu worked for the u. 8. Raval Shipyard 1D Charleston, South Carolina, and the llonllanto Chealeal Coapany. Ia June, 1953 he entered the graduate school of the Voiversity of ~lorida where he rece1Yed the d,gree of lll&ster of Science in BDgineeriDg 1D January, 1961. lie is a aellber of the Pbi Kappa Phi honor society and the Allerican Cheaical Society. 116

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This dissertation was prepared under the direction of the chairman of the candidate' supervisory committee and has been approved by all members of that COIIDlittee. It was aubaitted to the Dean of the College of Engineering and to the Graduate Council, and was approved as partial fulfillment of the requirements for the degree of Doctor of Philosophy. February 1, 1958 Dean iJf 80f ~aeering Dean, Graduate School chalnaan

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