SOLUBILITY OF NONPOLAR GASES IN
POTASSIUM HYDROXIDE SOLUTIONS
SATYENDRA KUMAR SHOOR
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
UNIjVERSITY OF FLORIDA
3 1262 08552 8304
-n, -uthor wishes to express his sincere appreciaior to
Profe7 or Robe:rt D. Walker, Jr., the Chairman of his Supervisory
Comn.r.Lee, for his guidance r.d encouragement during this research
progra.... HE is Lsp-cially grateful to Dr. Keith E. Gubbins for his
inters anir valuable suige=tions turin the entire course of this
investigation and for helpful disc'usions during the final stages of
thit work. The author would also like to thank Dr. R. G. Blake for
acting on his Supervisory Committee. Thanks are also d-e to
1.r. Jack. Kalway and ..r. Myron R. Jones for their help in building
'Th author also wishes to acknowledge the financial assistance
of the National Aeronautics and Space Administration, Washington, D.C.,
who sponsored this research project.
T E-LE 07 CO:;TE:;T.
.. . . . . . . . . . . . . .. . . . . . . . . .
'. , .L - . . . . . . . . . . . . . . . . . . . . . . . . .
LILST 0?F h.'-L:
L SI Ci C........ ................ ............................... ....
1 . RC U C O ..... . . . .. .. .... . .. ... .. . ... .. .. . .. .. . .
S 2 ................... Th ri s G s S l ....icy. ........................
2. El ros.:ic T.LJeo leI S................
.. 2-.2 FAC 10 ..................... .o y....................
... C.............. .............................
-.1 Cd-sT y. ic of .s.olv,. Gases ......
s Gas S.. L V-. L 1 z .u ...c..... ........
e. ........... .......
1H 0 d U i LeD. L z (3-1 ) ..... .............
.C. sic: T.. .o.. .s.........................
.2 Te o Elc...- :--c. c Theors...... ..............
..- a. . F '.. .. .... ....... . . . . . ...
5.2. a Theory of Ds:.-c T- c, ...................
I .2 T f De..- y I . . ...............
;- o Co a . . . . . . . . . .
C., To : o: ac '- d P rL -cle T'- r .................. .
.- C ior, C L.. --c-1Cos:a:- T-.Lori, s and
:h -o.o.ed C '..-t:' :.-.od... Saed <.- c.led
?ar cic a :ac .' ...............................
TAEL. OF CONTENTS (Corntinued)
J. CCACLUSIONS AL RHECO2iZXDATIOXS ...................... 137
APPDNDICES ..................... .............................. 139
1. Surface Effece and Solubi ity ........................ 140
Esiae of Accuracof fc E:xperir:.ntal Solubility
e:a sure~m n s ......................................... 143
3. E, S for Hydrogen, Helium, Argon, Sulfur
Eexaf 1 oricde, Methane and Naopeanane ................. 144
L GR .......................................... 163
LIC ",.- -HICAL S ETCH ............................................ 168
LIS^ OF .AB-ES
1 .. -.i:v Coafficilnts, x o ,76
1 .-.c .i y Co; fficients = x /x ...................... 76
2 .:;-:p w:_-.e U::1 System~ and Conditions ....................
3 Sol'i''ii.y,' of Various Gases in Watez, (G.mule/litre)
:-. i,. . .. .. ... .. ... .. .. . ... ... .. ... .. ... ... .. .. 9 0
Pari-al ..oll Hents of Solution, H 2, cal(g.mole) .... 96
?Prcial :.,1.1 Ener;ics of Solution, cal(g.mole)-.. 1CO
c Partial Molal E.--.;opies of Solution, AS, calg.mole K)1 104
7 Sal:ing-ou: Coeffic-ent, kS at 250C.................... 109
& Values of P_-: ..-ters b, rh and ....................... 111
9 Par:-_L '.ol-! Volwr..es of Gases in Water -t 50C........ 111
10 Prooerties and P~rameters for Solvent Species........... 118
11 Properties and Parameters for the Solutes.............. 118
12 Various O-.,ni:-_s of Equ.cion '126) for Solubility of
0 sta 25 C ..................... ........................ 124
13 Values of ln(j K ) ..................................... 127
1- H E2 for 02/2; KOH Solu.ior., calg.mole). ............. 134
15 P-ramater a for Solvent Species, A .................... 134
.. ... .. . .134.
LIST OF FIGURES
1 R-dial Distribution Function ......................... 34
2 schematic Diagram of Molecule of Species j ............ 4
3 Pair Pozencial Betwcan Solute and Solvent Molecule of
Species j ......................... . ..... ............ 45
A Sphere Having a uniform Surface densityy of Charge... 57
5 Ap-aratus for Gas Solubility Detarminations (Method I) 61
6 Schematic Diagram of Method II (Dissolved Gas
3tripper and Concentrazor) ............................ 68
7 Schematic Diagram Af MeTho. I II: ....................... 72
c Activity Coeifician:s of Oxygen ....................... 81
.-.ctivizy C.efficienzs of yozogen ..................... 82
10 Ac-ivi;y Coefficients of Helium....................... 83
11 Activity Coefficients of Argon......................... 84
12 Accivity Coefficients of Sulfur Hexafljoride.......... 85
13 Ac:ivity Coefficients of Xethane ...................... 8
14 Activity Coefficients of Neopencane................... 87
15 Ac.ivity Coefficients of Oxygen at 25 C. .............. 89
16 ..c.vity Coefficients of Hydrogen at 25 C.............. 92
17 Partial Molal Heats of Solution for Oxygen............. 97
18 AL vs. C/k ........................................... 99
19 Partial Molal Energies of Solution for Oxygen......... 101
20 E vs. /k.............................................. 103
21 Partial Molal Entropies of Solution for Oxygen......... 105
22 A S vs /k ............................................. 106
23 Experimental ln(y K ) vs. Polarizability for
o-ubility of Rare Gases in Water at 25 C............. 117
L:ST OF ."IGLUPES (Cornci .ud'
-" --" r,
L V- .ri.o U Car.c 'c s of Ecuation ( 12 ) for Soiubili .'
i i:'ccc: of T- pracrre on.1 Ac:ivicy Coeffc- ciec- of
C .-.y, 3. in 2C O Sol ca n . ................ . ... . .
- .-.-. 1 '*i-;-
? :':ial .:-01
?E 4- J -1Jl I
-L jr de .....
-rti: l :-:aJ !
P." i : l l- l "
flujr : de .....
?-.r: i ":. ...J a
Parctia! !.o 1
ea-^ of Sol Lcion for 7 Vy e.... ..........
H-.ia: of S IL:ionr for H li n ............
Hea:s of So-.tion for ..rgor..............
eacJ : c. o lu :io for Sulfu-r H :-:-
.."c o;f ol. c .. for ch .ne ........... .
:. czt-s of Sol :-or n -:r .' Cpe .C .. . . .
E.-.o'icc s of S--uCion for :,ydr-ogen .. ..
r.i:r e: cf Solut^on for H lium..........
En z: iec of Sol tior; for .r-gon ..........
Z-.c~iLie of Solu:cor. :jr Sulf.ur He:-a-
:r.ersbie: of : So c ion fo: : .:e h r.ne........
Zr.C e:igie of Solution for: ::eopentnr e ....
Encropnls of aol'con for Hydrogen..... .
2rnc.o c of Sol'Lion for Helium ........
Ercropies of ScluLion for Aror ..........
' .:! :M.ol--1 r.ropies -u Sol~ior. for Sulfur He::L-
flo r ide .. .. ....... .... ............................
'-0 ?jr:i L .:o- 1 2-::-o of Solucio rfor Mecane .......
?r- P C.i .-!- nc:opic of SolCion for ieo rncar.a ....
KEY TO SYMBOLS
b,b Radius of "n Lon
C. = Third virial coefficient
C = Concentration of electrolyte, (g.mole/litre)
D = Dielctric constant of solution
D = Dielectric constant of pure water
E = Partial molal -nergy
E = Partial molal energy of solution
e,e. = Charge of an ion
= = Fugacity
G = Gibb, free energy
G = Gibbs free energy o- a mixture
(G)d = Gib's free energy of an ideal mixture
= ?artIal molal Gibbs free energy
_G = Gibbs free energy change
o = Prtial molecular free energy
g = adil distribution func:icn for the presence of a
component j around a component i.
H = Partial molal enthalpy
^. = Partial molal enthalpy of solution
K = -enry's law constant (atm. )
K = Henry's law constant at zero pressure (atm. )
k = 3oltzmann constant, (1.36x0-1 erg.deg. )
m = Gram ionic concentration
N = Avogadro's number, (6.02_ 1IC" molecules mole )
n = Hydration number
n. : .b r ,. io3u , .' e i a ur.lr volume
J J o
r.. = u:'".b -" or -.les o: .ob.p.rar.r L
/ = Tocl pure-i.re
D = ?:'obab.~fic
P= tc'-" p aEure
p = ?oL.rizst licy of con'-;or.n j
S = G s co c Lsc.-. c
R = -:-'ici- l radisLL
2 = .:. pr:ar:;er in DLeby, 's equacin
r = Variable raius
: .-:dius of -.n Lo-.
= -v''-tion r_-.zus
r 7.-ciu; cf: salcins--j: sphere
S = 51, .iliz:y of conponer.c i. electroly,-i solution
( .- -- I
- = So'ubKlity of co-.por._nt ir. ure \.:rer (..molc .licer )
s = :u..iber of !: L..Js of ions
r = ..bsoluce :-mp-er-:ure, ( 'K)
j = ?o:entl.. er--ry
.. = ?:ir n.tcraction be u.een seces of: type i anr.d j
. ',= .'olL.:C
S= ?'l.,c- i .o .olume
v = Volu>me po" r.olecule
= -ee '.,ol ...e of o Uo... .L L
v, = Fi ld st:-.-r.g:h
-.: *= ..L- _Lc LL
:-. = ..0. r. cionn c -3 co.r..po- r.. in pure w.' ar
y = -OLi f. tcion in .s phase
Z Comprssoiliity fac:or
Z = Average number of ..onelectrclyte molecules around c.. ion
Z. = Valence of ion j
S- PFarizabilicy of c mclecule
S= Thermacl expansion coefficient
S= Scond virial coefficient
p = Compressibility coefficient
,3 = Zrpirical constants which -etermine che change in dielectric
= Activity coefficient
6 = Solubility parameter
= Represents a differently increment
= energy para.ater of Lennard-Jones 6-12 potential
E = Electronic charge, (4.7:8x10 e.s.u. or (erg.cm.'l2)
S = culntity proportional to the square root of ionic
strength a.d having dimensions of reciprocal length
= Chmical potential of component i
= Dipole moment of component i
L.,L S standard chemical potentials
S = Volme per ion
'. = ;umuer of ions of type j per molecule of electrolyte
= Charg-ng parameter
o = Density or number density
I = Denotes summation
S = Dissance parameter of Lennard-Jones 6-12 potential
J = Surface tension
S = Surface density of charge
= Fugacity coefficient
= Standard chemical potenti-1 per molecule
=Volume fraction of component i
= Potential at the position of jth ion due to ionic atmosphere
G = Gas phase
L = Liquid phase
E = Excess function
id = Ideal state
m = MixtLre
, = Mixing
O,* = On ca.ote standard chemical potentials
Up :o ccicn 2.2.4, 1, 2 and 3 denote warr, nonelectrolyte
solLu and electrolyte respectively. In section 2.2.4 and subsequent
secli-ns, 1, 2....m denote solvent components (e.g., 1 denotes water,
2 denotes K and 3 denotes OH-) "nd a denotes the nonelectrolyte solute.
-.btract o: Disertzi Presented io tna Graduate Council
in Porial Fulfiillent of the Require=ants for the Degree of
-oc:or of Philosophy
-3LSILITY O- .:07?OL.- GASES IN
?OTASSI~ L.,YL CXID SOLUTIONS
Satvendra Kumar Shoor
Ch irm.n: D. Walker, Jr.
-:a-or Deparz..ent: Chemical Engieering
.easurernents of he soiubilicy of nonpolar gases in aqueous
potassium .- droxide solutions -re re or:ed for a partial pressure of
o..e a:.tophere of sol_:e gas. The te.-perature range covered is 25 -
1C0 C, and the electrolyte concentrationn range considered is 0 60 Wt.7
K0:. Th- dissolved gases studied are co.:.psed of roughly spherical
.olecules of various sizes cnd include helium, argon, oxygen, hydrogen,
sulfur he.afluoride, methane and neopentane.
T-.-. xparimCanal m.eohoc ianvoved stripping the dissolved gas
from solution using a carrier gas .ream; and subsequent analysis of
this scream by gas chromatography. For all the gases studied the
solutility falls o-f very rapidly with rising electrolyte concen-
tration; thus for oxygen in 50 wt.j KOH az 25 C the solubility is
approximately 1% of the value for pure water. From the experimental
measurement. calculated value. of activity coefficients, heats of solu-
tion, energies of solution, and e.-.:opies of s i.cion are obtained
a a :runc:ion of ..-. concen:-acion, temperature and solute gas.
T..e above e:-.perimental study has been used to test various
c.iorli o:f gas olIbility in electrolytic solutions. Electrostatic
.oreas : .'.c!h ma:e -is of c:h concept of a continuous dielectric
.ed_ ~-re shown co be inadccuate in explaining the salting-ouc pheno-
re.a. .. cav.ic:, del based on the scaled particle theory is proposed.
T.:is Tl oc" posz.ses several advantages over existing theories of the
solb- ii::,, oif ga-: in electrolytic solutions and is shown to predict
che solubblXvy for the systems studied in this work f-irly satis-
rco.~L1 u-, co an electrolyte concencr-t-on of 53' by weight. The
is:.lc~n p:..aomrn a-e ,hown to arise no: because of the ionic charges
as Indicjced by earlier theories, but from the presence of particles
(ior,z, h.v1:.i rolecular p>..r~,ers (size, polarizability) different
cher. ct.se of 3- cer.
A .nc.:ledge of the solubilicies of g-es in electrolytic
so-utions is of practical impor-ance in a variety of operations of
hnnmical engineering interest The solute gases for which measure-
ments are reported he-e were chosen to represent a group of nonpolar,
roughly spherical molecules, having a wide range of molecular diameters,
and include ga;es of direct interest for fuel cell operation. Potassium
hydroxide solutions are particularly interesting because of their
use in ful calls and battcries.
Previous studies have indicated that gases pass through a thin
film of electzolyte e-ore reaching electrocatalytic sites of porous
fuel cell e.-ccrodes (1). In hydrogen-oxygen fuel cells the mass
transfer process at each electrode consists of a diffusional flux of
the dissolved reactant gas and a flux of water. The reactions are:
0 -r 2H20 + 4e-i+ -,0 (Cathode)
H2 + 20H-- 2H,0 + 27 (Anode)
.n a recent study of electrochemical kinetics at porous gas-diffusion
electrodes, Srinivasan, .urwitz and Bockris (2) have shown that con-
ce:traticn of the reactant gases near the gas-electrolyte interface is
a co.troll ng factor in obtaining higher current densities. They
concluded t..at elimination of concentration polarization would permit
current densities which are about 103 times higher than those obtained
in the presence of concen-ration overDotential. Under such conditions
a knowledge of the effect of temperature and electrolyte concentration
on the solubility, and diffusivity of the reacting gases is useful in
esti.at ..* desirable operating conditions.
In addition to such pragmatic considerations, phase equili-
brium studies over wide ranges rf temperature and electrolyte concen-
tration are of interest in resting theories of gas -olubility under
conditions for which the intermolecular forces are quite different
(involving ions, dipoles) than those occurring between nonpolar
'Te i.or.. reported here formed part of a larger program to study
the thermodynamic and transport properties of potassium and lithium
hydro:.-d. solutions. Bhatia, Gubbins and Wliker (3) have studied
mutual diffusion in -cueous potassium hydro:ide solutions. Other
aspects of the program .re continuing, and include phase equilibrium
studies of gas-lithium hydroxide systems and diffusion of gases in
potassium and lithium hydroxide solutions.
For potassium hycroxide solutions the saliing-out effect is
particularly large for all nonpolar gases, and the gas solubilities
to be measured are very low, of the order 10 to 10 mole fraction.
because of these low concentrations, conventional methods for solubi-
lity determinatior. cannot be used. In tre present investigation, a gas
chromatc-- -hic method has been developed which can be employed to
carry out solubility studies when the amount of the dissolved gas is
very low. No previous studies of gas-electrolyte systems seem to have
been reported in Taich the concentrations are as low as those experienced
i. the present work. Tn addition, on- for one or two electrolytes
nrs a systematic e.perimental study been -ane for a series of gases of
widely v-rying pnysica_ characteristics over a range of temperature and
eleczrolyte concentration. Such studies are essential for developing
and testing theories of gas solubility. A further problem involved
in testing theories has been the discrepancies often existing between
the -esults of various investigators.
In Chapter 2, a brief discussion of the phase equilibrium
relations which are applicable to gas-electrolyte systems is included.
A review f available theories of solubility has also been presented
in th-6 chapter and this includes :heories fcr both gas-liquid and
'as-elictrolyte systems. Previous attempts to account for salt effects
have been along the lines of the electrostatic theories of Debye and
Huckel. Th:se theories assume the solvent to be a continuous medium
of a unifcrm dielectric constant, and apply only to very dilute
A cavity model ba--d on the scaled particle theory has been
previously shown to predict the solubility of nonpolar gases in both
nonpolar and polar solvents with reasonable success. This theory has
been extended to electrolyte systems in the present work. And the
model and its development are given at the end of Chapter 2. In
Chapter 5, results obtained by employing both the electrostatic theories
anac acled particle theory are compared and discussed in terms of
-ssumptions involved in each case.
2.1 Classicl :.1 .Te:od -n.ics of i-szolvcJ ases
Consider a ror.ceal liquid solution i: con:acc .'ich a xapor
p .-se, a: c'u l.-b-ium, for any component i
:c.'-: supe:scripcs G and L reier co gs and liquid phases, respect vely,
I:rc fi is ch -h. ;-ncl pozcr.:ia (partial roll Gibbs free energy) of
com.?onnc i W-e sh.11 be cc..cur:.cd or.y l'.'in pure gab dissolved in
2cuOL_ Iectrolyct SOLIoOs-.. The ;as phase will therefore contain
che SC .. and '.'atcr vapor, '..'ile :he 1quid contains water, solute
gas, :.- the tc'o ic.ic species (in. or case 1 and OH). because of
the i-lctro-nauts-al-iy condition the ch.m.ica: potentials and activicy
cocif:icienLs Cr the ct'o -ons can be speci-icd by a sir.gle value for
Tch ilssol-.d leccrol "e. W!e shall or.ny concern ourselves with che
chemical rpoccenzia of AI, soluce 2as. V' label wacer, solute gas and
elccrolyte as compon.er.ts 1, 2 anc 3 respectively. For the gas phase
S = 0(T) RTinf. (2)
- 1 ..s ?- 0
-.:c fugac.cy f .s relaced tr.he pressure oy the following re:a:ion.
r. = Qoy.P (3)
The ci.;. coefficient 0. can be obtained from the virial equation
in. = 2Z yi - p y.y.C... InZ (4)
In the liquic phase
L= 1i(?,T) RT lni-,x (5)
The choice of the standard state for the liquid phase is arbitrary.
However for gas-liquid equilibria it is convenient to choose the
following standard states. For water (1) we choose the pure liquid
at the same temperature and pressure as the mixture (pure liquid
standard -taie). For the solute gas (2) choose pure solute in a
hypothetical licqud state which is defined by reference to the behavior
of this component tz infinite dilution and in the absence of component
3; i.e., by reference to Henry's law as defined below. We shall not be
concerned with the activity coefficient of the electrolyte (3), so
that specification of its standard state is unnecessary. Choosing the
above standard state,- i:..lies:
LL.1 -+ 1 and Liny2 -+ 1
S-- -> 0 (6)
x3 = 0
henry's law is defined as:
x2 -+0 f2 = Kx2 (7)
..:e ,-c is che Heinr"-'= .. co.-.Ecanc for c: ..: gas dissolved -i pure
w-. er. .ror e -:.a io.. ( 1), (2) ca d (5) for che dissolved gas
:.) RT ) .T
I ; ---- T..
T'i, "2I;.- .-an.c s- c. o :'r.. bo'.'- e,-cu:t-on is independent of the compo-
slizrn. Therefore usin2 che standard s:ace a- cdfined aboove
Tnu. for an,, cor.cenrracior,
o -, -, (10)
.,2 = .^.. (11)
I <1) z.e He-.;ry's conscan: depe.ds on pr ensure. To e:-:plicL ly,
accour: for -:.-. dependence, differeniJce cqL~rior. (9) with respect.
to ..;ss rc a. co.;-.:r.c ct'mperacure trnd co-.rpositcio
t RT.. n .,
a (1') T
.L. iti c i-._; -uation (5) it. The foL-m
^(?,T) = .4, RT~n-,'':.: (13)
a-_ diffe--eni ccir.ng vi. respecc to ;-.-_-s_ re at constrC r coposicion
r r e-.'pera rL: _- -.-es
/ D'- \ / 01 n':.
T T..... R (1n
= V RT (15)
whre V is nparial r.olal volume of comp-.onent 2.
iow' consider a solution such that :x: -+ 0 and x3 = 0.
Ecu tion (15) becomes
where V is partial molal volume of component 2 in pure water at
infinite dilution. Ho,.eve-, since the left hand side of equation (16)
is indapendern of composition, it nolds for any composition. Hence
/ 1nK, V,
Integrating, one ct-ins
K2 = K dP (18)
where K ceno-es the Henry's law constant at zero pressure. Equation
(11) can now be written as:
K 0 ep -f2 ] (19)
2Y2 = yxK9 exp dP (19)
Also from equations (12) and (15)
1OK, V _1_
S- o (20)
'sin :- cc -cior. (10), c.Luator. (20) becomes
-l )\ ..-
,- ) RT (21)
.his cq _:i-. c bn b uL-:d cL determ-ne V7 if experiments are
.erformcd a: Jif-crcrt pressures.
T..e above' i._-tic.-ls are r:-orous. However, for low pressures
sch as "hos. used .e-e, cte creca.a-nt may be simplified somewhat. At
1 acm. prcss-:c for non.dlar casess :he error introduced in assuming
I= is -.e;iia' .-..so, a- such low pressures the pressure
depe.-der.c of :-e .-.nr:, ':a -_ con.sctnt may be ignored, so that the
integral -. equion (1.9) ry be om-itted. Thus equation (19) becomes
Py = -.:K (22)
CSuato0-. (22) .ay be LL tC oczair. y, for gas dissolved in an electro-
i'te luior. '. a.d ::, re k-wn from experiment. may be
four.d f o-.. e:-.p:c.ir.enrl -: for the solubility of the gas in water,
.- the lim.c of -r.f.-.ic: d-.ution :.'here 72 = 1), using
,.. = (23)
H-.nry''s 1-w shild a.pl.y zt finite concentrations provided that the
concrnLration of disoI'.'vd oas is sufficiently low that intermolecular
forces becaw-n ;a.s mol.ecu-es my cbe ignored. Since the molecules studied
..--c :.'e nonpolar, che interirlec:lIar forces between gas molecules
fi off :a:d': -.; dscarnc (as :- for dispersion forces), so that
Hen.-:y' il.' should be a good assumption for moderate gas partial
p:e-jures, where the mole fraction of dissolved gas is in the range
1G to 10
artia" .ral :at of c tonsn:
Differ eniating equation (9) with respect to temperature at
constant pressure and composition yields
n Pn \
S / c ./T 0 /T
S OT R dT
T R1 Rinx (25)
T T I n 2 2nx,)
and differentiation of equation (25) with respect to temperature at
constan: pressur- and composition leads to
^ T P,n.
- R ( Y- ,n
[ ) P,n.
where E is t-e partial
molal enthalpy of component 2 in the solution.
of equa-ion (2) gives
- ( 9 ,
Assuming thc gas phase to behave ideally, we can write
c- -- 2 -
:.nce lef: harnd E1d of cqacion (29) is noc : fur.cion of coTmposilion,
:. .' ... ur.'... ..r :s, ., ? ro:-cf.es, ur.lt'/, s w.e -. .e
d .(T)/T o,
h 1'.,*. < h Z. :L. e r. .a.o r o'c.. pure solcute C s at a pressure
suffricic.:y lo'..' : for -he '.:por phai 3 acZ e -s a perfrec: ga .
i.-.. ecu:zifns (24), (27) -nd (10) are combined one obzains
/ ln ,,
- P r
it r:' be :.oced C-ar bach sides of _quaco. (1) a-r, i.rn. er.dent o
co .pos-c-or.. Reaz:r.-:ing equation (31), one obtains
?, ln(^K) K n
(2 h2)_ ZH2
Usin, equations (10) and (32) yields
(H h ) AH2
'..'her.- .1, is rhe partial m.olal enthalpy change on dissolving 1 mole
of :deal gas ir. the electrolyte solution. If equation (27) is applied
co a sol-cion such that as x2 -+ 0, x3 = 0 and y2 -+ 1 we obtain
S /Tq H
wh.re He is t..e partial mol. enchalpy of zco..onent 2 in pure water
Lt infinite dilution. equation (32), then becomes
S. G ---
?,n. RT~ RT
H --2 i s n arD--a! oial ena -""
.nr is he ?r-al .olal- enthapy ch-nge on solution at infinite
cilution i. pure wazer. This equation holds generally, since the left-
hand side is composicion-indpndent.
.rtit. .1 al Entro," of Solution:
The partial .olal free energies of component 2 in the gas and
liquid phases -re related by
L G -G -L -G
2 = H H,) TS S ) = 0 (36)
Assuming the gas phase to be ide.l, we can write
S2 -S= (37)
2 = T
w..ere AS2 is the change in en-ropy when one mole of ideal gas dissolves
in the lectrclye solution.
Parzial '-la Enerry of Solution:
The partial molal enthalpy of component 2 is given by:
-L --L (G3
-( ) ( V. ) (38)
and for an ideal gasacus phase
-- G G -G
( E) + p( V( ) (39)
= (Z< E,)
E?, kM RT
* L.) --''
-(r L L
(1nc ;e k"-)
i.er-- is chance ir. In:arna-L nergy when or. ::.ole of ideal gas
dissolves in ch, electro5vce solution.
.:: c-- Fnctcions.
Te eiaxcess fr.~e e-ergy of solu.-on is given by
S= I (G~i (
.r- G ds che f -ec cr. -r:y of inonide mTx::ure,
(GtC is cte :rce energy *:i'f id1c. 1 :-:cure.
No'.. G r. L
S n., (P,T) Ri Z k S .-
and (G = ( P,T) + R .-. Inx
Sps g n by. i
The parciail :l.a1 i:-:ecess free energy is give by.
1 ,'' TP,n
The ..x:cess enIropJ i
E = T oT (RT r..ln, )
- n.1ny. RTi n -I -
) 2.i- a
The ar;ial molda excess er.ropy is
The excess enthalpy is
n G TS
= TT i --
The partial moial excess enchalpy is
= T (-
2.2 T :eories of Gas Solubility
Theories of gas solubility in ronelectrolytic liquids have
been reviewed by Batcino and Clever (4). Recently, Conway (5) has
surmarized the important modifications of the electrostatic theories
for electrolytic systems. The discussion of the theoretical material
presented here is in four sections, and reflects the different
The first section deals with the electrostatic theories. Most
of these theories apply only to dilute electrolytic solutions, owing
to the unjustified assumptions made. The majority of these theories
assume the solvent to be a continuous medium having a uniform dielectric
constant. However, the unique structure of water results in a
characteristic organization of water molecules (a hydration sphere)
around an ion. In between the hydration sphere around the ion and the
m:.in. body of che sol.'enc, here t.:y be 3 tr r.sit ion zone i.'hich does
roc hav'e any, s:ruc:ure. These cifficul:Ie come more serious when
che ions appro-ch each other, i.e., -n. concentrated eleccroly ic
solucins. A.so act '.i-er conrcer.:r::1ion, che higher terms in che
serTcs e:-.-.ori. o: -- Sol:z::.annr e:.:o rntial discributior factor caznniot
be r.C c:c ed. .'vercheless, -.the hc ory s r .markably effcci'.e for
c-Icuati. c,-:he li iciir. 1:s fo cr.e d&'.'la ions from. ideal behavior
as the solcte concencracion approaches zero.
a- sco.Cd Seccion deals %:ich che regular solution theory.
Thi- theory gives quice good res'ulcs for ct.e solubility of gases in
nor.ol:r 'icuids. In che case of electc-olyzic sysccer.s, howe,.'er, dis-
cr:ibution and orier.ccion effccts ert not random. There is a large
volume ch.nL on -.i:: -nr r. :h as;sum -.pons 1isced or pJ1e S3 are no
lorner '.-id. Ir. v.'ie. of :'.e na'r.y as-um..pion needed in applying che
ap:oach :o single r.onpolc.r syscrE:.., an atenpL co introduce scill
fcrcher mod:cfic:ions co che theoryy so chat i: may be applied co
elecrrolyZe solucEtns Oc3s noL appear promisir .
T.-.e ct.ircd -.cd fou-ch sections consider so-called "ca''ty models."
The solublliCy ptoces is assumed to be cccurrir.z in zwo steps. First,
a cavity a su:-able siz. co :cco-.odace the soluce molecule is
forr'Ld in. :he- liquid, cnd then the soluce molecule is introduced into
chis c'.vi'y. th och chese sca involve energy chan-es. A cavicy model
based o-. scaled pa--cicle cheory is co.siderrd in more d.2ail in
CSeccion 2.2.4 :nd ch-s -odel ha- been e:.endd o squeous electrolycic
soC l:i-is. This section cor.cains er. chcorecical corcribucion of che
p--esenct 'o The theory dc.elope :he-e is cesced in Chaptc: 5.
2.2.. 2ectrostatic Theories
The addition of an electrolyte to an aqueous solution contain-
ing a neutral molecule frequently tends to decrease the solubility of
te neutral species. This corresponds to an increase in activity
coefficient of the molecule. "S.lting-out" of this kind is not general,
and examples of the reverse behavior of "salting-in" may be found.
The electrostatic theories discussed here attempt to explain these
phenomena on the basis of coulombic forces.
A comprehensive review of electrostatic theories in relation
to salt effects was made by Long and McDevit (6). A review by Conway
(5) summarizes the recent important improvements made in these theories.
Debve and ".cAulav '7'
The earliest electrostatic theory of salt effects was that
of Debye and Mc.'ulay (7). These authors made the following assumptions
as to the nature of the electrolytic solution:
1. The solvent molecules are tre-zed as a continuous die-
lectric medium whose dielectric constant is uniform throughout the
2. There is a continuous charge density function around a
given ion due to the ionic atmosphere.
3. The solution is very dilute with respect to electrolyte.
These authors compare two solutions, each containing water,
electrolyte and dissolved gas, and each having the same total number
of moles of electrolyte and dissolved gas. However, the first solution
is infinitely dilute (i.e., contains an infinite number of moles of
water), whereas the second solution is the system of interest, of
ir.ice corcc:.::: a r., zo.-. inir .-i ,, n,, ... n. .... n ions per
cubic c nt c-.LLer o:- c'.arges ... e .... etc., sul trin
fro .' -.oleculs of elcc:roly:e. The f:rst solution is converted tc
one avin thr.e e sae in.:enr e properties as :he s5co.d solution of
firi. concertracion by the follouir. to s:e.s.
1. .c-..o..ing c. te ch2r-es e on the ions infinitely slowly.
2. Comr.ressinr. he solcuoer. isochcrz.311y and infinitely
s.lo:lvy o ~:ce tir.al v-cl:-.c, by -.ans of a piscon semi-perneable to
,.:tLr :r.! finally restoring thc charges infir.itely slowly. The
elccrical uor'.: '. involveC in cischarging :he icns at high dilution and
r-c'-..argig Lm inr the solucior. of finite concentration is then con-
sidered. Sincc Lhe potentiic a tche surface of a spherical ior of
radiuses n fs d-U cL-- o diemlecarl c co.w.sLani D -is cha the .ork
:- .ne De t e ir. roceos (her,9) is calculated. The pte
s -' e Gd' s 'r,.e-
=C j 1
..h-'e ? t c.rSi.n porat Le ion du hich the ionic atmosp her charge,
oe n.creasds fro:-. to e e-. Siiu theory ():he work of discharging is oba'ned
s r.. .
1 J ( .,3
:e:.-:: r'.-.e .'.or dcie to rha ion.ic a~rras-here is calculated. The pocten-
ial "',. at :hr posjLion of Lhie ior, j deij Lo the ionic atmos0phere,
o'c, t ncd fro-., Debye-Hiucui l theory (.- ) sa
" -\ Dk
( ', r. .
where c. Z
Z. = valence of ion j
6 = electronic charge
V = volume of the solution
n. = number of ions of type
6ork due to the ionic atmosphere is
tq. = S n / d-- e
i j 3D
j in volume V.
3D= n.e K
3D j j
The appearance of Kc in the above expression results from the fact that
< is proportional to the charge . As a first approximation the total
electrical work obtained by the above processes is set equal to the
increase in free energy of the system. Thus
Ss n.e. s n.e. s
2D b. 2D b. 3D n1 j
1 o 1 j
The dielecuric constant, D, of the solution is represented by the
D = D (1 pn p'n')
where n and n' are the numbers of molecules of nonelectrolyte and
electrolyte respectively and S and p'are empirical constants. D is
dielectric constant of the solvent. By substituting equation (47) in
equation (46) and neglecting the higher powers of n and n', the
rolio.'in: cqu ziorn for free er.e-: ch:r.an is obtained:
o o 0 j o 1
Comu:r.ing che ccrrib; .tio co ch6 c.:.T.ical poj-ncial of the non-
c lec crolyc:, by c:-.. addition of elec:rolyce and usin. its cherrodyna-
m-c r!1a:z;ionsh t: solubilict, give's the final eqaacion of Deby:e and
:c..ulay (7) :h-ch is
l 0 s n.e.
I,; = -- ---- (49)
u.Tre andr S are soilbilicies of nonrelectcrolycc in the absence
rad r .encc of eleccro"',ce.
icdadl 1nd Faile, (10) cesc.d che v'a.lidicy of equacion (49)
fo: se,.VLrl nonc!ccrolycte-u'.ccr-clec.crolyce systems up co an
elccrol'e' c -o.cctcra:ion of 4 :-.ol1. Ic was found chat concentration
dc.pcncance of salc effaccs is predicted w'izhin the limits of probable
.:.:cacri'tcn .:" e error i z .r.:- cases.
Dy,'c (1I) :acr d,:,eloped a -.ore exact theory to obtain an
e:-:prcsio. o" the concncr::ior, of a r.nelec:rol,'ce -olecule in the
presence of a spr.eric ion or radius b. as a function of its distance
fro-, the ion. He calculated che free er.er,, for the real solution by
caking ir.co accou.c :he energy: of che electric field surrourdir.n che ion.
If X is cth field scrcnz.- in a 2-.'n volume element, che
enrcrgy ?er ur-ic voluz is giver frmi elecc:ostc cs by,
,' i:. ',J
where D = dielectric constant of the medium.
For an ion
e = (51)
Thus the energy of the volume element at a distance r from the ion is
Tht total free energy of the real solution is obtained as
S ( kT.x) + n + kTnx2) -
where sub'cripts 1 and 2 denote solvent and nonelectrolyte, respectively
n. = number of molecules per cm. of component i
(i = ri/s (54)
If 6nI and 6n2 are small variations in n and n2, then
n e 1 2D
6 = 6-(1, + kT8x 4 2 n + 6n2(02 kTlnx2
4 ) dV (55)
8r D 2 J
By using the condition of equilibrium, 6& = 0 or 0 is a
minimum subject to the condition that the total number of molecules
does not change, and assuming no volume change on mixing, the following
equation is obtained:
1 2 e D D 1
vlr. v in r v v
2 0 1 x2 8 kD 2 11 2 r
1*: 2, OT -
where v. is volume per molecule of component i, and x and x are the
values of x and x2 at a large distance r. Debye (11) then treated
tha saltirn-out of component 2 by considering
- < 1 and--
very large so that equation (56) becomes
x2 = X ec
R e vi (59)
8 kTv D n 1 on
1D 1 2
If we assume a solution saturated with component 2 (at low concentration)
in the presence of r n. ions per unit volume, the average number of
nonelectrolyte molecules surrounding an ion, can be obtained from
Z = n dV = L dV = e- dV (60)
v v 2v
1 1' 1
The integration is over the volume v, at the disposal of an ion.
Similarly, the number of molecules of component 2 in the volume
element before the addition of electrolyte (which is the same as
the value of Z2 at very large r) is:
Z =2 dV (61)
Using equations (60) and (61) and recalling that n. dV = 1, (62)
the fo--owi.n equatior. for salting-ou is obtained:
>= 1 n. (1 e-R/ dV (63)
For dilute solutions, this becomes
S2 -(R/r 2
S = 1 1 n (1 e t )1 dr (c )
Debye (11) simplified -quation (O4) by expressing dielectric constant D
as a linear function of the mole fractions. The integral involved in
the equation (c-) was evaluated by Cross (12) to give a series solution.
Long and AcDevit (6) compared experimental activity coefficients
with chose calculated from Debye's theory for a variety of nonelectro-
lytes in -queous electrolyte solutions at electrolyte concentrations up
to 1 molal. Their conclusion was that the theory gives results of the
correct order of magnitude. However, the theory cannot reasonably account
for the marked variation in the effect of different electrolytes. Long
and McDevit (6) attributed discrepancies between the experimental and
theoretical values to the fact that Debye's theory considers only the
primary electrical effects and does not include the "displacement" and
"structural" contributions. Long and McDevit's argument is supported by
the fact that the theory usually gives the closest predictions for just
the cases where the latter factors should be minimized, e.g., sodium
and potassium chlorides.
Gross (13) extended the theory of Debye (11) to include the
effect of the ionic atmosphere. This effect requires that the energy
of the volume element at a distance r from the ion increases by an
C -,2 2 -2
dV = -- be dV (65,.
.D r (4 Db
i.re .-: is a para. er uir.ed by equation (44) -nd b is the ionic
i>ulcr ( -'r
Eu:er (1.4) obctine.d a relay riro very similar to thtr of Debye
,.c :.!:cAulay (7) by a sli-hrly different procedure. However, c- is
easic- to use since it is e:..pressd itr, er.a s of -ore accessible
ro'ecul!r quanit ies. He calculated the electrical work required to
-rin a -.olecule of co..ponrenc 2 from infinity to a disLance r from che
ion "y the e-:pression
W = / PI ? '" Y'^ (,L o )
....re ?., 3 = p olr iz c ion produced per unit = a,
= polarizbili:-y .of r.wlecule 2
:* = filed strc-th
o= Volu. of molecule 2
Thus, cha ttcal electrical wor!: to bring a molecule of com.pcnen 2
frr. i.,fin.i:t to a distance r from tn ion and displacing an equal
v.olumca of cc.rponcn 1 away from. r.e ion is
a:-:c, tch Boltz7.ann equcaion for the distribution of molecules of
ncr.electro!ly e '.*.-s ssum- d :c. zbtair.
-(a l ".) -2 :-
Srom equation (66) the amount of nonelectrolyte salted out by a
single ion per cm., 2 is obtained by integrating (Z2 Z), the
deficit in the number of molecules of component 2 per cm. at a distance
r, over the total volume. Thus
ri 1- 2 e v2 2
a2e 6 4=r dr (69)
SkT 24 2
v 2D r
In the above, only linear terms in the expansion of the exponen-
tial of equation (68) have been used--an approximation which is justi-
fied only at very low electrolyte concentrations. For the solution
containing mI g.ions of charge el, m2 g.ions of charge e2 ....per liter
equation (69) becomes
2 S2 a a2 276v2 e mjN
0 kT 2 b 1000
S D j
Belton (15) modified the equation of Debye and McAulay (7) for
the case of a polar solute gas in a polar solvent. He added the work
done due to the permanent dipole moments of the polar components to
the electrical work obtained in the case of nonpolar components (14).
His final equation for solubility is
S2 47r a. n. 47Tb Z.n.E
log = 2 ( ) + DkT (1 )
2 2D 0bkT 0kT
where b is the distance between the centers of the ion and (71)
the nonelectrolyte molecule at the position of the nearest approach, and
pl and p2 are the dipole moments of solvent and nonelectrolyte solute,
rc-pccively. -Th. author used ,qu.-tion (71) to calculate the activity
coarficic~ or five solutes in different aqueous salt solutions, but
did no: ob:-in ;oc2 agreement with the experimental values.
ECckris c: al. (16) sought an explanation of the salting-in
ef;ccts for benzoic acid by tetra alkyl ammonium iodides in aqueous
and e:ahyl'nr glycol solutions by considering the dispersion forces
betcwc-n :'. ion ar.d the noneleccrolyte molecule in addition to the
coulorbic -orcns considered by previous workers. They obtained the
foilo'.'ing expression for the work done in bringing 1 molecule of
ncnuleccrolyce from infinity to a distance r from the ion and dis-
placing an equal volumem e of solvent away from the ion:
(1v 2 vZ- (X X
9- = + (72)
'..ere subscrip-s 1 and 2 denote solvent and nonelectrolyte solute,
rcsprecti'.'~, and .. is a constant for dispersion forces between
co.monent i andJ he ion, obtained from London's dispersion formula.
Usig equation (72) and following the procedure of Butler (14),
the follo'.ing cquacion for the salt effect is obtained:
(0 (a -v 2 )2-c, Nc 2 v
1 V Z.m. v2F 47N
PI X )) 3000kT
3o L 1000 D kT bi 1 v J
.-.ere m.. s or. of charge Z.i per liter of solution.
lThse authors compared experimental values of (S2 S )/S0m
w*th those calculated from equation (73)for salting-in of benzoic
acid by five diffLrent sales in aqueous solutions; they found that the
theory gave the correct sign and order of magnitude for the various
systems. However, they pointed out that equation (73) will not hold
good at high concentrations because of the unjustified expansion of
the exponential distribution factor and the neglect of the ionic
Altthuller and Ev,-son (17)
Altshuller and Everson (17) modified the theory of Debye and
McAulay (7) by taking into account the variation of the parameter ,<
with concentration of nonelectrolyte. Their final equation is
0 2" 9
S. .-DQN ( S m.Z. r S
in S- = - m.Z (74)
2 2000 D~kT 1 i
These authors compared the experimental results for water-ethyl acetate-
alkali halide systems up to electrolyte concentrations of 1 molar
with these calculated from equation (74), and with the equations of
Debye and McAulay (7) and Debye (11). It was found that none of the
equations were fully satisfactory. Altshuller and Everson suggested
that hydration radii and not the crystallographic radii should be used
in the equation of Debye and McAulay. This would remove the objection
to the latter equation that electrical work tends to infinity where
crystallcgraphic radii approach zero.
Mikhailov (18) introduced the concept of a salting out sphere,
:he -adiLS of which is defined as follows:
r 3 4 (75)
t.nere -. is the number of ions per unit volume of solution. He
pointed ou: chac an allowance should be made in the derivation of
sc-in--oc e-cuations for the reduction in the salting-out sphere as
c.:. eec:'c-role concentration increases. This implies that the integra-
tion in ec.acions (64) and (69) should be carried out from b. to rn,
rtcher chan f-on b to co, which is justified only at infinite dilution.
Z. = / Ze 4r 2rdr (76)
hec V-.'. = .or.:: term given by equation (72).
ikhaiilo.v .'.:o=;e the work in the form
S= + (77)
i 4 6
i.nrc E. and D are given by the first and second term, respectively,
of ,qul:ion (72) without r. The integral in equation (76) is evaluated
by dividing it into two parts; from b. to o, and from r to oo. A more
" 1 n
jJscif'able e::pansion of the exponential can then be made for r > r
l'U dec-eeses rapidly for large values of r). In this way the equation
for salcing-ou: by 1:1 electrolytes is obtained
S 47XC -W./kT
-- = (I e )r-dr)
o o00o 3 i
Soo 4/ (DI/ D2
3- 1000 s 3000 1 2 S
.T'n .~ E: S = S.
where E7 9 -
and C = molar concentration of salt.
Mikhailov (18) used equation (78) to calculate the salting-out of
tributyl sulpante and benzene by various salts up to 1.5 molar salt
concentrations. The agreement with experimental results was not good.
However, correct estimates of sign and magnitude of the deviations from
the limiting law were obtained.
Conway, e-: l. (19)
Conway, et al. (19) showed that limitations in previous
electrostatic theories arise from an unjustified expansion of the
ex:ponential distribution factor and the neglect of solvent dielectric
saturation effects in the vicinity of the ion, where, relatively, the
maximum salting-out is developed. They followed the method of Debye
(11) and made important modifications to correct for the above limita-
tions. They started with a distribution equation very similar to
equation (60) which can be restated as
dZ, exp[-Au/kT]47r dr (79)
where dZ, = number of nonelectrolyte molecules in a spherical volume
element of thickness dr at a distance r from the ion.
Au can be evaluated by Debye's (11) treatment and is given by
l1000Z2 E 1 1 1 (8
u= -) (80)
4 D D NS
To obt--. ..e nu-.ber of nonelectrolyte molecules in a volume associated
ic'-; one ion, the expression must be integrated from b to R, where b
is the radius of the ion and R is a critical radius (very similar to
t:he siI.-..-out sphere radius of Mikhailov (18)) corresponding to the
'.olu.e a'.':ilable per ion in the solution and defined by
R ~= o4,m 3 (81)
.here m is ;. ion of electrolyte per liter of solution. Thus,
::0 f -Au/kT 2
Z2 = -e 4u/ 7r-dr (82)
U'Js-ng the above ecuations, and following the procedure of Debye (11),
one obtains an equation for the salt effect in the following form:
0 0 R
z z s S R
2 ) 2 4-Nm -Au/kT 2
10-- 000 -( )r dr (83)
2 2 b
These authors pointed out that the exponential Au should not be
expanded to its linear form, as done by Butler (14) and Bockris (16),
because Lu is usually not small in comparison with kT near the ions,
where the largest contribution to the salting-out effect is expected.
It was shown that there are two regions in the vicinity of an ion. In
the primary hydration shell only field-oriented water molecules are
present, so that the dielectric constant of the solutions very small.
Consequently Au/kT is large and expL-Au/kT] is small compared to unity.
cyond t..e primary hydration shall _u/kT is small compared to unity
c-ing co the rapid rise of D with increasing distance from the ion.
Hence the e:xonenzial in equation (83) may be expanded retaining only
the firs: term of the series. Thus, the integration of the salting-
out equation is conveniently carried out over two integrands; from b
co r,, where 3D DO, and from rh to R, where D;D0. The equation (83)
S S ," I
-- = r-r + (-u/kT r-dr (84)
S m r.
To evaluate Lu, a limiting) case of Kirkwood's theory of dielectrics
(20), applicable only at low field strengths, is used. This is per-
missibl because the field strength is not very high in the region
r. < r < R. According to this theory
S V2D (9/22 (85)
P 4/3 a(2, O -_ ) (86)
where V\ is the m.olar or partial molar volume of nonelectrolyte, and
is the dipole moment of the individual nonelectrolyte molecules in
solution. The parameter 7 is the vector sum of the moment of the
central molecule plus that of all the neighbors which may affect its
orientation. Thus, for a non-associated polar molecule, we have
'lu Z22 C 2 1
u (V, (9/2)?,) rh r R (87)
8k XD D 0 r
and equation (84) becomes
S S "' 2 2
s 5- 3 Z 1 1
0 3 (r b +2 (V2D /)P -
S0 2m 2000kTD h
The first term in equation (88) is proportional to the number
of water molecules held in the primary hydration shell. This term
is obtained by a different but equivalent method, i.e., by considering
the salting-out by ions as being essentially determined by the extent
of primary hydration of the ion insofar as the water in the primary
hydration shall is effectively removed from its nor:-al solvent role.
The first term of equation (88) can then be replaced by
where n is the hydration number
m is molarity
d is density of solution
W is molecular weight of dissolved salt
With this substitution ecuation (88) becomes
S S 3 22
2 2 iSn Z- 1 1
0 1000d -mW (V2D 0 -(9/2)P )(rh R
S2m 2000kTD- h
Conway et al. (19) used equation (89) to calculate the salt
effects on rare gases and other neutral molecules by the alkali halides,
and they compared the results with experimental values. It was found
that the dependence of salt effects on the size of the nonelectrolyte
was predicted fairly well, whereas the dependence on the nature of the
ion for a given nonelectrolyte was predicted well only when the non-
electrolyte molecule was sm ll. For large nonelectrolyte molecules the
agreement was poor.
Recently, Ruecschi and Amile (21) introduced a procedure which
was very similar to that used by Conway et al. (19) to obtain the
following equation for salt effects:
-2 $2" 2 / 4 3 ) < [ / 4 rR 2
3 = -i ( h ) n"i 1 exp r) 7r2dr
where i,. is number of ion per cm.
r has the same meaning as R in equation (81).
The first term of above equation is the volume of t-.e hydrated ion
and is evaluated from hydration theory. According to this theory the
ratio of the solubilities in the pure solvent and in the solution of
an electrolyte may be set equal to the ratio of the volumes of the "free"
water without regard to electrostatic forces. Thus,
S2 1 n.V.
2 i i
Lim In = 2 n.V.
n. --- 0 2
V. is the volume of the hydrated ion.
2.2.2 Regular Solution Theory:
Regular solution theory has been frequently applied to gas
solbli Lcle. :ildeIbrand and Scott (22) define a regular solution as
on.e -in ,.'hch oraier.:ng and chemical effects are absent, and in which
d--cr-b'~o io ar.d orientation of molecules are random as in an ideal
solu~-or.. Thus a regular solution is one involving no entropy change
:-.en a s.-.al Iaounr: of one of ius components is transferred to it from
ar -d.al 0olIcior. o the same composition, the total volume remaining
unch:-.,cd. :'.:h chis concept of a regular solution, the free energy of
ni::ing, F" can be written as
= LE" P-V' TAS
-= E TeS (91)
w.iere he- cer. -V'" is assumed to be negligible.
H-ldebranC a.nd Scocc (:2) derived the following expression for the
free -r: .-o., o: m.:-:i- g of N, moles of component 1 and N2 moles of
_E = 2 + N1 V) 2 V l(g )rdr
12 2 L V
2e fo r o + 0 ordr (92)
where subscripts 1 and 2 denote component 1 and 2, respectively.
', = volume fraction of component 1: N.y.
N. = Number of moles of component i
C.. = potential between the central molecule i and each surround-
ing molecule j
g = radial distribution function (probability of finding
molecule j around molecule i in the mixture)
S= variable distance from the central molecule
g = radial distribution function for pure component i
g.. = gii/~.
The above expression has been further simplified by making
the following assumptions:
1. gi = g
2. Additivity of tne energies of molecular pairs
S ii n 6 (93)
where j and k are constants for repulsive and attractive
4. All radial distribution functions can be expressed as the
same universal function g(y) where y = and d is the
position of the first maximum of the radial distribution
function g(r) in the plot g(r) vs. r (Figure 1)
5. d = d = d and d = 2r; d.2 = r + r.; d = 2r .
M o 11 :2 1 2 22
6. The geometric and the arithmetic means of the molecular
radii are the same.
7. The geometric and harmonic means of the ionization poten-
tial are the same.
8. London's formula for dispersion forces is valid.
us, the si ified expression for M can be written as
rh-us, the simplified expression for AE can be written as
Figure 1 R.c..;l Ditcribuiorn Funczion.
1 / k \1/2 k \1/2 -2
12 V1 3 V \ 3
1 8r 2 8r2
S ( 6-2 (y)dy (94)
or V 1/2 V 1/2 2
AE = (NV1 2 2) L 2
wn-re AE, is given by
V 27N k1 ,"I
AE 3 / V-4 g(y)dy (96)
Defining a solubility parameter, 6, by
5 = ( V )(97)
Equation (95) becomes
AEM = (Nv + N2V2)61 2 1/2 (98)
The partial molal energy of mixing for component 2 is given by
AE = V,[61 622 (99)
To derive an expression for AS2 Hildebrand and Scott (22)
made the following assumptions.
1. The internal degrees of freedom of the molecules (rotation,
vibration, etc.) are the same in the mixture and in the pure liquids
as in the dilute gas.
2. Tie :r-e free v'.olur.e is accessible to roch soecies in
thie m-::ure and this is a'-al to che sum of che free volumes of each
com.. r--n .
3. V V
'..'i chtese assumptions the Flory-Huggins expression (23) for partial
molal e r.croy of mixing has been obtained.
S= -_R Ir= ~ l V (10
If V, is assu1ed to be equal to V2, we get the ideal entropy of mixing
_ % -Rlnx,
Usrin equations (100) and (101) for AS2 in equation (91) the following
e:-:pressions for partial molal free energy of solution, AG2 are obtained:
S .,2 V2
For V AG2 = V21 ( 62) + RT(lr.: 2 +i( V ) (102)
For V = V'., AG = V2 1- 62)- RTin.x (103)
If the puLr component 2 at the pressure and temperature of the solution
is chosen .s standard state,
AG5 = RTlnyxx
.'hs.re "Is activity coefficient for component 2 in the solution.
Thus, r.e final equations for a 2-component solution are
V \V2 (61 6)2
In-y2x = In 2 1(1 ) R
Irny2x = Inx2 -- (105)
Equazions (104) and (105) have been used extensively for
correlating the solubility of nonpolar gases in nonpolar solvents by
many workers. Among those are Gjaldbaek and ::ildebrand (24,25) who
modified equation (104) to give for gas solubilities
2 V V 9
-l = -nx 1 In (6 56 ) (106)
SV V 1
i 0 i
where x2 is ideal solubility, given by f = fx
f2 ) fugacity of component 2 in solution
O = fugacity of component 2 in standard state, i.e. pure component
In obtaining the above equation, these authors used the condition
N29 N and thereby set and 1 of equation (104) approximately
equal to x2 V and 1, respectively. Gjaldbaek and Anderson (26), and
Gjaldbaek and Niemann (27) studied the solubility of nonpolar gases in
polar solvents. They included the empirical factor W1 of Hildebrand
and Scott (22) to account for the dipole forces of the solvent and
obtained the following modified expression:
i + 2 2 2
-Inx= -Inx +-- (6 6 )- + -
2 I 2 RT 1 2 T RT i (107)
Gjalcbaek and Anderson (26) calculated parts (A) and (B) of equation
(107), and found that the difference between part (A) and the experi-
mental values of Inx2 was approximately proportional to the dipole
moment of the solvent. However, this difference was not equal to the
part (B). Thus, they found that equation (107) failed to predict the
solubility of nonpolar gases in polar solvents correctly; they attributed
chis failure to the unjustifiable assumptions made in the derivation
of cqction (107). Gjaidbaek and Niemann (27), and Lannung and
Gjaldacek (28) also correlated the solubility of methane, nitrogen,
:rgor. and ethane in alcohols and water with dielectric constants of
hhe solvent and the polarizability of the solute gas. However, they
did not find good agreement with the experimental values.
Prausnitz (29,30), in a series of papers on gas-liquid solutions,
contended that since regular solution equations do not take into
account the large volume change accompanying the dissolution of a gas,
they cannot be used without modification for such systems. The
required modification was achieved in a two step solubility process.
In the first step, the gas is condensed to the partial molar volume
which it possesses as a solute in the liquid solvent. The free energy
change, LAG for this process is
AG2 = RT!n (108)
where 2L is the fugacity of the hypothetical liquid at one atmosphere
f is the fugacity of the pure gas at the initial condition,
taken as one atmosphere
In the second step, the hypothetical liquid-like fluid was dissolved in
the liquid solvent. The free energy change AG2 for this step is
AG = RTlrry2x (109)
Using the condition of equilibrium i.e., AG) = AG + AG = 0 for the
dissolution process and the regular solution equation (105) Prausnitz
dissolution process and the regular solution equation (105) Prausnitz
.-e ..-.a fc lc.'._.-. ra. ^on fcr so -lubilicy of a .-.onpolar gas in.
.cor ,- so :-_'.'.ts:
--- e. (110)
lu de:c.i. e ?--r :..c r cr he -.yph-tical liquid stare, he
hyp.zh.si- c h rdud fugciy, 2 is a universal fruction of
-dc t .... To o", wan as.amed ch-t its value
i i f h ol t. ha r si.1ula..eou oly cstimatcc the
3 para. crsi -- 1-,. -r.c o..'-c .he a::iair. solubili3 y data for
:h_ partiul- i. \'-:c-, -olv~. by fit:-.g he dacz to equation
.-). The fi--..o o :his eCa zic:. aas cone i.n such a way that the
values o .- o;ey rh: c-rr>e- .Lin. c:c:eas -z; when plotted as
I- c fou c
a.. .. s:- redcc te.e-- u = fouc=a ecuation (1l0)
cor-rela:e th.e c.v il ble ol^ilizy caa cuire well for most gases
Prausn.itz za.c Shair (1), an a.c-;- t to correlate the
solibili:y of no;pTlar gass ir. polar solvents, rewrote equation (110)
in =ha folo:-ing form:z
< - J -
in,., = V O rooertie of colver.t) (112)
and th_ paa. ..=as V, 5, and pc.. ., only upon solute properties;
[h c'efore, t hce could be de:erm-ined fro, the solubilicy of the gi'.en
solute as in o:'.Inr sov.'er.ts. -hus, :h'.y could correlate gas solubilicy
cacr in pola-: sol'.en:s oD plo-_zir.l g soct-erm of ( In/) /V; '.. 6 .'
'-. and .cKe::a (32) hi' e presented a correlation of nonoolar
gas solubi :ies in polar non- sociated li.ceids. They used cnc
foliow.ing basic equacior. for which .as obtained by sec:ing
.. = p- i-. ecuaCion (92):
*E =- 2' 1" 1- 2 11 L r2 -- 1 I rd
I Lr2 1 2 1-212 v 2 I
0 1 0
-- rdr (113)
Ho.-.'e'r, tc:e authors cor.s:dered the electrostacic inceraccion among
r.-e polar -.olecules by usin' ch: Scock.yer pocencial, i.e.,
S 2 O (114
;where is pocencial er.e:gy of incerac: ion of polar molecules
-. = Lenard-Jones ninir.u.. pocerntial er.ergy
r(6,.:) = angular dependence of dipole-dipole inceraccion
It \-.'as sho.n :hat inucrion for-ces betrw.en the nonpolar ar.d the polar
molecules w..,re s-mall, and cheese were neglected. They r.ade che same
bsic assum-pcions as those used by Hildebrand and Scocc (22) in
obc-ining equcaion (105), and obtained the following equation for che
ac-ivicy coefficient of tcie soliue gas in the solution:
9 9 1 9 1/2
RTlny2 = L + 6 262(6 + A) ] (115)
1 1 2 1
- ,I IF r:( dydOd d 9I
S= dyd91de2d2 2 -1
V 0 0 0 0
and is a contribution of the dipole interaction of solvent molecules.
For the solubility of a nonpolar gas in a nonpolar solvent,
A = 0 and equation (.-5) reduces to equation (105).
Yen and McKetta used the two step process of Prausnitz and
Shair (31), described earlier, to account for the volume change on
mixing. A procedure similar to that given in reference (31) was used
to obtain the parameters V 6, and f2 for the hypothetical liquid
state. It was shown that the values of these parameters, as estimated
from the solubilities of nonpolar gases in nonpolar solvents, could be
used to predict the solubility of nonpolar gases in polar solvents.
Thus, they obtained the factor A as a characterizing constant for
each polar, nonassociated liquid. It was found that the value of A
increases with increasing solubility parameter of the liquid.
In a recent paper Loeffler and McKetta (33) presented a thermo-
dynamic correlation of nonpolar gas solubilities in alcohols as an
extension of the correlation developed by Yen and McKetta.
2.2.3 Ca-: tv Models:
Cavity models have been proposed in an attempt to explain the
solubility of gases in liquids. Since most of the earlier cavity
models are approximate in nature, they are only briefly mentioned.
The model of Reiss et al. (34), based on the ideas of the scaled
parcicle theory (35) and e.-:er.ded by Pierotti (36,37) appears to be
rore e:-.:cc and ha- s therefore been considered in more detail in
Sectr ion 2.-, ,.
It :'.'as LiliS (3Si) 'who f:rs: considered the solubility process
co a; made up of ci'o scep- (1) creation of a spherical cavity, for
w.- cr. .'or:k ts done -aer..s the surface tension; (2) introduction of the
solute mo-cule -r.co 'Le c-avity, h.'ich involves energy terms arising
out of intceraccios bec'.uen solv.'en and solute molecules. Considering
tl.cse energies he obtained he following expression:
inrc. = T
....re c = Cs,.:,ld solub.licy coefficient
C = surac cen-.sion
= er.er2y of in:eractzon
r = radius of c.Loe solute rolecule.
Elley (39,40,41) accounted for che energy and entropy of solution of an
Inert gas molecule e in wac-r :nd organic solvents by using the same two
consecutive sLeps as considered by 'Jhlig (38); however, he calculated
cr.e energy and encropy of formation of the cavity by the following
approx::i mac tr.er.odynar.-c relations:
..'here a. = r:.-.rr l e::-: .i:or. coefficient
S- compressb-llcy *coefficient
Iarsaz and Halsey (42), and Volk and Halsey (43) also assumed
the solution process to be made up of the two following steps: A
vacancy appropr-ate to contain the solute molecule is first formed in
the solvent; the partial molal Gibbs free energy of making this void
s G = H S Secondly, the void is filled with a solute molecule
V V V
and allowed to mix with the solvent. They considered the Lennard-
Jones-Devonshire model in which the solute is in the center of a cell,
surrounded by solvent molecules. By considering the free energy of the
system in the gas and liquid phases, these authors obtained the follow-
log -= c /kT + G /kT log(v/kT) (116)
x9 0 v
where L = minimum potential energy
v = free volume.
Equation (116) cannot be immediately used because the theory does not
give directly either G o or v.
Kobatake and Alder (44) proposed a Lennard-Jones-Devonshire
form of the gas cell potential similar to that of Karsaz and Halsey.
2.2.4 Scalei Particle Theory of Reiss, Frisch, Helfand and Lebowitz
This theory is a refined version of the cavity models discussed
in the previous section. However, it is discussed separately here
since it forms the basis of the theoretical approach used in the
present work. The principal advantage of scaled particle over previous
theories of this type is in calculating the free energy of cavity
formation in a reasonably rigorous fashion.
Consider a mixture consisting of components 1,2,.....m (the
solvent) Irto chts m:i:-:cjre a soluZe -molecule o. is introduced. The
-al 7-oleccles are ass.sed to possess hard cores of diameter a.l
i ,a .-.ssE-ing chat the total Cotential energy is the sum of pair
potcn:ials, cthe followinr.g e:-:ression froi chemical poteniial of the
SOlCte can DC oDtained (i5).
: r u. (r, ) o
= :Tin.. + -, dr g (r 5)4rrd (117)
S= r.Lu.br density of component ]
u (-,E) = pair wuse pocEnZ1al between soluce and solvent component j
g (r,c) = radial discribu:ion fjnccion becweeno soluce and solvent
S= a c-.:.-ging param.,:zr (seec ref. 45) which allows the solute
molucule to be coupled wi'h the solvency.
c.'e nonu h: only in:e'-act: cns baween :he soluce a and solvent or
sEec es j are Inv.'ol.'ed in :.'- ecuatio.. Ir. equation (117) the lower
ar.d upper integracion l-:..zts of S correspond to complete uncoupl:ng
a3n complete coupling of the soluce .molecJle, respectively.
The pair- poter.l:i u (r,) is assumed cO De of the following
form (see Figures 2 and 3)
u (r,.) = ub (r h) u (rh, ) (115)
j c h 1 s
7or con'.-'r.eCnc.e, we use subsc-:pc ai to denoce solute molecule
and subscip:s 1, .... r. to denote solvent species. This nomenclature
Ss noc the same as u.ed in che previous sections.
"Soft" Outer Part
Schematic Diagram of Molecule of
Pair Potential Between Solute and
Solvent Molecule of Species j.
'a.erc u .(',.. ) ard u .(r,s ) are respectively the hard sphere and
soft ,orcions of che potential bec een so!iuce ar.d solvent com.porenc j.
. a-d re charging -aranecrs for thc hard and soft poent.ials,
re pEC z v'.' .'.
u .r c / a = (119)
u (r) = 0
Sr > aj
.j(r5 ) = E a (r)
-s A jL
1 allowir.; .- o vary fro 0 co "charge up" the hard
pa.t of cth po:encial. The cerm. is the 'scaling' parameter (hnce
che na.c 'scaled particle cheery ). Thus wher.. Eb = aj the hard core
of sole a s fu!ly co;L;?led to Che rest oi che system. 5 varies from
0 to 1. ..e-, E = ., The soft part of che po-tential will be fully
coupled. .A value o- =.-ro -assignec to boch Eh and E implies that
solucv a is decoupled fror. che system.
In solute chemical potential :.a n.ow be written
h C '
= :i:T n.:..'. + i -v as (120)
S =1 h t-
L = -i J -I ^C a -n 2]h -s
a -3 s aCj O h tj s
The ch.. i' procedure involved in equation (121) is tantamount
to first introducing a hard-sphere solute molecule of diameter a
In evaluating g a solute molecule of diameter (-a ) is introduced,
and then scaled up -o its full diameter a .
To: a vapor and liquid phase in equilibrium
G = (123)
where and 1 are chemical potentials of the solute molecule in the
gas and liquid phases, respectively. The chemical potential, u can be
wr itren (45):
S= kTln ( + kTnfG (124)
where f is the fugacity of the solute molecule in the gas phase.
By equating (12C) and (124)
4G -h -s
ln k) +k InkT (125)
a kT kT
The .ole fraction is
-G -h _s
ln + I+n(kTE p.) (126)
x k kT j'
or in terms of partial molal quantities
In + RT + In( n.) (127)
x RT RT V
where Z n = number of moles in volume V.
From equation (0), we have
From equation (10), we have
where is the activity coefficient of solute a in the solution and
K is che Henry's law constant defined as:
lim f =K x
x -+ 0
x. = 0
Thus equcior. (126) can now be written as:
In(y aKa) = I ( Z n.) (128)
E'.'a luat ion o :2
-A ________3 T
=a cc h
M / u (r C )2
= d h r h g(rh's = )4r dr
5y applyir. >'-c treatment of Reiss et al. (35) to a mixture containing
. sol'.'er. components and assuming that the concentration of solute
is very low so that u = 0, it can be shown that
-h r a7
S= P Gc. (r)47 r-dr (129)
where G .(r) is the radial distribution function for solvent component
j around a solute molecule a when the two are in contact. The quantity
on the right hand side of equation (129) can be shown to be equal to
the work of introducing a cavity of radius -2 into the solvent, which
we term 2( -_ ). The word cavity here is used to mean a spherical
volume f.:-o which all hard core parts of solvent particles of all
species a.re excluded; i.e., the cavity does not i.:ply only exclusion
of solvent particle centers.
Lrbowitz et al. (46) have obtained an expression for W( )
from probability considerations, as outlined below.
From the relation between the probability of a configuration
and the work of creating that configuration, we have (47)
( -- ) = -kTlnP0( -, ) (130)
where P0( ) is the probability that there are no parts of any
a a a
solvent particle in the cavity of radius For 0, W( ) is
obtained as follows. Consider, for example the case of = 0, i.e.,
a point solute particle located at a point X. The nearest the center
of a j solvent particle can come to X is a./2. The probability that
particle 1 of species j (a particular particle) is in a spherical
volume of radius r is:
and the probability that any j particle is in this space is
For a sphere of radius a./2 this becomes
-F 7( I- ) Pj
Similar probabilities apply for other species. The total probability
that a molecule of any type is in the sphere of radius a./2 is:
I / 3
It shoId be nod be t tc.at the shell radius a./2 referred to varies wiith
the spec-es invol-'d.
Tre probabilicy chat a cavity of radius zero exists is then
3, a 3
The sam.e a.,er.:s aply for any .value of 4 0, so that
S l/ \ 3 a
P ) 7 - C -< 0 (132)
usir. ecquation (130),
a / + a 3 3
1.' = -kTln 1 r
-- ( 0 (133)
From therm.odyr.amic considerate ions, for very large r, the following
e:-:prcssion for c..e work of formation of a cavity of radius r can be
.-ri L n (3 ,35)
'.'(:) = : ,.-7 ,-T-.- 1 0 f(.. ,T) (13-f)
0 L r I J
:,.'hre P is the pressure, 00 is the ir.:erfacial tension between the
Eluid -nd a perfect rigid wall, ard 5 is a distance of the order of
for :-.e curvature derencence of the surface work. f(p T) is an
arbicrar,, fur.tion of density and cae-,pracure, not dependent on r.
For r positive but small W(r) is expanded in a Taylor series about r = 0,
1 2 3
W(r) = W(O) + rU'(0) + rW"(0) + K r r > 0 (135)
Since W(r) and its first two derivatives have been shown (34)
to be continuous at r = 0, the first three coefficients of the series
can be evaluated by comparison with equation (133). The coefficient
of the term in r can be obtained by comparison with equation (134).
( ) r 6( a 12C
kT -l( 1 3 2 1 C3
is,82 2 4 P a 3
2 2 +3 kT 2(
Evaluation of g :
g =, ds u (), (r,ah = a 4j' 4 dr
S] aj h a s
=0 a .
7g can be decomposed as follows:
_s = es s+ p (137)
where e va and T are, respectively, internal energy, volume and
entropy associated with the charging of the soft potential.
.:. a-ospheric pressure the rer.- in p" can be shown to be
srcll and can be neglaccted in co ..ar sor. to (36,37). The Ecnropy
of cnarg:-.g is negative because -te system becomes more organized
upon ch.arg'i. Slnce iC is difficult to make a quant iLati'.'e estimate
o: cn.s qou-.-ity, it 'll be neglected as a firs: approxniatior..
e can De obtained as folos:: Cc-.sider a shell of thic-ness dr at a
distance r from Le sol u:e molecule.
The r.u-ber of parcicls of solvent component j in chis shell is
g i.ven by
( --"dr).g (r)
Scan r.o: be r.Ticte:: as
g 2 = I u .'- -:.. .(r)dr (13S)
C.. .2 j o'. J.J j A
Evaluation ofr by the above equacion requires a kr.owlede of
S.(r), which is difficult to ;,bcir. for the systems studied here.
a.s 3 ficit appro::i;:.ation it ..ill be assumed chat solvent particles are
uniforrmly distribu:ed around h.e soljce molecule for r larger chan
a i. ,
.(r) = 1 r > a
z u .47r -dr (139)
Interaction Energy, u
The interaction energy of the nonpolar solute molecule in an
aqueous potassium hydroxide solution can be written as the sum of the
individual pair contributions u u 2 and u 3 where subscripts 1, 2
and 3 denote water, K and OH .
If contributions due to quadruple moments are neglected these
u u = U + u (140)
where u = nonpolar interaction
u = induced interaction between nonpolar solute molecule and
the permanent dipole of a water molecule.
i i u ai i = 2,3 (141)
where = induced interaction between the nonpolar solute molecule
and the electrical charges on ion i.
The nonpolar interaction energy between the solute molecule
and the solvent components is made up of dispersion and repulsive
energies. It will be assumed that for the systems studied here this
contribution is adequately represented by the Lennard-Jones 6-12 poten-
J 12 \ 6
u = 4 -- (142)
raj aj L r r (142
The following relation is assumed between pure component Lennard-Jones
parameters and those in a mixture.
/2 a 1+
e = ( )E.. = (143)
aj a a.j 2
The interaction between a single permanent dipole and the
induced dipole in a neutral solute molecule after statistical averaging
over all possible or-entaLrons is ( -):
(L,ind ) .1-
where is .-.e permanent dipole r:o.ent of uster molecule and pC is
the polariz bili:y of the soluce r.oiecule. In the present case, a
olucE r.olecule is surrounded by not one but several water dipoles;
therefore at 7r.,' instnrit of ci-e the dLoole induced due to all these
dipoles should 'b considc-ed. Tne e:-::.cc calculation of this ccntribu-
cion can be made only if :hc distribution of the water molecules around
cht neutral solute c-lcule is k:noi.Tr. Hoieo.ver, in this model the
dipole, ar assured to be freely rocatirg so that we can average over
all or-er.ca:ions of each dipole. Consiequercly, equation (144) for che
dipole-induced dipole interaction can oe used even in the present
s it uation.
The following assum poions are implicic in equation (144) for
the induced inceraccion (49).
1. The solute and uater -.olecules are electrically neural.
The permLanenc dipole of che i'ater molecule is characterized by two
equal charges of opposite sign.
2. The distance r bet.,een moleculess is large compared to the
separation of charges within each molecule.
3. The field produced by each molecule at the other molecule
T.-e soluce molecule is polarizable and possesses isotropic
polar abil ity.
5. Each dipole moment is that in zero external field.
6. The effective mutual potential energy of the pair of
molecules is the ensemble-average over all relative orientations.
The ion-ir.ducec dipole interaction is given by
(Ci / (ind)dE (145)
"Laii I (nd) (145)
wh-re f is the electric field produced by the ions considered at the
position of the neutral molecule, C. is the charge of ion i and (ind)
is the dipole induced in the neutral solute molecule due to the ions.
Assuming external fields to be small, ) is given by:
S d)= p (146)
In the case of a single ion
.. 4 i = 2 o dr
ai f-I a rd5
In the present situation, the field, is not due to a single
ion, but to all the ions present and therefore its correct value can be
obtai-nd only if the distribution of the ions around the neutral
molecule is known. However, we have assumed that the ions are uniformly
distributed around the neutral molecule. In other words there is, on
the average, a spherically symmetrical charge distribution around the
neural molecule. For such a char -ge istribution, The electric field
ar an- points Ir. n:-.e neutral moleculee can be obtained as follows (50).
Cons idr- a :po-.ct P ir. che neuct:- r;-olecu-le and imagine a
t.-in cor.e of solid angle .. and 'cr:z:-: ac P co cuc che sphere in
areas i.S r.d S (Figuree The cihtc eccion of che cone at 5S
coiC, or S- =
"1 1 coa;s
and if is the surface der.s:t-L of charge upon the sphere, che charges
upon S ana .S_ are
CO )C COD..
The electric field at point P is given by
cr- = o (14.5)
r cos r coD
Ths w-.e sce tha: for a spharically sy raiecrical charge dis-
cribjcior. around che neural solte molecule, the electric field
produced at any poinc in the Zoluce molecule is zero. Consequent ly
ce Ir.ccced dioole introduced by all che ions acting cogecher is
zero; hence chore is no contribution cue to che ion-induced dipole
irnc rac ion.
.1 :'.-.o che above a:rguent is valid for such an average
Figure 4. A Sphere Having a Uniform
Surface Density of Charge.
sict action, jt ar.y i..ta..t '.e shouic e::pect for a real solution chat
a sr-alsnl fIrce uct1.atinA field e:-..:cs at the point P in ;he
solute rm.:culc, so :hac at s-ch an instant the ion-induced dipole
(Ci,,ind- ) ?
= / raL = -(
I1s contrriobui1n to the inter.o!1cular poeer.5tal il i.'0)ays be
neati,,e (an atcractCve force) for r / 0 regardless of the sign
or -. The cor.crtlbutionr indicadi by equation (149) is presumably
small, and a ne:lected i.-. this world .
Thus ::e potential energ'e of interaction of the soluce molecule
u >212 p p,
Sj r U' I r
.: j=1 1 J JL \ r J r
I Ck 1
Substitatinr equation (150) in equation (139), we obra:n
1 L6 1g2
Ac3 n b& t c n s
L j ,1 3a1 9a 2
j=aj aj a3 l
.Ac a = e can be written as:
S ,- S 7I: 1 (152)
'a *=1* 3 .A.-.3c
EXPERIMENTAL APPARATUS AND PROCEDURE
A variety of approaches have been used to determine the
solubility of gases in liquids. A recent review on the solubility
of gases in liquids by Battino and Clever (4) describes these methods
in detail. Consideration of the existing methods of measurement of
gas solubility reveals that while there are many approaches to
measuring solubilities precisely, only a few methods are suitable for
determining very small amounts of dissolved gases. In particular the
very accurate manometric methods (56) cannot be applied when the
solubility is as low as those experienced in the present work. Gas
chromatography is particularly suitable for the measurement of low
solubilities; moreover, it is rapid and has the necessary versatility.
Sample size can be varied to a large extent, and the dissolved gas
can be stripped from the solution and concentrated by a suitable
technique before analysis.
Paglis (51) and Elsey (52) have employed this technique for
the determination of dissolved oxygen in liquid petroleum and lubricating
oils. Swinnerton (53) described a method for the determination of
dissolved gases in aqueous solutions based on gas chromatography.
Gubbins, Carden and Walker (54) made important modifications in the
method of Swinnerton (53) and obtained gas solubilities in electrolytic
solutions. Most of the data reported here were obtained by the method
of Gubbins, Carden and Walker (54) (henceforth called Method I),
whereas some of the data for systems exhibiting very low solubilities
were obtained by a modification of this method employing a concentration
.-chiqaue (ie:'r"hod iI and III).
Per: in-Elmer gas chromatograph ecuippec with thermal conducti-
vtcy a.d fla-e ionization detectors was used in this work. The output
s-g..al f:.-. t-.e detector was recorded on a 1 m.v. Sargent recorder
(:odel SR) provided with a disc integrator (Model 204). All analyses
,:,re r-ad uinr.; c.e tharial conductivity detector. Helium was used as
the carrier -gs rfr all solute gases except hydrogen and helium; for
chcse niCrogen Wcs used as the carrier gas. A gas flow rate of approxi-
mae IY 30 -.1. per minute w.4a used in all the measurements.
Tne solution sunple to be -..alyzed was injected into a glass
acripping cell -uuside thL chromatograph (Figure 5). The carrier gas
flowing though che sample line of the chromatograph was diverted
chrou-. he stripping cell and its associated equipment before re-enter-
:ng '-.e a2-.ole column. The glass cell had a medium porosity glass
frit (fine frits were found to give rise to excessive pressure drop
when wetted) and was equipped with a rubber septum for the injection
of the sample, and a teflon stopcock to facilitate draining of the cell.
Gubbins, Garden and Walke: (54) found that a cell having a volume of
7 ml.ws most satisfactory for general purposes. In this work, however,
attempts were made to increase the sensitivity of the method by
increasing the size of the stripping cell to accommodate larger samples.
Increasing the diameter of the cell led to excessive broadening and
tailing of the chromatograph peaks, apparently because of mixing in
the gas space above the liquid. It was found that a stripping cell
about 1 cm. in diameter and having a height of 70 cm. could be
1: O-7L -
'. ----O, i u )Ld <-
!! -.. .. \6 < _C
ajccess:ully employed to -ncrease the sensitivity of the method. It
~:as la-er found that Swinnercon (55) had also used a similar type of
gla cha--ber in his work.
A solution sample of known volume (20-40 ml.) containing the
d-ssolved gas was injected through the rubber septum. The carrier
L-s :a diipCr.F d by the fritted glass disc into a stream of fine
buboL:e and stripped the dissolved gases from thL solution quickly and
conop!cey. Before returning the gascs to the chromatographic column
the-, wc- poL--d through two drying columns containing Drierite to
climinr.c w.t:- vapor, followed by stainless steel coil immersed in
a .'a:er batn to bring the gases to ambient temperature before return-
ing :hem to the column. This was particularly important when deter-
m-r.inS solubility at very low or very hign temperatures, since the
sudden cooling or heating of the gas stream otherwise caused base-
lin, ir.ntability. Care was taken to keep all tubing of small diameter
to prevent back mixing and broadening of the peaks. The drying columns
were 1 c.... in diameter and 30 cm. in length. The use of rubber tubing
was compl-,ely avoided to minimize contamination by air diffusing
This technique of introduction of the gas sample by stripping
from a solution results in slightly wider and less symmetrical
chromacograph peaks than those obtained when a gas sample is injected
directly into the chromatograph sampling port. However, it does not
sacm to result in any loss of accuracy or precision. The amount of
the dissolved gas was obtained by means of an appropriate calibration
For these gasez whose solubility in water is accurate-y known
at 25 C, the calibration factor wa, obtained by carrying out the same
procedure on a water ac.ple. When -his information was not available,
.n accurately known volume of pure dry gas was injected directly into
the chromatograph to berve as a sctanard. The relationship of the
amount of dissolveCd as to the instrument response was checked and
was found to be linear within the limits of the experimental error.
Large discrepancies often e:.-ist between the solubility values
reported by different workers. Couk and Hanson (56) have listed the
following factors which need careful attention in order to minimize
1. Complete degassing of the solution
2. Ascer-aining the true amounts of gas dissolved
3. Attaining equilibrium
4. Making certain that transfer of the gas from the primary
cont-iner to the apparatus does not involve contamination.
Each of zthse factors will be discussed with particular reference to
the procedure adopted in this work.
Dezassing the Solution:
Solutions were prepared from specially distilled (all glass-
teflon still) and degassed water. The method of degassing water was
similar to that employed by Clever et al. (57), and consisted of two
stages. The first stage involved boiling the water to evaporate a
portion of it and to remove perhaps 90% of the dissolved gases. Then
in the second stage this substantially degassed solvent was agitated
with a magnetic stirrer under vacuum. Po-a3sium hydroxide pallets
used for prepa-:rcg cqueous solutions w-.cre Baker analyzed reagenc grade
and concained a r.a:-:-Li.um of 1. K)CO otccles concair.ing pocassium.
hydro:x:-de solution i.ere t cf-Ce ..ltch glass bulbs containing ascarice,
.o t.-.ac a entering :he bottle ac h c inre of withdrawal of soluc.ons
.'as ifre fro. carbon dLo:-.:de. Sc-u:.ions prepared in chis Ijay uhen
injected zr.co che chror.a:og-aph af:er equiloLbrallon wi:h che carrier
gas. gave no P--c:.
fCjraci on :: hoc:
S-:uraSed soluctons o nf :e as in cha electrolyce tijre prepared
by tbbb!i.- -he n J by means of a mediun porosity glass frrL through a
set of oresa:Lra:ors and then Lhrough che sa:urccing vessel. The
L-ura r ig vessel was a 3 neck-:, 500 n-il. round boc tom flask. Tne cencral
nck;: accomod:ed a c-flor. clad grour.d glass rf cL:ing in which in curn
w.as inscAlled the glass frL: for buZbling che gas. Ti-. other to
opening i..are u.ed co \.'icdraw saIples and as an exic for che gas. The
gas leaving he saLuracor- bubbled c.rough a glass ces: cube containing
Lch sar.:e soLtc-on as in che saLuracrng vessel co avoid any contamination
due co aLmosphlrIc air. Srples er removed by nmans of a syringe
frttcd :o a :talor. needle dipping in che electrolyce by means of a
HamilLon ctflonr valve.
.::ar.n-meno of equilibriuc \as chec':ed by withdrawing samples after
difference nrcervals of sacuration Lime and injecting into che scripping
cell. The equilibrium solubility was taken as the value measured when
at leasc 3 samples withdrawn at different times gave the same peak area.
This process w-s repeated at different gas flow rates and it was found
:ha: 2as flow rate did not affect the equilibrium solubility value.
However, to avoid -oaming in the presaturators and saturating vessel,
a gas flow rate of about 30 ml. per min. was used. At this flow rate it
took about 25 min. to attain equilibrium.
The possibility of supersaturation was guarded -gainst by the
following procedure. A sample of the solution through which solute
gas was bubbling was removed and analyzed. Bubbling of the gas was then
stopped, and the KOH solutionn maintained under an atmosphere of the
solute gas. Samples of the solution were analyzed periodically, and
the results compared with the original values. No measurable super-
saturation effect was observed in these experiments.
In order to investigate the relative importance of surface
effects in the saturation phenomena, a relation between the solubility
of a gaseous solute in a liquid solvent for a curved surface and that
for a planar surface was derived. The complete derivation from the
appropriate thermodynamic relations has been given in Appendix 1. The
ratio of the solubility on the curved surface to that on the planar
surface was calculated by means of the relation obtained for the 02 H 0
system. It was found that surface effects were negligible except for
bubble radii below about 10 cm. Consideration of the numerical value
of the quantities involved in the relation for surface effects
suggests that the error will be approximately the same or smaller for
strong KOH solutions and/or higher temperatures.
Transfer of Samples:
Samples of the saturated solution were withdrawn by means of a
gas-tight Hamilton syringe vith a Luer lock to which was attached a
Hamilton teflon valve also with a Luer lock. While withdrawing samples
from che saturatin.g v'.'eseo, this valve fitted on che valve attached
co :he teflon needle dippir.g in t.ie soiZiton. The samples were
wic~d--awn e:.:c-enm, sloly lowly so ha- aL no sCege of Lhe sampling process
*.'as the flask or syringe placed r.der reduced pressure. Several
samples were taken and rejected before the final samppling was made.
.s a chec. on che procedure of sampling and degassing, blank samples
constising of KOH solution saturaced with carrier gas were injected.
:'o peak was obtair.ed, ir.dica:tng char negligible concaminaLton with
atmospheric or cther gascs occurred.
For ex:perimencs a: temperatures of SO C and below, two pre-
sacurators conLaintng tch KOHr solution b:udied were used. For the
e::periment: at 100'C additional prescaurators were necessary. To check
chat the solute gas srea: contracting th- sample was fully presarurated,
samples of the c:.it gas were analyzed for w.acer vapor. In addition,
the concrrat-on of KGOH ir. the solution conctaned in the saturation
flask was che-ckd ac che end of cte ex.:erimenc.
A: tmpe-rarures of iOOC, concencraced KOK solutions rapidly
cracked gliss frirs. A. this temperature refion frits and teflon
presacuraLors wee- used. The whole assembly, consisting of presacura-
cors ar.d rhe saturating '.'essel, w.as completely ir. ersed in an insulated
rtanless sceel water or oil bath. T.e temperature of the bach was
controlled to 0.05UC by means of a proportional temperature controller.
Th.rrmnomecer: checked for accur:- y against -ES calibrated ther-.ometers
were used for measuring the tce..perar--e.
Xethod I was used to measure the solubility for systems where
this was above about 10- g.mole of solute gas per liter of electrolyte
solution. However, the solubility values for SF and neopentane in
eleczrolyte solutions having more than 20% by weight of KOH were much
less than 10 and thus could not be measured accurately by method
Therefore a modLfication of the method was necessary. This consisted
of incorporating a concentration technique in method I as explained
The principal difficulty in extending method I to lesser
solubilities was that samples larger than 30-40 ml. could not be
injected without loss of accuracy, because of broadening and tailing of
peaks. his difficulty was overcome by concentrating the stripped gas
by means of low temperature adsorption (58) before it entered the
chromatograph. This provided a means for stripping larger volumes of
saturated solution of the dissolved gas and permitted the rapid intro-
duction of the concentrated gas into the chromatograph.
Figure 6 shows a schematic diagram of the apparatus used in
method II. The saturating vessels (not shown), the stripping cell and
the drying columns were merely enlarged versions of those described
in method 1. Solenoid valves 1 and 2 were set to permit helium carrier
gas to flow directly through to the sample column of the chromatograph.
Solenoid valves 3 and 4 were set to permit stripping helium from the
drying columns to flow through a concentrator and a moisture trap and
then to the atmosphere. The concentrator was a 1/4" dia., U-shaped
copper tubing containing a 6" length packed with activated charcoal in
its central portion to adsorb the solute gas at liquid nitrogen tempera-
ture, while allowing the stripping gas to pass without adsorption.
Stripping helium was first purified by an ETI Standard Laboratory
Model helium diffusion cell and then passed through a 6' long 1/4"
dia. copper tubing kept in a liquid nitrogen bath to remove all adsorbable
impurities. It was then passed through the stripping cell and the
drying column. The stripping gas together with the stripped solute gas
flowed through solenoid valve 3 to the concentrator which had been
immersed in -iquid nitrogen. The stripped gas was adsorbed in the
concentrator, while the stripping helium passed on through solenoid
valve 4 and the moisture trap from which it was vented to the atmosphere.
The moisture trap which was a test-tube immersed in a liquid nitrogen
bath was necessary to guard against the possibility of diffusion of
atmospheric moisture into the concentrator.
The saturated KOH solution from the saturator was injected
in any desired a-..ount into the stripping cell and the solution allowed
to strip for the desired time (usually about 5 min.), the concentrator
having been previously cooled to liquid nitrogen temperature. At the
end of the stripping process, valves 3 and 4 were set to stop the flow
of the stripping helium and to connect to valves 1 and 2. The liquid
nitrogen bath was removed from the concentrator and replaced by a bath
of boiling water for a specified period of time (5-10 min.), which caused
essentially complete desorption of the adsorbed gases. Valves 1 and 2
were then set to direct the flow of carrier helium through the concentra-
tor and the dissolved gas sample was swept into the chromatograph for
analysis. The calibration factor was obtained as in method I by
follo-.-ing che above p.ocedu-re and using scar.dard v.ol L-.e of wacer
satu:-aced -..'ic. c.e solute gas instead of 0OH solution.
I: may be r.oced .hat che length of the packing in the concen-
tratco ar.d che chro.-cog--aphic colu-.mn size should be carefully chosen
so as co avoid base- line Lnstajblltcy which .ay otherwise occur because
of sudden fLuctuacio.ns ir. che carrier gas flow'. r-:e on swiching che gas-
scream co pass through the con.cOnrator. The packing in the concentra-
to:- music be suitably chosen so chac it adsoros che soluce gas completely
and rev'.ersib 1y. .s a check on che adsorpcion process, the following
e:-:parinrnt was made. A sample of pure solute gas was injected inco the
scripping cell while che helium carrier gas was allowed to s.we'p it
into che- cr.roma ograph through che concentracor without: being adsorbed.
The same cu-nt icy of the g.s sample .was gain injected while the con-
cenLraDar had been i-mersed in the liquid nitrogen bach. No peak was
recorded. Carrier helium o che concentracor w.as then stopped and
direct rec :y to Lhe chromatograph. The solute gas in the concen-
crcaor was desorbed by the procedure indicated previously and swepc inco
the chroma:ograph. peak was obtained whose area was equal to chat
ob-air.ed ,wichouc adsorption withinn the limits of experimental error.
This showed cha: adsorpcion of the soluce gas was complete and
Si-.c the method is based on low emperacure adsorpcion it
cannot be used for gases which ooil ac ce-perazures lower chan that
of carrier gas. E:-:remely pure stripping gas is necessary in chese
e::periren:s because very slihtc concenZrations of impLrities become
concentrated .. th:.e concentrator. I. -od II was successfully u-ed for
the measurement of the solubility of 02. However, an error in the
saturation procedures was discovered after these measurements were
made. Therefore, they were repeated with method I.
The above procedure was not found to be satisfactory for SF
or neopentane because the activated charcoal used as a packing material
in the concentrator adsorbed these gases irreversibly. During the
course of a search for new packing material, it was found that SF and
neopentane could be trapped completely and reversibly at liquid
nitrogen temperature with a column containing no packing. As a result
no heating of the concentrator was necessary to recover the trapped solute
gas. Thus method III, described below, could be used for these measure
This method is very similar to method I. A schematic diagram
is shown in Figure 7. The stripped gas, after passing through the drying
columns, was directed to the concentrator, which was very similar to that
in method II but did not contain any packing. The gas stream from the
concentrator passed through the stainless-steel coil immersed in a
water bath and returned to the chromatograph. The following procedure
was used to make a measurement.
KOH solution, saturated with the solute gas, was injected into
the stripping cell, the concentrator having been previously cooled to
liquid nitrogen temperature. At the end of the stripping process
(usually 5-10 min.) the liquid nitrogen bath was removed, and the
condensed solute gas rapidly evaporated and passed through the chroma-
tograph to give a sharp peak.
There was a slight base line disturbance when cooling of the
concentrator by means of liquid nitrogen was started and again when
the liquid nitrogen bath xas removed; however these disturbances died
ouc almost instantaneously and did not affect the results.
The follow-ng equation was derived in Chapter 2.
P2 = K2Y2x2 (153)
Let p' = vapor pressure of water at 250C
p = vapor pressure of KOH solution at TOC
x2(P) and x2(P-p') = mole fraction of solute gas in water at P and P-p'
solute gas pressure, respectively.
x (?) and x:(P-p) = mole fraction of solute gas in KOH solution at P and
P-p solute gas pressure, respectively.
P = K22x2(?) (154)
x() = --P (155)
For fairly low temperatures where p and p' are small K2 can be
considerconsonstant with respect to pressure and
x2(P-p') =- (156)
L' a si :T r a SSu~ ?cion regarding K. in case of KOH solution,
From (17) and (-I)
0 0, ,0
: ( P- p ) ::: (P) -A
.7 ?-*) ?-p -:. (-) =
.'h;e and A are peak areas for .'azer
..,( ) .?)
and KOH solution resoecci,.'ely.
The experimental data for the solubility of various gases are
presented in Table 1, where activity coefficients of the solute gases
in KOH solutions have been tabulated. These values have been calculated
from the experimental results of the solubility of a given gas in water
and in KOH solutions by means of the following equation obtained from
equations (22) and (23) of Chapter 2.
2 x (161)
x2(P) is the mole fraction of the solute gas dissolved in a
KOH solution in equilibrium with the solute gas at 1 atmosphere partial
pressure, and is calculated from the experimental measurements by
using the following equation derived in Chapter 3.
o P o)
x2(P)= x2)P 0 p p
Vapor pressure data for KOH solutions were taken from International
Critical Tables (59).
In all cases, the solubility values are the mean of four or
more replicate measurements. The absolute accuracy of the reported
data depends upon the amount of the dissolved gas present in a fixed
quantity of electrolyte solution which, for a given gas, depends upon
the electrolyte concentration. Considering the errors involved in
saturation of the electrolyte samples, transferring of the samples,
chromatographic analysis and KOH concentration measurements, the
0 0 0 0 0 0 0
0 0 3 i '\ 3
0 L-\ CT\ C\ --CO
1-4 cn c m m
0 UL\ 0 0
0 -- 0 C Lr\ ON
0 r .\ N- co --4
r- u L\ 0
0 L\ 0 0
0 CO 0 0 0
O i\,D 03
0 1 0 0
0 C 0 \O n '0
0 L, 0 -0D 0
S O vC6 C0 0'
0 OC .- .r\ t 0
0 0\ 0 0 (-0 -i \.O
0 0 0 0- 0 0
0 0 \ 0 C0 N'- Cy
0 xT\ C(- '0 0 0
7- .j -~ z LIN
C, _-. 0 -- 0
0 0 -0
0 .CZ) 0C 0
3 C\ LF 0
0 r C\ 0
o m '- L\
0) C. O C.
3 C0 r -
o3 o >- N-
03 O 0 000
00 C.\ 0 I0 c3
1 o ,- .- o o CO
C O c 0 O 0 0o
S.- .- i i (j
c00 0\0 0 C.-
cn 0 C XC) 0 ) C\o
0 0 o 0
O 0 O O 0
.0 .D r . 0 0. . .
CC) 00 N c- N
o -- c o 0 c - n 0
0 .' 0 O O 0 0 -
- 0 -3 \ CO Lr- 0 cO G CO 0
C O O O
CO 0 L \ o0 C) L\O 0 0
0 0 \ C\- '\ 0 tO r\ O
0C C-c-C -ot CC) o o.-
D0 r00 00 tOO
00U O ('t 0 O XC C
0 -C 0 CU 0 0 o
-- 0O O O 0O O \ OC M O
S0 0 0 00 0
0 G N c\ 0 X o i0 C) Nc
co! 1 n
O 0 00 00 CO N 0
0 0 0 O L0 OX C) O1
OO 0 N CN\ 0 0 L C\ 0
O OC 0 0 0 O0 uV4Z--
^u o c- v:o -" c c 'c (^
-- --. '..
C -- .I, CG
- C- 0
- .., -.
*^ Cj -0 L
C'. _- 0
.J L [-, u-
overall accuracy of the reported results is estimated to be about I :f
for solute gas concentrations up to 10 g.mole/liter, and about 61
i? the concentration range of 13- to 1C g.mole/liter. (See Appendix
2.) Solubility values for pure water lie in the range of 10 to
10 g.mole/liter and the results reported here in most cases agree
with the literature values within 20. This supports the accuracy
quoted above for the solubilities in dilute electrolyte solutions.
The estimate of the accuracy for the concentrated electrolyte solutions
(dissolved gas 1C-5 1C0- g.mole/liter) is difficult to confirm
because few reliable data are available. However, the agreement between
the solubilities of oxygen at 25 C obtained in this work and those of
Davis et al. ('C) and Gaffckan (61) (discussed later) suggest that the
accuracy estimations are reasonable.
The range of temperature and potassium hydroxide concentration
over which the solubility of each gas was studied is shown in Table 2.
The activity coefficients of the solute gas at each temperature
have been plotted on a semilog paper with abscissa as potassium
hydroxide concentration in g.mole/licer, and Figures 8-14 show these
plots. The semilog plot has been used since most of the electrostatic
theories of salting-out (Chapter 2) predict a linear behavior on such
a plot at moderate electrolyte concentrations.
Comparison of Results:
Measurements of the solubility of oxygen and hydrogen in aqueous
potassium hydroxide solutions have been made by Geffcken (61) at 15
and 250C for the concentration range of 0 to 1.4 molar, and by Knaster
and Apel'baum (62) az 21, 45 and 75 C for concentrations up to 10 molar.
E.LP7RIME.C ..L YTE'MS ..:;D CO:-DITIO';i
'LCn. tcLuLC. C 6.:ncc,. 'J.i
c- I0 -6
2, 40, C0, u C 50
2.5, 4T 0O, SO 0 50
2, 40, OC, so C 50
.l4, -0, GCu, Z 0 30
2-,, -,, go, S o rc
25, O4, C0, 50 0 30
: ,' --u, CC "" .0
:5, :-, co, So -c
U d 0 12
KOH Concentration, G.Mole/Litre
Figure 8. Activity Coefficients of Oxygen.
4 8 12
KOH Concentration, G. Mole/Litre
Figure 9. Activity Coefficients of Hydrogen
? / n 25 c
< L:6 ho
r/ 0 6o
I 0 80
0 2 4 6 8
KOH Concentration, G.Mole/Liter
Figure 10. Activity Coefficients of Helium.
:KOH Co.ice.n tcion,, G.ol e/Li-er
Figure 11i .Ac i'.'ic:, Coe f iciencs of Argon.
I I j
1 1 -
o 2 4 6
KOH Concentration, G.Mole/Liter
Figure -2. Activity Coefficients of Sulfur
A c 6 & 1o
KOH Concentrtcion, G.Mole/Litcr
Fire 1, Ac;ivit.y Coeffic en s of 1Mechane.