Title: Intermolecular interaction for polar and nonpolar molecules correlated with properties of gases
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Title: Intermolecular interaction for polar and nonpolar molecules correlated with properties of gases
Physical Description: Book
Language: English
Creator: Bae, Jae Ho, 1939-
Publication Date: 1966
Copyright Date: 1966
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Bibliographic ID: UF00097845
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000568445
oclc - 13660342
notis - ACZ5179

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INTERMOLECULAR INTERACTION FOR
POLAR AND NONPOLAR MOLECULES
CORRELATED WITH PROPERTIES
OF GASES







By
JAE HO BAE


A DISSERTATION PPE:ENTFD TO fHF Ir.R.A.UATE COIJNCIL OF
THF LINIVIRirTY OF FI.COPJD.
IN PARTLY FULFILLMENT OF THE F.EQULIPF MINTS FOR THE
DFrREt OF OCT R OF PHILO'OPHt"









UNIVERSITY OF FLORIDA
August, 1966


.Iiiii


1111




































To il,. PFarent-















FR.EFACE


..ince rt e stZtbl ii rnenr Bt tri evruiri t f t' thi- ccIn urt'y

ct'-mi: :c l ,'hgl1eeri:r g has rst'a.: 11, t p.cL.'3 'vith' t :

1. gre.-- iin other' bLe'.n er: .- ,- n.e and e.r in:' ring.

TI ad ,'arcts. in rmi: .." l-ar ph .3:,S. .s p'.t i.t :',hc cI e -'T nt

r.:l ..:' lar co.' eri. rs at. tie r itp'- al of che li'c l e1 -urineei.

T1'iu. the; ar.: able .to oi ;te m-acr., :sc' ic pr.o..e r.-.:s l '

... :,ta. t-:-e t rhi .:r,:zcc.pic moc. iecl.al p}r : pe r ic r, to obtain

r, 13n :, U..f l .*, :. re' lationrs a r:i bet rer ..lesign pr',ce,. r-'; s that

cat be; u til :e in1 rt-ei c i-a illenging t :-.; T .: ta.i .-.r i.al

r, eci:.?h- Ti. L e nab e.? r.temrr to inter'prr,:- t al l tle tc le rid,:.'rani.L

a3nd tran..OL'ct p ,rc.p tte.i of rn'.rerial. in r me"t.s of inter-

II,:,Iee' a. forced. In idc- the ir teiir ile ,ula r f -'c: play

highll,; impi.rr.rnt role- in th i ar'sea. ielu.ih ha. bo-rn I:noi.m

b. t m ,.'n lIas --et. to: be I:rn .'r .aicit,: tihcse irite-rmnoleculai r force .

In this wc':,i e .are primarily concerrued iith ti- e

F:r-dicrlton of pro.-erri .-, of p:i' ar nil nronprlar pgazes by

means of int--nri rlec .ulart potential ene- gy- fir cti n- In

Chapters I a.nd II tlhe hardl.-cor loe rse pot.ctntial is ill.resti-

.ate.- for nonr:rlar rrnolec.ulcr in an effort t..:, firid a potcritial

rim:-del vi:-icli can be applied. to pol,-at.omi as r'.ic1 as moioatornic

milecultes. In Chapters III through Vr tlhe aniSe-a''eraged

potqnt.ial rnod.wl with the temperat.ure-d'epcrndnt paramnetors








l're enri plo:,'y'1 ] tr cr':c '"elIate. pFc rop .tiel of,~c c pcI ar Ea 3 z s a1t,]

miC:-:t'.res crn tain rng polar cClriprinle TheI parlr:aeitePs' o1

thi. model are estimated from the cri ic al i.e-n;ip er i.tliire

and poliri:zabilitiee. Ini MCaptier VII r:jariport poC .'artie:

of gaecz. are predict ted from ,satut .ed i:) i -ii-nsi i.

t.ihrcl.ouh rhi e prin:' ipie of ccOrre; pcOiirnig -3 ;:.

The rc.adc1e 1 assuritd 1.0. be n :. ii':, i. ti he u-hbje.: .

It iz intended that each cha1:ptrlr i-. Complete inl it ent~ii e,.

Therefc're rno e.'iaustLi tie v-'.. ie i included. In t3.:,

chapter ha, ij_.3 own brief intr riduc tion at the btegl'in iin

and full discussion an-d c-oncln. usiz n c, ih the Cou.! ,.:: of rhe

chapter. Howve'.'er, all the .:apcers are- co:, ely c rlace] t'

one another

The authi r wiz-hes to' e::pre.s- h'i3 app:re:iatiorn t'

Dr'. E E. Guhbinr for zervinLw .- thre ccmmuTiitte.e. He i1

espe icilly indebt.:d to Dr. T. [i. Reed i.'hro dir;c..ed r this

reseamrcn ald se'r.ved as the chair.ian of rti: sup,'is-visor:,

c.rnittt. ee. He is also recponnible for ilf luencing the

author to idnrler in the junCle of "Nolecular a'iherrmic il

Engineering .



*Jae HTo Bae





.:iii














TABLE OF COIITZIITS

Page
FFEFACE . . . . . . . . . . . .i

LIST OF TABLES. . . . . . . . . . .. .. i

LIST OF FIGURES. . . . . . . . . . . . 'viii

LIST OF SYFI OLS. .. .. . . . . . . . . . i.

AL ST ACT . .B . . . . . . . . . . . ii

C iA PTER

I. KARPS-COR:E M.O'RSE POTENTIAL FOR TI-E SECONiD VIRIAL
':'EFFICIEI TS . . . . . . . . . . 1

II. SEC'jiiD VIRIAL COEFFICIEIT O'F BINARY GAS MIXTURES
Oil Tr-E HARD-CORE I IRSE P'TEliTIAL. . . . .. . ..

III. AilGLE-AVERAAGE'i PAIR-POiTEITIAL ENERGY FUNCTION P R
DILUTE POLAR GAS PROPERTIES. . . ... . .. ..14

IV. TRANSPORT PROPERTIES OF POLAR-iIOIOFLAR GAS MIXTURES .26

V. SECOilD VIRIAL AUD JOULE-THONSOIl COEFFICIEINTS OF
FOLAR OASES. . . . . . . . ... .. 55

VI. ESTI'RATIOi: OF 12-6-6 POTEIITIAL ENERGY FUIJCTIOII
PARAI'ETERS FROM CRITICAL TEMIPERATFURES AlND
POLARIZABILITIES . . . . . ... . . 44

VII CORRESPONIDIING STATES CORRELATION FOR TRAJISPORT
PROPERTIES OF GASES. . . . . . . .. ..51

APPEDITIX. . . . . . . ... . ... . .. 91

BIBLIOGRAPiHY. . . . . . . ... .. . . ..97

BIOrGPAPHICAL SKETCH ... . . . . . . . 104














LIST OF TABLES


Table Page

1 Parameters for the Hard-Core iH r.ie
Potential . . . . . . . . . .

2 Ptential Parameters for Ilonpolar J icllecules . .5

3 Critical Voll.ures and Pclarizabilities . .. ..5

4 Cross Secona Viri'l Coefficient.s ,f Einary
Gas i:-:ture . . . . . . . . ..

Parameters for the i2-6-6 Potrenti l Dertirmiined
from i 3osities. . . . . . . . .

6 Second Virial :Cefficient for Polair Gase. . .

7 Empirical and Trheoretical Dis.persion
Attraction Con tants . . . . . . .

9 Fotential ParametnSers ard l.IclecEular Constaniit
for olicnpolar Hoie les . . . . . . 70

9 Viscosities of Binary iixiture:.. . .. . ... 71

10 ['iffusi-on Coefficients ic EBinar' Mii::t'.ires . . 9

11 Potential Parameters for the 12-6-6 Potential
Determined from Second Virial Co-efficients. . ..32

12 JJoule-Tnomson Coefficients at Zero Fre;s.sure. . .83

15 Empirical and Estimated Values of c*,l-T. .. . '4

14 Empirical and Estimated Potential Parameters
for Polar Gases.. . . . .. . . . ;

15 Second Virial 1,efficlents .of Freon.. . . ....0

16 V'iscosities of Freonr . . . . . . . .;7

17 Liquid Density Parameters. .... . . .. .









LI-'T OF TABL.E..( COTlI'INTiEDI


Table tI

l ReIJuced Viscocitie of .:iSipie ,-.7.e ~. . . ,;-,

19 Fe.duced [D i 'f i'.'i :ies : .inple Gases. .. .















LIS T OF FIGUREt'


Fig.urPe P- Fe

I Vi. ':,altie^s f1'or Hloa arnd .:-._. . . .. . ,-,

S'Vis.-oslcie.. for HI HI. HC1, IH .-c H- -.H an.:
I .'H C . . . . . . . .. .

2 Vi3c.aer. Ltie-, fcr CH ''1 i'.' :. anu CH 3H. . 2.

STheYr, .il Diffuei-r, Fj t,. ,-,r f,.- ,- '-~- H '.rvim.

T "Lei-rmal Di'fusi.nri FEcct rc, ( r S30-+i-) I ',':tem. ,

C Tl-ermTal Diffusi,:.n- F.-icr.ors, f.or.I A -r+HC-lt and
Ile+ H-I C .tem . . . . . . 2

7 u:-;.':onJ irial Coeffi ci inr- f.:.r ih.,. CO ? n.1
H 2 .. . . . . . . . . . "r

S Se,':*.:d .'i\irial C..eff ic.kiert-P.F.:r C'H.UiC'HO.
I CH-13 2I CO ar. CH CIi. . . . . . .

Sc.'.nld Vir'iil C':,effi ll eri for ,.Hr 3 1 ar-l
.CHI . . . . . . . . .. .1

10 Disper.AioDn Atraction Cornstarntrs fo Fl..iar
G'C s . .. . . . . . . . 4-


,viii














LI:'T OF .:1 [."iOL..


' Fiiliu.: cf cph: ericail IrEe jri tri-e h '.rd-,cr? losee p'oten1t i l .

a* Relc...ed c ,e r 'Jiu, d.iefined L., Eq. )

a r .' ab-e Lefined L' E'. ( '

A V .' i:b :l efine-ti ,'. Eq: i. -'I .r i''4 I.

Vi la:iri:'le d l:efic- e b1,. Eq. l l 1.



r *i3i/oline defined P.y Eq. i?..

5 .ec.'.'nid '." i'iil coeffi' : i nt. ..-L&L,cri.C :'i t- r. efer tC.


B V:ariable defiti-lj r'.r Eq i 17 .

E F:.zsiti': e c.:ontgrant defi-ned t.,', Eq. I ,i.

PB tedu-ced second "i,' ial *:,,efficient. 3ub.z:'r-irLts refer
c. temper .it'.lrE-S .

c ,'cnCtant in th,- !i'rd-c 'io'. poter t al mncldel.

'c. Icl: rioa heat capi.city.

C' i-.ola i heaI t capacity, at ; .ro pressure.

D Dif fusion ccef ficiernt

t Re..- ed J. d flififusi-.n coe, fficien! t Jefinec by Eq. 5 i

D Fe,:lucoca diffusi1.n coefficient defined b; Eq. (62i

fl Factor defined by Eq. (25).

fr Factc.tr defined by Eq. i26.
g i:: Function defined by Eq. (121.

k Boltzman constant.









m ittr-cttC tl:n ex : ocrent .'f 'thI- Cin- por nit ial F.odii.Uc 'J
m--, lecular ',: ic lit inr Eq. (4.).J

M [,: i ec ularI weilh-,t.

rn Rep].l ic, ri e:.Fpiinent of th n-m p t.cri, tial Mb ..imurn
riiutber rf .-u li .at i n ini E:i i I.

S a *d ra n i.a r .

P F re ra.u. ;'e.

', V' ,.a l.ab I '.led -tiiied in C i. a rpt.e' r I'.

C IrnteimcL.].e,;ular s.?p.'-.r :'i.n.

i1 Inrte ,riC(ie? 7i.i e ir .epcitrat i.:in 't M' 0ii' rrT I p tential eri r'g,.

'' P-uced e-artll iiti:n aL ini .-tentiti e-e r'' ,efiie;i
S b.' E... 4,1.

r' T.iri.ia ure -iepe -.in t I nIic e patr. tr ;Ili tert
2- m.,:.del .

S .'criable definedJ in ,Cha ptc r IV.

t Tenlpe ratu r: .

T Ab:.. 1 u l t -.e mp
T* FedlL:ed ibs-: lute tempeiatuciir defirne.i r.,ji Eq. i'7 .

T Rid.uc .- t em mperat u rc defined a. TB A.

U Inteirmilnrec ulfir pa, r'- potcji 1 ti n'rg;

U* Rediuce, intemilec ul, ar p: aiir- ptent 3 tiaL nr. ry .lefiine1i
by Eq. 2-- .

V Molar .'ilime.

x Variable defined b.- EqI. 5'I'. -Subscriipted '.-aiabls
refer to mole fraction.

X Variable defined in Chanterr IV.

Y Variable drefli&d in Ch-ptc.r IV

Z N.iirber of electronic in an at;rm -or a molecule. Vari.iabli-
defined in Chauter IV.








S Polati z3bi iir .

.j ^ Tri i' ,.mil ,iffu i..-.r. f3 n: t,_-._

.I'

T ',-.n r- nt .:l-ef'ineJ b.,r E.. iL 5 I.

S IlinimurnT I p r enir l ie.-erG; :it

T': TeirperatLire-depenri eji t nerg; pA-t'Ameteiv in he 12- -6


TemlpierI.tu.l'-irJepende-r ene rg ,. .r..Arter in t-he


n Vis,:,:'sit; .Su3n:sc'i:pts ,'ier Cto temijieriatitr'e .

r, y-Viasit., ,f mi:,:ture.



rrLi
r, I L, e: v :c.: i r .efiri.r b:, E 1 5 .



S ri 1,,:', I e I na r r, r en .
o- Jo u'l_- -Th, ,:iiis ,rn c,,f1i'i.i irni; .


-- J, i.lle'-Thomorr o f'J i':c''fi, ientt :ii: z 'er'? pre. LuIe.










n 'riti l '.alues..








Abstract of Disserts.tion Pr'esented o o tihe Graduate Co)'nlCil
in Partial Fulfilment of the heqiirements for ejt Degree cif
Doctor of Philo.io3ph:,,


IIJNTF'IOLECIULAR IUTERACTIOi FOR POLAR AUND iJiPFOLAF
I.lOLECULES CORRELATED WITH PROPERTIES OF CASES




Jae Ho Bae

August, 196-F

Chiairwman: T. Hi. Reed
Major Department: Chemical EnL-i'ineering


This work is concerncY itlth t.he paii'-poter.ti'al

energy functions for the prediction :'f rierrimodynamic and

transport propertie(- orf polar and n.:onpolar gjases.

The defect in the Mlorse potential eneri-y ftinr tion

of th ile fi'ite value at zero separar ioni is avoided ty assigniin

Fpherical cores to molecules. Tables for the classical

second viiial coefficient. on this rmoel are given. The

potential parameters for ten nonpolar mole'i.les are determiiiLei-

from the experimental second '.irial coefficients. The e:xperi-

mental data are reproduced very well and the agreement is

comparable with other potentials. This mode.l is also e:tenided

to 12 binary gas mi:xtiures fr- which the second virial coef'i-

cients are predicted quite adequately.

For polar molecules tne transport properties of

dilute gases are repraducd accurately by their 12-6 pair-

potential energy function vith temperature-dependent para-

meterr, c and r*. These parameters are defined from trhe







classical electrostatic points dipole-dipole and dipole-induced

dipole interactions by s-ati st ic al a.'eraoin;g over the relative

orientations of the moleciues, anrd adding nonpolar attraction

and repu.lsion. t.ersri. Th'e rio,:ll is -also applied to binary

mixtures of 3 polar and a nonpolari.r gs's iLith param-ete3rs

determined frorr the e::perimental viscosities. Li-lth simple

coribining rules for unlike iriteractioni the ,calculations of

viso'?litry, diffusion and thermal diff,.ision factor shou very

good agreements between experimental and calculated values .

The usual 12-6 Lerinard-Jones integral tables are used witt

the temrperature-d.ependern parameters.

The paarram-ters are also determined for this model

from- the second virial Defficients of polar gases. The

.alidity of these carsmreters is further confirmed by

computing tie Joule-Thomson coefficients at zero pressure

for several molecules.

The qutuaIntLm mechanri.-al expression of I-lavroyannis

anr: Stephen foi dispersion attraction confirms the empirical

values obtained for the nonpolar or dispersion attraction

constant for small polar and nonpolar molecules. From this

expression and the principle of corresponding states a

method of estimating the parameters of above model is devised.

The estimated parameters give reasonable results in the

calculation of both, ehermodynamic and transport properties

of polar gases.


xii








The trriL.J'-o,'G t pr .Fc'i'ties ,lo: f'r'pi,, i*p tfslS :Sire

co''rr.iated with th satiirated l iq-uIid i'r'Lilt- rar-i::er.z

through the principle c'f correspondLrin tat3-. T-iu

viscosity,' anLd diftf'.imn coe'fficients zre predict -:d wirhi.r

experi'imenriri e-ror for simple molecules.














i HAFTEF, I


H,",i,,-,l :',:, l.E, Il,':-,,E F 'Ii'FiJTIA ,L ]- F. THlE
.3E'2C IF.i'AL .L'1EF FI'I ilT


i,'t ., t. .-- f .: ri rial 1.,.j l.:s a'.' il able fi- n.rinpol r

mnoie.. l. : piir -..i : 1 rt .. i ,' r-.i.r l ,:e:-f i. ci-'. 1 q i t e

U: lra'. l i l,' ''-r' a rea n l t nl: :ra ii e range. I- t:.. '.er

tne c r.:-irar ; brecorrE.':,m u ,o':r,. az thie oi'le,:t.ile.: be,:,'-rne la rge'

ani f.r.irprn r ca lr. Tn a-i ei' rrt a Iii c rotei ial 'Iiih

c I'n i- : -,.'i 1:.1 13rg.. nari.Csphri 'al a 'c li** 1 1 r.:' crr i

.pneri.:al iarc] i -:.: l> -, r.h ha i.rl-c :ore or-,_ p.-' ten ial is

ii s'. igat: i ir. t it : napt7 .'.

'T'h i, p1a1 i ,o, 3 te.rr iia], riginaely p roI'Op'jSc

"''1'r t'h :-,'- ..: icl..: a.\ ton'e, r r' gie l. l Ji rze. 1 i s ic.,C.,ssfi.ll .'y

e pi ,Ei i i.r th-re Le ,r!:i .I l *'.''1 f i ent bc K.noi:-al,: ,
I .:i C ti t
t at. L.jc a at : 6-.,a in.:.ttl tre f-'?tel f)

the bi.ar",m iti r-es rSa:.. na ainif PEahe-tni. 0 i arnbrlir aLnd

L1.1:: enI 1 a1 :S"ar used i: moIr l or he carrelat i Cor

of t :'lra'ncp,,rr r.r p.r-c prtp *:r i ilut-' gases.

lii the !'ar.i-' ore ilor'e p.r rial:. the C .'oe:: core

rrmod..il of l:i.nr at- el 1 ,' c otib ie'J ul rn th, Mbrse ptentlal.

T: -.,3s tre- p nc.r.. tial ,*nerg, c1' ir-.terac: t iorn .1.3 an..3sLIrIcd to

t pernd o i trne unriort e.1-t .ir, t.arice betweeri core surfacess arid

tr. b. the frirctional forir. of the Morse. potential. Toe








conr.'ex cor. .anr tia;- ar-:, shapi biL t onlD t-ihe .ph-ri-tt al .-Cr..

is conrssid e u-d i r:- The pot e*tr ial 1 :



ii(. = :. I( '-tr,] ) -?2expLJ ( r-rtm ," a (1
I r-,:r = r



' ale'".. 3 i t ohe -r radi.is. is. tie- s, :.. -'ti, r' n a zer. '.
potential ener .2- 1y i. tle irinim.ir, potential I-rner- : it 1.

iniQ 1r is the sepjr at-'r t o bLe triiie- thie i:C cr -- itis The

O.nst nt. c hc s te it-sae i '-inrirng as r i: rt- or e p tliti' r. .

Iii redi.'ed i.'ir, .-re ha.e:


U'( = li. E = ::p [- I -i [- r-r ,I' * (






,- j


II 2





It can be easily snoui that tl-e i educed szepa:ration 'at o the

potential inrnimutm is:


S = 1 + ', + ll ')lii2 i'll


Eq. ('i) chous trhat r of this model is the sum of of
i m
the Morse p'tri-etri.al and tir-e redu ice core r-.diui In f ai:r

Eq. (2) is in e-xai.-tly the 3aile formm ai that a01 thic. Moirs:








por renititl ex':.: t t i 1. 11 3p!iace.: b', rhs distar.:: a .

At rd : ing t i c ia si 3 1 titical ,: IteC:h ni's r -'h

e,',-r .ir i: lal coe i.ff :ci t I,',:r ar i --i- r- e .'- r t p tctr ali

is wrar t.r; a:.







ih-ier = i 1 the Alv. o-'Iga r_, :iurribe-.i. 1 i 1 -kT. at,. !: -s thc

Boitrrian constai By ithe b's i uti ir o Eq I' ) in to

Eq. i( .) a id partiai itL.errat i nri ,I g- et El(T) 1i' j 'ir']':rece

PfC il Ia f'-,'llo,:'



*'. T'..: ,a = a + H- 1 -e T ,-'- *



\ v Il. -2al







-(7I
[-:ehl- r I :tuadir at1. i. .jaSE e:pl-o '.l it is gI'er by:

S+ ,1 ,' ri
'l-' i l-r-2 1 dr. I ;'(a (8)





ae. = cos ( '.) 9)
k n )

This rc'Triuia is accurate and sJipe toi use. '.10.11 In








order Lt: fiailitate its use iiiriilice a new variable .




1+r"


Thenr Eq,. i '3) becomes:


1+ I a
E*- Ta .c ,.a = a.. + r / ci :.-)( l --. (I ;.;- a 1ill,)i
a -. + E _ICI J -1.1 .)


wire re

gl::l =l-e Ilil+a --J- -- ) i'2




U I. = -le- ":.p (- i l -1--I i ,_.L., -.1 ti_



Sic.For m r* or c :: r,, s nt thJ i i t gl: ai i b,-- rrgar je.l

as, an een ln t i e-,,. F'i ally, by E.p i:. I and (9T) -.- bkair.:


B`(T*,c ,a l = a + ,-' gla 1. in ?J1- n 114)
rn 2 n I


Thi,- calilll itio ,ns rlere cal riegd out ur l ri-ih ci:.ol!mplutlT

and the .'valu.es o f Bp 'l'T*.c.s -) arie gi'.i l -en .iLpr.enld :.^

For most cases rn = L60 ;w-s suiniciflnr t.,) Eiv.'e ne[r: pirr p,:r'

thousand acr-uracy but for thei- e:.:cr-eme case., *e... ri.:ll

T*, large c and large a-. n up to sjO was ised. Tlh,:

accuracy is believed to be far berrer than one part per

thousand for most of the values. The computer prograll

was checked with a* = o in which :ase the model redii.e ti:








the Iloti.c .,t terItal. The t-es- Llt c:hite': d .- c o.rnlei te agre rnlent

ui h the e-: :r.-ig table: f, r all the ..:al i. s f T and

Pc.entiail patramr t.r': for :en nonpclatr trile:ul.es

wi.er. deternminre. l ft :m imempirri.:l s.e.onj '.iral c'eff'lici-ients.

At first the FpararmeLter. ere ajppr:;-.:irisri d by 3 gir;aphic;l

mretho i.' r iF elrnall/ use, bt:, Le-nr ar d-J.:'es. 1 i The.y \i' :

then furthe, r efine.i on he cori.it:er' bt:' the least -1.:i -es

fit. T' 'ijas as umeri that th' -r'i r-. 3 5sc:..iar,.-i u. rh

sec i':.r .'irial coefficieni- t can be .]e .c ibe.l b.. .a Fc.is o.i

,i ;rrit ut ion. nThu.. a eight the inverse cr the obs--r ed

B, T) .iue-, 'h. s gi.-v n to: each point. Th-e resul "; a- .ii'.

ir Tabl- 1 where the foirt potential par m,-ters.. ILtmbt 'r of

data p.irts ius'id. mernorat..re range f ch- daa. r':,ot-me.n

s.-iare *,i;. iati:nr and rl feriences rto t he 3a.t ar gien i .

The ali :ic ,' '.f the pa'ameare ers ,Tc er .eri.l:. oin the

t.eTiriperatuIrr ranii:-g an L accuracy f the data. JWith tihe four

paramietr-.s. :.f ihe-t p--.';-rir ifoiel the data i a n3r-rc.w

termer tuiret tt r':Ia e -'ain be fitted tc:, se.'ral .ets of parariAsters.

Among h:- rmclecuies c-onsiered heere tie e rep,:.rted data :;

CsHa, n- 1CLHic 91id .3F,c- 11 jc I t' ) r oet c iZ t '-tuzS Sume

sct. .,:f data ,':ere arbitrarily, discarded. The fit '.-as

mrrade with chose data rt: wii.hich references a:e given in

Table 1. Alac a few data points were arbitrarily rejected

uher, they differed from the calcul]a ted a..'llies by mc.re than

three time the rms dv'iati:.n. They atr indicated in

Table 1.








Thie intr. rrli:l- :. i.l1i attr-9c tl I'ri plt.: nri:ti i .ier'i .:.1

from dispe .:icfz In- .. th ;I ic. a p,-.i .etiy e jn r1.-

DT-,.nmod, high, .i Smith -baineJ n mp.l .1

p -r'. ere e- ote:r tial i:-i, a 1pl 3 ri~o i 1a l in r- r ,: r ther- i ne t

ga3 molecules, and .4,a.si-sp -hel iical p l',, ,:it l rii,' I *lec ul: S.

Ait ilncoT.3is en',7' Of the ,L',iir,:i-higbt -Smit-h mrn,: 1 1. 1hit

the p:ai -tmeters .btairn-l- f-. thre t .h e m,'lec.il.:, c-::a

by ihose au thors d.i: r :t fit t.ie rieCLil-eme tz :. th

c'', I ei.ic.orlrifJ t, t tiheCrei. i h i :o .ie. t:. re uc .r

critical constants for %un.t'h a po:ti.trial fuIrnc crtini. i'th

florse :.rtejitiJl i 3 i'pllci tly pI.:. ri:.i!al in I I ,i th

th ir e par;. ier i- .

A Dilffic'.lrvy iLth the Ilot-se n .-ent'r! ial is trat at

r = o the i tenti l has z finite .Xiue. iThmi, .l- ii h

temi:er*at Lres moleculceys 'onr collisioL ';ass. th *ir.ugh 'ri-e an -.' ther.

This aefiect is o.e :rrc'oe by thi- i nr-: :u..r., ii' f in irj n- trali,

spherical hard ,ore, th- .:1e :.l .hic1h 1z a "',i.trth param tr,

to '1ie the hard core ic.ri- pr.tc-nr ial.

The paramtrr-rs, gl..ren it, T-able 1 e a rzec2on:abl.y

crcnrcitent among themzel:-'ec. Az the cr.cl-culal sile incieaseL

the Oalue :f c inC r e.a s. 'hich ,':rezpord.3 to Lhre nar i-uI ig

of the reed're pot.,tit l well. The .'alue o:f c. .' are

always large than thos- obtained for cther piaot. ntial..- 17

Compared with thoos f','r ether hrdrr-carbonis con:rsii:e'ed. the

value of E .k for C.Hl seems too smaall, but the imi.a -e.'i.:t.l

is much less than that fr-r other molecule. ..1.:, n cpore

sizes of the rm'lecules are :omnc-. hat large compared with








tho c. f Eihai 'a potential. Fo r eX::ampie, C her.'wood atn .t

Praurnir L. o-,btained the core size-. of :1. i'-1 A for AT

and 0.7T.9 for 'O whilc in th:;: calc ul tion ibe o'brained

O.6 ) i' anrid 1.' 6 A -'r and 2. P.1 3r I e p :. i l

Cor -ider, in the t rru tu'r *:.f the molecul,:,. the fi-:rmer :-.lues

.ieemi r.o small. .,in:e the pre -ent, r, iedel raI a f: iniTr.

p' Te nr i1 ene;-,r ait r = .', it nmu:,r lha'e lar er .,alue;. of

a at'd L t.hari tl'c,:. of 'the Kihara potent ial' to a e-..'e the 5a111e

reFpilr.ir cor r .iti -tion to' the &;e:on] vi.riil coefificient .

The core sizes, are i nriE.': ternt among A ,. r., :_F ?. and



The irm: de.'iatic.r b-erieer' cal.ulated ani experiienal

2C.nd '.irial efficient are c.:F.parable ilth those r f other

.oternti als for simplee Iolecule s. H ;we,.er, for the hydro-

carbornE this. m:,,jc gives ., btterl r areeent t .har, the L nrnmjdified

lIotrse potent al. [1e'vertheless the secorid '"i-iial c._)effii-

ciernts alone iae rnot -.fficrie, rit to determine th-e i.inque values

o:f tne f,:.r iparaametes'3. is with other potential functions. L

it ',ass p,. ibie to find several set. *)f luit.- .3atisfact.ory

.param er ers.

'.ich four ad.j. Stable .paramresters, the mcdel 1i very

flexible and from the rci.ilt.s of tnis caicullatior it carn

be cncludOd '.ith fairness that the model can be applied o

the ronpolar ;molecules with good accuracy. For more thorough

ormparisc r bet..reen potential models the calculation of

transpor-t properties for the present model is highly

desirable.














CHAPTER II


.SE.O;fD ViRiATL C.EFFICIEliT OF lEIlJIkF.i GS nMIiTIJPE2
''1i Ti- iARD-'COF i IORiF;'.E P.i'ElIi'TIAL


The hard-core i'-c.r e p,.--nti i Cf Cha- Ler I i

e:xtende.t tIo mi.-:to-s o:,f a: 3. z* since tner.r l xiIt rn r'i.,

c::er'imene t3l data oni the sec cnd 1 '.ii i c. r ficient :f

oinar,- gas mixLuie .

In or-ier to apo r''.:i'rr,,ito thc pt ieintie il .r.,az rier ee s

for the unilik-p'iir irltepac-rtion frinm the p arriterS f' r

the lil:e-p.air inters-ctionris :..mbiniiru riule: fo rhe pa' rrie.ei r

should be u.3-' 'Tne h'tard-core i'c-rsc potential c;rn be:

w.'irtter- in tne firm:


~ ~-?t = -b

Uliere

A = e:.p -- ) j




3 = ,: exp -- 171



b =- 1- I
'-2a


rind all the symbolz have the same meaning g as before. From

the theoretical conoid-era io ns of Zeneri 1 the p3 ameter








b for an uL 'lil.:i e iritr'ac tionn car, be obtained= .:I I:,:


1 ..
1 = (o + t,. -) (11'


:hi-Ire S it,: c ript. .i-r,,t inc i.,-: t,: .iOint b t :' -.n mliule. .1. ar

Fp- ec UnI ir tur, rt.?i'e,, no combining Iti] or the-









1*2
tl Il I- I C., 1 Ml -U],S of -n I Rn i c and S :e t r.ind






-.1
F ..a = 2AIiA.. ..?l


S- -: 1 2 ,
Ei1 = I .2 i 1 (21;


Since The cre: re imrpenet r'ble, rigid, hrird Zphries,

it i1 's or -bler- to u the ari:,rrhmerc mean f i' the

T:lar l'.iTner I a .


-1= ,a( + aR '&2)
2


Fr.,m Eq.-. ( ..nd (21) it fc.llous:


1 2
-1 = ': 11 2' (-;)


The deri%,atic, n of Ef-. (Ei) is r;ith,, :mrpirical but

Eq. (2 3 is th'e *:corrmo:, cOmbining. rule for 12-6 potCential.

Fol lowing Reed. Hudzcn and MPi,: oubrey,', and

[iavr'oy'annis and Stephen we have:


1 2 . ,


- 12 = 11 E 2, )


rf "








i;h e



d = 2 -f e C- r' i- I',1
1 ,- 1 2
f^ = "(VV .'V. ) / 1 + (V V l (:6)
1 1 2


aJlnd is p ,larizabilit.y, Vc JE .. e itir.i vol l..inco air.- ?.,.i ,' ip't ;.

den,:te molecular spFcies. Frc.m Eq. (]01 the fo.llTing

r',lationshi is chrain-ri :


n b I ,




cmbiiing Eq -.. 2'-,I andi (t T wir.'ith n r e :Frer::.ion for-

r. fcf Eq. ) wvre obtain t-he c.mib in. r il_ for 0 i2
an
as follows:


1-
o0a = I + :2- 23- )(,, -- + 1 ,
0 -- i _-.i 0+ 1 _:, 11 .\ _ _- S


Consequenr l:- Eqc. '22), 1 231 ('2'), i 7) nd l. ) give

thce desired comnbinii g r Li'les for 1':e par'mrte1- ac i, '- -,

Ci and a- .

The c1rosc second virial coefficient are csl'iiaLe,

for 12 tinary gas mi:.::u.:-c-. For trhe purpc'sc cf rompaizon

calcLtlations -er'e made on the 0 icrse potential arn Lennar-d-

Jones 12-6 potential whcnev.'er p aromecer-. ;-ere available.

For th3e hard-core Morse poteniti l the pa&ramceei's in

Chapter I were used Fand foLr ither potential thi parameters








used are l"i,:tel. in T3aiie 2. For the hard-cre m.d.-i the

.'ggestetd cLmbuinir-g les a3-e .,'ed and for the ulrirncidi lied

['lorse p ot-entis l the ,cnri- rule.j s ,arr- LIsEd iiti a = j In i'hii.h

ca:.e E]. i27 r-elLtu-e. t.-. arithmetic ri mer f r .'12. .je-ina

and Gambhir 's combinirn r ule for MHorse- p, rent ial i rmplies

-i lpli. it i, the arithmeti : mreaI for (1 ..'e, thi u th

app -arr-nt ,,- ldid n.-.t -no.,tic it. For 12-6 p,:ter-i tial m el

thIe LIu u'1 gE.iOie .-eric m je-n L I' or eCfnergy r p-araFame ltr a Tn.i .rit hmetit ic

neanr for ci:e :raineter: are ue,. All the calc ulatr ij

, re n -ae wit and i tho.,ut f-1 a. t1rZ our <: 1i ..e.

b'.- Eqs. 1.2' ar-.d (~41. he critical 'vol.irnes arid pula iza-

biiities nree;-ed f'r f- Vact;.rs are given in Table 1. The

I'result3 which Li'. e bette:- at reenrm nt t c the e;':pcr-'imcerr s

are S i.uTuTmai i7.e in Tabe The cases chenr f-factors are

used are inrdica, ted I.:,- a mall f' or- the right side of the

i-rst rou of 1 th at cz-stnr.

Fr all 1 s .rte',rscornI idered here the ..-"erall rrnE

de 'i t..ic.r in :c ..'nicle ics :',..e a nI 11i .44 for the hard-core

m.del and the 12-6 model, respe tiv.el/v. For the five

systems for which Lunmo:dified Norse potential is used, the

de"iat l't is .-.j.29. 5.1' a&id 9." icfr hard-core model, norse

and li2-6 potential, respect ivelf,-. It is noted from this

calculationr that tthe two pararrieter Lennard-Jones potential

is inferior to three parameter Horse potential or four

parameter hard-cor-e N orse potential.








T'iLe 1 .1l- .11 ''J zi- 1 l.ppr -nr _.i.iA: i.-. ii ., f h.

iLL"riodif-'iel Ulio oe -.'er i .hai-acore or.Ij'S potent l 1 in the

mi-.tl..e .c*alu la5tin.:* H ..'i .-ei 'i t-Ih A -' ? l. l:.;.

diefi:,ite i.-Ci. sitr iuo- ?:nr t e drai.'- It 1 Jell tI.iI

itat the r ieco d -ii l- :o.'Ieici ,: i ri :t .: fci l: i u i :..t

ueteriminie 'u. i.:,Ll 1'lIr:s, of c .c-r.1 [ ai r -ri Ctr.; ,f a ,.-,r ; i-il

rr.od. el The alidit,- ,,f the p&i ih.etei; de.eit-':i, --r ti h

temperi'tu. '. I ine .' 'L the 3a : l : oC.f r-,ie jIT i:- t ':' .l'.1

be pointed rl'- t t lhat IC1 r thl -e l .- i pi 'l:tnt Iri.l ill the remI -er -

turesz, i n trhe ti;;i iiit-e : al.llatli s li *Jithi the tempe::r ,,

rain e for' i ch parameters.- lere ,Jete L -,]iiJ e'.1 uhiije l- :r harji .-

o'. re mic. el thisc i c nrot tr-ue.

i-rm ng ithe 3,.-tem-s .,:orci .err,- here tar l+ r 4 the ,:1' l

z'-stem for r Jhic hl- the p ra-.!.ileta for ar.ir :'.oio en s :, '

uetei'mined f'rm the aot tni r:a-a for ,oth mo.el.. 'hS u E.' stem-

.horW esseln iall*, the iaie r e Lilt:. Fcr 7 '-'Hl4 F.1, *|i::'.UP-:

*aZ c,.,latior,'s .H-e riade fr o'm :1 .. I tr o .' i.I unil ,?H.i

ia: a.hlietersi of hai-,-. ore lHirs.e :,>.rnt, i..l were r .eterbilned

from th- daLt .Df 22 '."' to: K0 Ar 2..-'".- the :al: ; s.t' l

cross secondd "irial coeffirlent on the har'd-:r'e agree

completely Ki ;l the e:-x.1eriment. This trenr i. -l..: trie

with CH- + ,1'.,i .:, ""'tem. In the temperat,.u-e ranEe 01

parameter der't-r nation. the h :I-cr. e r.eJ.el J i'.'ei Let.ite'

results rtharn the iioise potential in the 'it.- e cases. AsL

for 1i'3Ha it shotied tlie laIrge t dJe -lation in, t.. parla'mete?

determination ior' the hanr'i-.Core mcJ-l ar'd] I rm therl t rl r-I

of the ayst2matic deviatior'. in CH, + ,.'He /stem, tihe

validity .of the parameters fior C oHa 1 atler i,.pe.t'-..l








Ir seem.t r. hat r.-e cmiai: -ir; Pu el7 -r- ti Ia act '.

Ib-rr it is iteret,*t.- ,ttnc at Vfor on' po.t-entiai mrioJel. uhei n

b- t t- r a r eme: i ob r i- ilne b, E.: i .?.li t i: by E-l .

the -arne i, t rue cr .te r t n:.t i al.7, Ev.'en rhe empire ical

c:.rrl ei ri:tn Hr f ff a 3id F.,: t l el:.iFe the :a i ad ter..

It spp-,er: th re arils. i thef ji faritiOari C:n ,f the

..:te-n ial e er'g., fun.:tic.n. the e:- C:er :, p: t =ltT iail lTmint-iIuMF

f:rI LPi-it il:lik in-ter:action can2 be apptr o:'.imate f rorri chose for

lile inter-s: tiois b., tl e s cctbinii. rule 4[-toC, ii"i,

;,eitlier Ef nor Eo. k2'% .seemr to. [,-r erit t .- ut :li:-.

inter-ac Ti.j-n piropcrly Ac tu ll rn- Jii-percic' attriac-tion

uconr tins trTns of higher order of i:n'.'erse '.e.araio: trr0-

E'. E 12 : 1 W itc w 7 i -:t i"-a d on r '- t-rm ,only is ji: t

truly Lh r.i--, : rtjcaI To ac-:- -: Cunt for- t e unlil: in-terat.-a tlor:n

,roperl,'y. 5 rn-r e elaborate combi-ing rul-?e or the --ergy

p .?:,et. sh:ild be d elopedpe.

It is felt tr-hat for more *:rir ic.al cormpari-i ,t.sori :f

.,,.te:-ials. T.ra-n.:-port propr ties on th,-e hard-core Hiorse

poctent.i.al lsh':uld be calc.-lared. Until that time the final

c Por'-,'izc,- :1i cZh-ould be rez, erv;e.e















L'Hi lTE., ill


A Ik.LE- AV.'RA,;EL.: FAIF,- .,TEiIT'I. L EtiE -,:,'Y FT.'.7TIOIi FH.,,
tL.iT LE i'LAR A', F :RuPE:'RTIE ;


'*L ille re -sa .- b een man: pair-pli titiil i neri.'

model. for' :pheric al rnc.rnpolar iiolec' ules thl ari i-depreii-.r

12-6-, Sr:.:landayer :.ictrntial i. the on-l -:.-i rtha ,,as 33 -.-

3i-,ie e::'censi"ely for th,- iJit. r : r ion a :,i f r : p lA

moiecu Il.: Ro iliri n d n : pi ,. r-- u ,.:: _I_.i

corpelation, oIf .eA orld .izi i l ,.effici-.nt: o :.f Olt:. i'a :.'. .

.;it t i [ o r.e tit l "..-:.: l : .::. .J'-'. itirn e

ricci.h b;y ii-ng 1d- -7, arnd ? -T-- pr" :' e r e -ipro: a

or f- inter to t-cuiil j e r..i ri.n 'z. 1-1 Fr 1j1 ,- -. ai ':

mo:difi.:e.l .it he ':to.: l!Ti er ipo, e-rir / br., il-tr.!,uiil r-g th.: Li!-ara

hard-core model frci the tr?,nrjoli r i ,cr t Ofi: : -le it e ,r in

inr pl ce oi tih Lerrnna ri- .Jor.- model. ? ic ':hiiL : rn.:i i o -

ha.-e appli.:ld the i -5 t,,l':ri' e po-te-nt i l m::- trne c:,:-- l -

zion of trar, sport prV-:.pc-'r-Tie cf dilute ga Cs.

A potential en-., fr.c. tior, tuich may oe called the

12-6-6 model, f:r pcl r r-polar ani]d ,o: poilar--inonp[:l pair:.

contains the cr.ati.ti call i,- V iht r-]m-an poi r Tentji.l, .'

over relative orienrtatioan, fori th-e c lassir -al eli.ec tirotatic

dipole-dipole and di-ple-induced dipole inr--act..iI:nI -' 1

together' with i:he Leitr,rj-d-Jories 12-6 potential f r h-

contribution of trn- dlioper-ion foi'ce iri-lte.rcition:








S: .' = ' i I 1 -"' P -- [U t .' .
1 j i j I


] -



a r' ar e i +- c 'L r.L t. .,I
zi r i .r. i J


<,[..i is the cto al ,.,eighred a'.'e'a e mutual p:ore ,ia l


cstaril-.- z.t3 ,.n i a cI':terii.-. of the ,i;.per ion inter :ac rtior

of rtihe mr, le,-c la pair i a rnd j. u i s d .i 1le tiror iein in re,-

e:~ er:-inal f el.-l. is mea ari zlrl ab lit.;,. arn r is (!:'i) -

It iS 3IStIIrned in th' ri' r jli.r ior ,.:i the uolar ilti]-'lC,?tic.n

:r tat c.iO e? le a--e poi. rit dipoles .1, r the n:m genr eous

field pr..du.ed bt, the molecule at The r-iiher. The e fecr i.'e

j.oteni.ial rnerg:, of L Ine pa.ir ,ft moi ec, le iz. aptrox:imat.ed

b',- The terra i r iin he :'ienrt ti.L ori-a'-veraged.l :-le- ri' tati

in-. er'a: t ion .

.:.p 1 s chti an ang le--independ,-enr potential bL; t it

iJ s un; ti :.n o'ef repeat ure as r'-quired by the statistical

s'.er-a gin *.:'.er the r'eiati'e :,rienrat i,.n1 .

'The ri'iht-hand side -of Ee:. ('29?) ,a', be arrarg edrd

:i o rihe usual 12-'- birr.: iprocal for-n,







arler'e E ad *.. Pre, itl.c tions of teir.erature,
-j 1J










S . = .. 1 + r .



i cI j 1 I I


ab f r J i 0 : 1 i i
-
i (i i i / i. rhi ri J



















sic igral iz u 1at.. ur- h -.1

'T :i ri.b- rl k irid las .,o .. the .:olli.it:n i L gral 1:. .:ia1 :.u lt

.,- -a func ..: ri.r i ,. ft i: i..i r, .i .' : isd i :. r i -r r i

fo ieJiiatl t:. gp-.i-. i equally t'i'r:. t tMo esa i : rl; n r.a-.\ In



ro'i" r h. fii'l and :r t ..aarin ioi 1 r fi .' -. i. ie rv i g r:'1 l iti ri .

rhe -ic in i po e t rLte ia 1 c. arrie:. ic- n .. f. t e dip: 1 -

, tii si-e.r1 1 1 .clar l i :. ati-r tl: t :1 i r'c 1- .t in t- r m o r tl ntia

of Ehq. I.' ). .1,' a Simle fwv.tio- and It s""Ol hEe.
a, sr: .. bl: the ,:oli :i.i.:i- i lr o nral ig,, .a 1 ui i? ,:,:
S- I'rrelatin .i[ .ir :'ir i: r'. i i.:i ritlut :. J r










d,,ie 3. It at. ul. i C 3. it Li. rid,: rstocd hE-e thr.:1.t he.-.. Ir t

both ':i is Ji-. tinc. tl; riffie ir t i' thr 1; -O i,: -e I -L -e li..

the a. g:ninge ,d pc.e-dii carried .ip r re-i. .:ri ~L h e ,lp: -

int.erac riols ~.-e sup".ir ee'-d n. nie lat r: .er to obt rinii r,._- t,.[.-r .











:.: ie -. sill .cripi-. rmiay : L-: d: t ],- .

'To c Dal u a' p .r.*.-rti- c i *-1 -, .qo ".i : ,i-

'.. pa a7 e ; : r an..r :: re, I a h: i pcle ,t -t1

an-i Li- i- ; :lr .?i : .a i Knt.v.- area re.G.i.ar i.. n 0t nt-ia

:jirarmer r atre r .btai e.:l b/ firtin th- t'i; re:r.-:t:.-l r'elatior'-

a'i".ip s t,- e .:xrp rim':,Ei-l i .t a. i z' ai Licd thi'it the ii:'le



'Tihe .-tra .isJed i-. C-he .,re ent : c aili.c in, s are tolc.3 ,:, ga.
I-I

r. c.:i te; : tr-ate 1 b- icl tci c'lk: 1 r r.1 l'ia n .

7rne rigcrou rinet ic rthe rv r -' gi'.'e the f:1 il,'ring

e.:p- ea iC:,n "-:,r i-r's t order a ,ppr :-.:ir.atio,.i 'i .'.:c 1 ,





r, :":10 -... C,; .' :
f 1 2, D -a *i I L.t





iihere it 1i m ie,.i lair '.-:,ighl t, T is tem:per-ature ir. '" ,

: is. t:-e ;epnarat ion in 1A at re'r:e p.otenti r al. and, '* i.

thie djniesioile;s collisioi. -ntecral. H-re c Ca,

replao.ed o' r', the ep ra. t lort a r the- po'.[ enrial .nTi.i rimtLUm,

uring '-e rel.a lon r i- ip h 1i. r = r -* r the 12- -- ._-trcrntial.

in.c t:.he e:eri errr 1 in the car' order of

margititlte za. nast o-f ti!e c crre-:. '.ion rerm for higher

rtheor-eti,cai apl 'o::iT:ia:tr.ion the first, appro.:-iirttijn in-.

adej e:mat.: here. Th? twc. Eq;. i. :'1 andi ( 0. ) ccnt.'in i'c' UrJ

LurkI-nor-Ci nr *: r". c, arind r'. Ch:.osini: i two t.eornTperat ur. s.

T1 aird T,'. 1.t4 octt r. sr ar ri'2* in ter'ir se of E a-il E2*









fr:im th-?c rela rl n ;hj.P 3 a::



1* = v 1a - E u r e
1- _- I


,i.e-r' rhe subs. -. ip, 1 anr ? ..c.. r rj l ;..:., riie t.-,;,-ip. rr,,r.-

The snme relar.i.-r;s-ilp for r.' a, ,e l. l iia br int:r.--.-,:ar

':f 3.1 Z1i -ipj 3 1 arni The : '- i-re eliiinare ,i fr>on r,,:>.

e.:qusti,:'n.: h.," Iri to,:..: ',r, : h l ~ng r h ':-;_ i .::-.--..res.=i,-i: f-:':.j

E'... i(5 .1 forC ea,* l r -em ra'ij.,:- .aur Ti]:, re'.' I r inr '.- '-r. r :.[ e 4 .. --

r ',.arrange,-d gi.e t he w.-,tI:infk eq.,ua' tir-,!'


l 'g* = ( "1 + I "


S 1 ' = ( i T a 1 I I :

E.he 'e

'- 31- t a T ir
A 2 ) L A i .
( .-'T i I -


an].' 3irr.ii3r-l, for A ..

ij'.- ] .. 'sc itie3 at. T? n.'d Ta arx-: I:-or.i- --eni t '

and c 5~ t'e rh_ c c .il, e:.;pl .l ir i. T h': of: .irn 7., in '.,:'. ,I -I nd

(;61. The '.alLies ,:, an?- L : i.'hi.:h .;.atii,'y t h,ese

iowe are rthe er-e g? raametersE a- Ti and 'T'. r1' rnil r-

are thenr e'.aliu3 'td .,- Eq. >4 1.

The e-emperari-tre-indepen-ident pst-arrireer -'r an,:l C '

are oLbT:.ain--, 2in t- er!rs of r- an' i a from EqsF 1.C.* I r:l I -



r_, ,- I I
S 1" r' '











Ir ti ,- .i D-- C- .;nipi1t d .;:. 1'fr ,m ti c.:K:.- .I'iniir aii:

.* j : C .T1 iEC .





1r..:, u C '. ,_,?t. nl. t a niL' ,' ', 1-,'. [e f +te ,,:ei L',U't i -,:.,0 ; .i tt

a: t. Di C. l mon:;Ti ;in : ar z. k,, zrr f -on, PI1ch -r, ic' : .'-irl '.I a .-n'

-an.i .f. i hrizabili ie. air.: L:'iL.n i r..-m L.'n.-i .1t-L-.ri .:zein Tal:.l e '

i -'Il "-. I *' I n l I .. i I ac i '.':9 .11".'e ") . :

f?, r .. I1 7 t L.:I tu .anI i -' lm tll p..:'l': 11 ,d**h m- ili -" ia .

.ipl: .'...1mn te-i : t; airi t ilr' A rap! hi::i 1 nL -tlrld .-:i-

, '::. :,i ., fin. i; i ,-.o ir in t-tio 'i,,'r",. Tn all ca' c"s..

e:, -rr -.r rri,- ttz1.e r'e CtV tr'r 1o jeit e.' 1. d z-e

i1".C=e '.r jtin :,f tLhe t,, : ir"- C,'l,3,11 '.+ ij- es.-'.ii;,'- .r.d ,3.. ,;l- 3 r ,t iy

i-'.(c re.. .'i i3 r- v.3,'.r L i "er;, lar ,i at -. rem rera 1- .i. '

I C- ,. = 2.- .':, :- t ? 2 ;.'i T.-_ _o-:- il,. t te t he 1i2-6 t l e

r.-. war.a r: '.' :p .r. r.- hirh C- en[z, 1 r 1er tu e eata t f Bo r. il.a. i:ranrc-

a d I' i 'er' s .-' ..: .t Iaa 1--l 'ij.:i it t i-i r. an'.' c or'r'-ec -

ti : l menti I.oncI I. tie .

Tn x e:1.perirr,-i t. .1 an id 1a iCu.teu ,Laz '.' t or. c itlec at

:.ar at:i ,tp -'e pm e re;.:. .ir? 3ar c m iiFp'iIreed in I'ig'.neF 1, aOr.d ..

Tle cat pr.:-int 3 -L-d in ti'. dtLennhr intiicn .' the paramt.?erz

a-e im rked bvy : -: Ge Artbi rati y h: I..:c n data ..ints are

ie o:. -'.u::ed i tI e fip-gu-e The -I': ve.'., : rar caci elated '.values .

For most C *:- the mr ..I ec nle :.. c: I-i rier'c'- tihe a 3 r G em rint i ia iti hin

the pF, APt-ir.entra i errIor'. Tihe de'.viation in H 1-O i he lar: -'.;t




































~4C'OKj


1000


5C'C0 i 15f0



Flgure 1 Vi:c,;.i rile. for Ha.'' .nj ,i'J


C .II~II.I








5a~si~











HI /


/
/

/

/


/ /
//
/

/

/
, /


fI, IL


iii'-'




- I-,


i -'y _,





ic.'jC

e'COu


20C ;5j 400 .,. 0 'j.00 700

F ~i i. 2 Vi.-.cr, sitic- 'for F I, HC]., fil CO .Oh 0ri Ci. L a'









_'-i, I


I -. '

,/ I, ,' /

$/,



S'-
2 '







0 /
I ,)










/
'- L














L I l i I i I



Figur'~, .11 3c it ez f'o :i-. ,2-, and. WI-1-1








it _r.i :ill t '-. n a i .- It: A 10t d -t r .-: r-. r1-.- hi -i

' T.T,_-,Y t' -,!.r o f -1 :' En1 i '.' 1_1 t, io i-i :. +' .: :_ ?: r '_,,. e -



I-'th .;'-:. ifi-a :' r nro :ia.ar Ca e -: ith th l..i 1 o.r-cn i l .

T'j i r r.c. I d' .nz-iiirg !.am';.j.; r.r.. :' T -::.er. ir.ern r -;

at ; i Z. r.ri-.: t-; o i :rd. I- .1c:.. roit ,: ;ier :.,r C, r r ii:

:..t.ie i:I fr.- u.;- nr. : ha ch -i".: ].'.: r.z r1hij-' k:lIjon ip l l--1 1) t .

T 'n- o' ,-r ?1 1. c-' ar -J 1, :l zhoul bei a,.:.ri;t ,-t a . I'_ -en


tri. .: ll. "-, '- i i-:ir I- cr' t-il.'r, .t u-- i ? .it.:? .''. T' *;t i7:'7.,1 .thi|.
r' tan. .li. t, A a r at re r 2lved -mr.erjt*i-, I3'Q . the'

S a..e .l I if fe I -r.e ,r .:u ,mbir.ati :'n:. Ti' I i. 0n.: t e, -*l, 1 --i.

l- h-har 17 i1r.i i r- r n other ; .

T'Ie r.'err-,:, t. n ri-. P.ef-r nt : A'i i : :.. r ir: F.. i 1 i i

I :2i' are- .ju Enjfl.i:1, 7-riti.'.iniI ;i l i -ling, in: r 9... r uie ;I;.

The t '-rr..r.r e'- 'diegenc-iLe 1 rateici-s c m--all for r- an':I lar,'re

:''I' .:' .: 1 i hen the 'i i e r'16 i has l& . leipfol icnrr

For the f'ebl',' pulaf r mile.il*::, 1:; HI .i Hi '3, ': '

i.. r..ir urity irHE for .Sl rnrr1- polir :rCojl.des, li:e

Ho 1 3, .d I- 2 i.-, large; .g. o. 'r' 2U

*:- = 11.4 27 .

rin ."r c.-na '.'iriial *- fi iEn c.;rpl. tr v ic : Ili adId

thie 12- 6 r blcz ir-.;d in -..a'rme-i c. Tc .1- -.. ar :hlc'.r'i

i.1 Table Thc .e.:n-rd 'irial .:-ef:'icient *z-ta for SO2 are

k...r, fr:.-c. vLanr t al wniid all c thi-rc.- f, r.m Ro lin.-n.2 .;+

Tn-e ar-Terien- bet ''r-n c.hser- ci. ai cli cultL-d valuc a're as

g od r as pno as' '-- thoa 'btairr .d i-!n'i.i.-tk and i!ac-,an' "2f-

A'it'i wn',: arngle-i. erenr-i>nt roten: al ci n.l 'iScoC.itY r.a'aiet.e 's.








H pio.renr iai h as-- b i..,- f-.ir.- '-'i h 1is :. .:; cEs:f- i i h a i

-r .f triaram.ter for C i -i.- n.r mi.:. ie.i pa ir f r. both







Fi-irr i h p: ir ni': l..irl-;^:f 'j .; ~ ':-If J- ': 1 -i11-l r r I-f Lr l 1rj. i
e uiliblj iuur an..r trac;s:1 ], t p. tt i .' :.f 1V:a .-.l- ,uIe .

uI .1 ," he tranr r,,-t .t it r.. Ie bai rIr t -r.,: 1 a!.-,

:rit r tn- f'3t'a r -et:-2 ,-, r- _:r.:.:- fIm ,i,-th--< ti ni',nrt pr' ir-tit, ..

zt h p,,a, rh leule und.-r -siderati n t cr1 n-s .i -. aD -

-e: e iir.i-ntal :liu-- I T h-- T-lf-- iiff :in .:.fifi.tienr i.:f Hi .

Theory ri. all:; tihe :s f-:;iffu ..i:rl 'c- i itnr, iti rn. .- : ,

S theu Iir fi ~sCl a pr'or:ir.ia. io-n is .;a ritt .--r- ;



l1 '



'.he ,- F' io rh-- pro'e .?.,.ut in .i-i r- r : t- i n ,il :.



rhe elf-, .if;' fusio i c,: .effi i e c. h l t II d ;"-,' rf j n c. t rrir t .j

t"- b:- 0 .1 61 fl i 1 ra Mole: r.] r [,e v:tarn'e rt., 7i l

If iu t -:e Eraun.r- arnd Z-l-hi ' ie .- .f .1'.i l Ji

c re'i'' eI" f rth r n : 3 ofc i3,-r.,,pii, c i-3. --rc bt l- l''l.-:'hi-- .:

nJ i'Ha.-cn th i..i .- 'iartion 1. + 0*. .6 i Hii.n: i. u li ;,i.it.niri

the e:-.erimi-rtal .'-r':..

'IThe pariherer: :, ai.._] .3. h'.'po.thiieti -all: are thoi .e

for- the dJisp-i".r:-n par-: r -ie t.:tal inrerml le ia" ihn:::a --cio r .

The theor-' f "1t'.r: annis ar. .'teplhen 'r intr-z-i r i:n

between ata.:,n gi.e3 an c:;-.pr:-essi,'' fl:or t"he ilne.r c, ti : ': n ran".

. e i' t-rrir, t ,f t-he l:,larizab.ili v;.i ,, .rij the ir.ttal

number of' elC' r tct s, Z, 2 in h.. molecule 2,.,:








I~j Ci- 3. 2 -2 3
=; I- .*' SI-:l


I. 1 I


Jher 12 1i tU.e? as Wz e rep'l.;v i.-'rr- e er'pc.'r-'r. The

:.E:-. tiJ. :e'' 'four timer .: .'r.' t, ;..,, 'fi .-rt ..ri r':

in tiC,- ,ipr,.-L energy intera: ti" r. 'Ti: rhc'.' --eic' l


.in m ,-i al '..alu. calcilatd witi h r1. srainTeie : o L i: 5.
]: l l ,1 : in Ta .i r 7 1 itih *L e 1:



Th-e :-,cr.e riTi.n is rather. .l1.:, e foi'r the crrn ll r l .:..,i d -',l-c uile:

an 'd 'C.'me F:.c r f-or the l: 'ger.l a t.:.LCa Cr i-..

il- a reemenrt b eti -en the i, '. 'n,:-. nr c! -. tO:.p h: ln rhec' :

anj :iata fo'r n' np.:.lar- :i: cule= is i]lustratedi i tie 1: r.

pa t r:. Tabc e 7. 'le ag.eemr rnt i- .:.r,- ;'.' :'c r.e r-c.nsL :'rriC

ai, 1. l Cit i- cl-: .l uleS a b.' t.:om.-. p ".' s a2 t]- rn.ii e ofi

'st-: r e.- er mni o ie.'le j r a Z.eS C .

Tr' :"- :ai .-.er.-- ':' ti..a r':' f -r che pcl 'r mr-.1le.: iules

tnI.; si-j.--a q: : fI ilfill h-i r r l,.ie a: r.eprrZ.e ai '.,1 e o:, the

di.r-- i,:, .rt of rl-he tot l interaction i a manner i.:'n

is .a-. :eaicti c -s the p'iAmetei for' tlh rcal inter-ac'taion

be't e .,:, t io no.np'olar' :ile. le:- n r 12-. i'cf r It i1

l.-iter t irng to firid t;.at the ar .'*.*nt. ,i t t:e phcn e::pr-'.;s ic'n

f'r j li'.e:-zic.ti it.etrae..ti.n CA fc ,..c rs el',' 1,'_fi .Z.I theL

e:-:e r im ital itrL ''actioCn .: cr tint for- s a l ,c Ule5 ,

b:th nolir and norinolar. The Lo- ::.n foc ,irT.i.i-ls, o.n the other

'.an', predictt values of '''c' hat are lo by a factor' of

1.6 fo:r mornatomli.: mole:Cues anrd still t.orse for diirtomic

'mnd larger mcl. iies. ( )















F'r:A TEF TV


T'F, ijPu. T F Fr 'EF. TILE.. '.- 'LAn.,-i 'i ZF' '1
,C .t i i T..TliF. :



ITTc a - .' r 2 .I :. _i. r i 1 e: ne ; .:. -
'.h' pt].-!; r.:- IlII 1iT, ail,_! ie,7i r,:. bi rt.q n i tu rar .- ,- ,'' i't a i il l't. "'-t r









[.1
a;s; es E.pi-i ic l r t: p.: 1 -nor : o:. r ,i:i.-.t r.=_. ; i .:e I









"-'.a -i r -i t e -l.- e 1: r. ',.
. ,i tr n:a 1 :



S I.
..e nri c .. an-j 'a .. .1 l-J ,-a i -m.-- i.. ne-.a .- .- 1 ..,-,1 c

11 .







= 1 .. + r' )j .



Usi3 rtg lif..:le n. o n c. i aiid ., -j.' _,z:,i'-,i it'.:z. c d r

can be .- ale._-..is t: .d .., E:qs. '..1) sad i';21 .

ten o;- nieT ,, ie pair i., -rr 'l r. ; .. e

p a .-. -, ] r,:, 'tIer Tr .-- .-,nde :; n.- I 1-

p p i ~. c h e n. el .. :r. .:'.'I-v -r i,. l e s s ,: . t n I: r .- .I. i r .

mean sit.F te *Jip: .l,- in.LIuced *.ipl, inir -* rij i:, i in. li..'ie-








!in -c po nr I al. i.iual l; t e inliuc.:-d mo;iri.?ir i .-n r iT, rij

zmaiT ller rlt ni t e inLDu .i in ri. .-i I-tie m'i,.:l i; rjlnst r le

-are rr th- 1i'-6 p r i i al. H',. ,r L, hi ho l I e rh'?,C

reall.i ic tiC n tr.-r- 12-6 mr-i, aii ls Z 0uLii r i-r 1i

par!:;n Trr,-rs3 fi t .teic 1i'-R -63 mcL"il SLiC--Les3 l'ji ,' ,l r;dlci ruti

p_',.,per'iF e.:s ,'_i ,:,1. ar-,-rli.n ,',l,-r mi i.-:ti: e ..

i'-akirl ise 1c. .the .l'* -i,.rri:iri r ir EC... i'2 .aI r-d

(4,) ad i he r rpirica .alr-s. tpre iou'i .:tr a ,,e I:o,,

's isc ci ..1 ec ar .. r-' in il. -pai r i el ,ri r.ns,

thl'. 'i.i,-o .Ir,: ,iff 'sii 'n -c,- f Vl',-i"ritr. an.-i1 r.iermp l] -ii: I''rsior'

a- ctor i r*C :. 31lc '.ila r and :oripareJ ri i e-:per m rri-mntal

prcpc rti t :es r tie b ir a r' zj: ems ir Tabl..-s 11:, I ri.

-'if- li; : 4.5. an': l .'. I i Z't' e:- n i al t ra r- i lte rs i' t r n rnpol tr

c .'.s s :.ei in thi ,:l .il riri' a :- i"'ei i 'i'. e -4 alor

'.'i h p.':-l. i_.-,abilitirs. Is Thermal c,: F ii i' i rut o.o,, lIterei

heZ bec. C IZ cfr i t d -pFeri'trda : i'r 'n 'ni it. l -ner ','a r i .

Fro'. ri,e i,:i rinc: riec',; thPie ex.presi'n for r.nle .viscosity

Cf bi tar' mi u r e car be i.'r trn as:



r, = (44)
n + y


arherc *:. ', ari. Z are Lif b it- ior ns of miole. ra' tionl'. m., lecular-.I '

,'.eight C_ Ile cilnc ri.en r and ih.i c: 111 ,ior ir rtecrals !'.)r'

Che unLli -;e-inter'ac .:icr Expressi.,:,s for ., Y, and Z have

..in i '.'er els 3 he-i ,i 3

In Tabiile c i. he .:aIcu.a d v iscoos.ri anri tic *i vira-

cions from experi mental ,ar.na are presented. Tre average

de'.'iaLtio-n of calculated values f'rc.'ni experiment is about








1.I'- :lich fa-'or-ablvy cm ,,par:.; itr- h. ie:;il .:,f i;,a;r.n

and Horr.icrk. '' The agremc. nt: i. within e:.:perim nrr 1 .- rpo

andi ncr wiC.o 'm t ian t r.:,e -.f the 12'- -.r nti3a r r.ii i l i

Buekii't irhtiam mc..ll i'or nr'nipol ar cph'-Pri, fl -imol- u ..

The diflfi" .ion c oelfi'icier't o.' b inar',y mr ..ir e ['

is c.alculJ13 td b : (32)


'.0 262' iT-, rl 1. 2
r'12 = p 2 (1,11 f I 51
12 12


A-' re m 1.3 ri -I iied moleular w;ighr, P the Fi rez.l ,rn

a31 rosph-ie-.. T in K1. anrid tne opar rl rin F r z'.r--, -,i'rntial

in A. The calculated va'li are compare.l uit i ::-nri.rr ir

Table 10. The a-.'erage de'.'i.i r ion !o' c jliul at.d va.3u z 'rorm

e:-'ip rirnme ral data is ab l t '3.'. 'ni-i a irn :Dnfii-rr, I--rar

this mr.-del i. a- go. a ,, itr e the 12- p,'t -r:rn i. l or thel

m ii.lifi ,_-6 Euc l:ingliam mo.iel Ior nionpolar m-:le.:cule...

It i inter' e-tri 1i 0 ccrmp,:il'e the par.'amE-iff ; I'o.

H20O + C. 3',Ctem I .ir tI h,-io- ,'ib rai n-d b ,-.tli- r".-.,. T'-h vb lTr:-:

by Eqs. I:1 anl (732) are ..na = .h9 A .and I : = 1.7.7 '

which lie 'he rcen MRac:. an-d 1lnc,.Iic Il.'z ( c2 = 7'.'72 A.

C '2l*,'k = 2390K) for the :Stc nr.ai.pn.'er potential andwl al erl:e ..-

Westenter 's C4o) 12 = 3.;.5 A, -..": = Cc'E for rth-

12-6 potential. The zystems involving H20 i3 one conu!rrtr:nv

show improved agreement with e::,peirrimetal C.c, r Ha:,r-, and

Monchick's resul l..








The therim l lifful i o.' n f&a tor '. an .: .-rpI'-:: Cni. t i ion, r.C

terp ri r itui *c,-,ri,. ent rati ron arni' m')'e' lc r' n't' i : t ion. t

1.z hard i:. p -..l .: r th ;. 3 I-r.rP rt the:-r li: all . T-i,

.r., ;:..3tin atr th,-cs ,, Cf-ha[.mni-Cr''.] r arid Ki'iai : -

.Hazon. 6 -' Ki hiar !irsi't ip[pr.'::ri:ir tion ;rw s e:l because

'.f it simT, licity. This is i-n,-itn tr give more 3ac.-.: rate

re .ult- than Criar.man-C -Oulii ag 1 firzt 3pp i :.:i tior r.d

'1.,f ri f'r the zecc',nd a..,prp ::inat.l n r. :, e'- per '.. nt.

In Kihai a' t'ir st applc::.imati:on. rtn tlerriim l dLii fu1 io

fa t,- r. 12 i ttetn ias:




S+ : '' + ::.1 :-' :. 2


where -: i :.l2 i j ra.. t I.n rfr t-ihe comi oner t ri E:.:p'e..iors

:for r Z '1. .h'c :i aQ ha,. bee1 ei'.en by M n

but tlhr.y a ie c -,mitted here beca3Lre ot their lernth. C,0*

is the r- tio i. collision in te r-al C* i' ~ 1 1 '.

Cfot the un l il -r inLercaIt lonr.

Thi e::perlmental jd'tar for the sys tems H-la + Hs. ( ")

3,02 + Ha, A ir + HC1.-Hnd e + .J 1 re compared

rtn-i cal-ulated values it Figu'res 4. 5, arid 6. Curves refer

to the calcularterd 'alues and c.irles refe~i to tlhe -:xperimenrtal

vslueL. In Figure 4 open cirZles anrd curve 1 refer to values

at 56.6': and rolid circles and curve 2 to those at 6;;EK.

Itn Figture 6 cut ve 1 and openl .i. rcles rc fei to t h vIalu L)?

for At' + HC1. The temperatures for i2O + H2 is 3576K and that






















O 0


0


S0


L,









r-,

c




j
, ,




1"-







I..I
.r
--










-.-i


i'L
'I~


'-4

a
H























0


0


0
O


0






0






0
O


-,.















r
'1
ci


i-I
Lj











rr,






--





rr '



-
-I?-













,-I








0


1 I


L ~I I 1 I













r.







L I

o '-I

I c-














+ i








0-

0
O o -c








rO








'Li



CI I I,



0 C, E C








fol- l Ai + H.'1 .a ir, + iJli. 'T1-- :v..rall : 1 ,'e mn.:n

i. fair .r,-i .:,.i.l..iare. jitrli m:. .-1 i,: ul tr.i rri .; r r jcl.. l r fc'a.?

Fcor th. H ', + H? :?".-.t-rr tt :13t:a Of IFrnail- ; .-::iii r iO :..r:i-tai n

wi rli r .-- t r.:- j o. rtI,. : 3l: 1!Lairc:I '.'1a u :. Io.i rt :

i- + i -I2 LY',' er.i lioi a :' i c *:-e rr ri T. r lr '' in .:- i L..-iC

p'o.int. I. t'' r i"y ['eJ." i r 3pi/ -t' I, Fi i .

It .:;a be :.-aid fi :m th=e te'-. :lt-; i.nr it rihe l 2 ,--

poteti.ial ..rSn be nied rc; pr lar 1:' t s- I,..' -uritic: li; thl .ub -o^ .

Thie L2-6.-6 mTdl ir-. .':3 -rlati'. niir at ie.r t3 3 Cod 7C .

,;, ":- .;ti ree th:n i Hr. .- mor' e ; .:.ri5, o r..: m,:,,- f 1 1 *oni. nL, l-: a nil

il._incn I-,.:';- m i..it: .i r: .:,'"r _t. _i-iin pol :,3'-i.. '.i. '-*. i.'r'-i, coni" aT I'-lni

t i -r w.ilt on '. i .:ocit:1 C'f i1,ar' lii .trl i .-t.:.? tch s

St iO mod: ]]3, on c ho .ild b-.a in miriid flnar i- .nchl:l arid I.la.o i



.te cal.:Iul te.: '. i al..- r fit a t 't it- s of t I r c .'om.p1 it on

1. n~c?. -ien the .'il.: Lla t-.. i ; '.:o3itr',' 113a, ul3 d fcr 1 one

'::.IhipOS 'i it H2 + I' 2 .hi i C' :,'t 't ti e d i-'. at ioin .J th-e

l.:gi't,' ?. .i:' *tAll tn s'- ct-.emTs i. sed t i, t ri.-ir caalcul1 tio i .

InI thL- a3.,- cof thOI.s.? "'s t::-Ti r-c rta t.'int, H as on-e

:lciptjC'jI -i, t. thm i dr viat..n is tie 1 arI ge t a t -e 'ipola' e r

f1" .:cmrnlp' ti.:,r I. Thi, arfi. ss f t-m thli fac.t that uJhenr ti.

parameter's f,:.r iJH2 wer'. obt.iined from the vi.'cc..itie.s at

tic difii'fer nt temperatures the Jev'iari.ons at 'other T.empera-

turco wer- rather lapge. Thus, at low tIempe"atulres eCar

t.hose- ui;ed in the fit., rhi;: ti eid 'rlisapli eas.








Az. tie ;re_. -n -tr i not ., ry -, c I, d 1' th- t l- 'l

diff l. iorin i.. i. i rie 'Lt'r. s .I 1 .' t' i ii



..au ':, i. e f'c i ,--.i to' i'..v'- r',if tte r 3. r mr,9 ,L- ,Tr cr. 1"ei .::a'.' *:--'', .-?, i'i -?.,:t

a i'. '.'i . ,zc ,.Ai"l r: n H, : -_ I t.' ar i .'--i nn' i, r I I. .TI"iJ_, 1 t1t.,;, l-'-


in th r. e *:'nbir.iiL ri e1 .

















*EC, '1fD V F.IF1AL AHD J.TOUL.E-T!il,.'i:,.
COE 'i-ICIE;]?T. CF' i-OL A f .':; :E


In ,:'ll- .-:t I I it :. p r- ,Iet r, f r t ti il -a :- iar-e-J



i.s.: r.tie of p.:lai ; g The .':.alcil ti: n.l l I t.arsp ir

prr.ertie 'jif.ln ti-h :.'c .ara, sret i. wer- 1i.--[, S 7: .If-ul biut

-thL .'.. ; cz .-' r icnd '. i i: i ?o ffi.: l nts ir .' ni :t ir r--.s iv.e.

li'i this. ,i:i..t.i t :- .i arrm.-t r.. ar e J-et r mine-i f L-rri i he

:.-:i 1iri ; e-c: 'rj -irial c.?- e-ffici-nt.: f ,rl. i g .'-. The

'."~llidit:.*- f : the pa: r.lete-" r fu r .er e tl t -i .' .: ; rIom -iiutirig

th.- .T:..le-T; :*m .:Or-i .-f'i i.in'tc : r ze o [ -es- '.e foo c e'.er l

m[T,..:? '.1I.:. for ili-. -.C o: eiimtn t.sal da1 t :ire ar "ailabie.

To 'et~cnI. i'-i e T-he p -_iram. relz-? i : 'a cn.-J ri"', from rh-l

ri:ndi virial c'o'fic i nt.,, a Limilar i method r, r hat. E :

C '. t: III is, c :e:-. F,-r the i2-' p'te i aC th.e se,.ond.

. -.i.r:il c-efficiert i i'.'i b',



EIT) = ii r B* (47)


'hc.,' ti-he s'Mb l.: 1i3.'? the .-ame meaning a:; bef: ci-e arid. values

of B* have been tab.l' t,:r''i cel.s iheri :. U-.- :: hoo soc' two

teiFriperi i.t Lr:, T1 anT, d ''. arn'd r th c rr-sp-.ondid n g values o3 f








5l.Tl B.r andi. B_,, Iu-iere ,iab.. r-ipts 1 and 2 r fer 1:- rl-

l.rr-ip rat i:r Elliin-ir3 tinf -. from theze .A : q ai: ons b,-

the uL se cof Eq. 1 41 he ,i.:.'l% iir' e.-i r tI ionI l f i ., ( 7- .

anr ( i' .) are- obh ained ri h.



+ 3L
A' = 1. l-7 ',-J,' 7 i 1 ,I ",-,l



aind similar- '1 mi -T : c.m.' l; e irn t. -'"a2e lnic
as before. Wli h t'.i. I:i'ourn .1 nd .i- *jLt. 'T'1 :Il P c-h

va LIu-z :f c anr d r .. 1 o:i c seqi tl- r ho-,.- O. f r-

aid r"* car be e.ailu te i. "Tihen b_, Eqs,. i) an.3 4 S I
o an r c n b :' .--i pti L .

'h.h pIo) -te- trial paI 'rm-:ete, for .e:.-iral p,:iatr a .Z 3

ritcccrmii ined by this tr ,,:t ai given il, 'Tabi 11, V iai1ue

of dipole moment-. and polarizabilit in C:hapr,:r III ar- ui,.:.,i

*2:-:c'.?p, i- foil,.,wirg.


p ,'Jiebe ,A-
CH;Cii '.44 4.4

CH-CHO 4..3 4. ;-

"HC,1 ?.05 6.4


The value of o f- CH-CI- l is aken fr om Pliceirn-H he -

and for CH-,cHn is calculated frroT the bonrr po:larizabil1 ie.:..

All *-,ther' -aluez; ai c;,i'.'en in Lainric i:-Boti n,' ir Table. .

The e-':perimel-nal second virial co.:ifficl-'iet: of SO- are- tal:en

from Kang, ec al.("cl ar others from Roi]in.To.1 1 The

values of c I aind .c 2* are found gr-phicall,. Huie.:-r,








th.:-;, c, u.l nr.:t b.i i; fo.' it *:-.' ri :.-' j [r -. l U.Lr ur i.:h

thi c- ur.'r by E. s. 15 I anrl I. '- I TLra p-ral lei i.

T'1,he J.o.ule-Tri:.ins.n co.-e f : i e i rt i1s ,i c-iz ri,.c .*-L rthe

r .ate f c,, ,.h:r.ge ocr tr.per r-atui- :ith pr,:.r..,re iin an 1 .*nthalple

e::pani:-tr. n This property' i;s Pr ated rc. the- eq:ati.r tl i onf

Lsate .b:






ier e I is the. J.olle.-Tlhomi.n oefficienr, V is -he volume,

in. is rhe eat capait ,f h.r- Gas. This equ.tatiorln can

be e;:p;inded by e r .i se of the irial equat' i:.r, of jrate and

in tn l r4it l ing ca.e of p = ',.. the J.Tou'le-' rTlnsl.' .oef ciient

At zer~' j' re c, is obti n :-r as follows:


AB
SI 'T ,:iT 0)



where C, is the molar he:rt C.a-p:a:ity at :ero pr.-sisure arndi

at that part.i.cla_' t-emrrperartue ",nrler consideration. Since

thle potential parameters are' temperaturl -reepenclent we have:

,: 1Sb. T dB-' dE -

T -E = b (T db -Bl + TB' -. -, be (51)
IT dT* T fi dT* dT


wTher-e l, is (2,') ni I o and other reducc-d variables are

Ct-'fincd earlie-r. Eqs. (I1), (32. and (51) co-mbined with

(50) Cive the Joule-'ThomJc'n coefficient at z.ro [prre sur-c

for the present model.








1
c 'T,,* I b. j
Li [=,.'--- ) *^*' "-



S..T -I J



Mhen molec.le. n-: rior[p.i:;l..f .:lv rii 'i[-,r r i m a ei

Eq. I' .") emaini -'ich is rth Mule- 'ni'o:rr ni .:o rfff.i.l-rn

i-nO' l'ar mol-rule E, the i:rwc.l i.g :- .-irher rthi.o .-or.-i

'..'irial Ic,*-fficient r nd itz deri.ativ. ul I .:.Pr.eI; i :.

t'mp"-rial- r-'- orc the pc t i.: tiit 1 pai ''Lir imr ter.:. i'_- ,J-.i,-Tl'-ni.:.ri

coeff-icien: at z' 'r. pr'eZc-,rU Cal L easily : .i:iiliAr-.i.

TaDles 'Of T- '.'e been cci-ipiite'J f-.r r e .?- pc i-eti-al.
dT,
The ..Toiie-'Th'.i,'-.:'-.n c-el' .ici n-t. art :-.:. r re -; ,ur--:

calciilat lY b' ii3if E the prl .am-eter : J t :-rinfi 'l f' .:i .-he

:ec inil '.*irial ,:,ffil:i-. l-r are .?vCp.?:ii'ed w;irh the- ,;:7.-, i ,ltti.n

in Tabl,- 12. Tihe el:.T.-. 'irT.?r[taJl tlar'. e-- rai. e., : ,i -:: [iA.-F- i' 1

Th- h-e1 t capaciti t -atr pr}.-rsuir for 0. O aI' H.-0 ar,'c

trail:.n ftiom Houge in e t I ( ) ard thr e of IiH ir ii 0 i..'t ,

et al.' '

The er.':perimentAl and l.. ulated se-on..i '.'icial c-' rfi-

icrrs ai'e cc-,.parei:d in F'ic cirea 7, : and itheire the i., .

are cRsl'. iltsrd shalw.-. T-he data. prO.int: used iin th-e .et'i ha-

tio:i of the p'ratmetei are marl:'r: by crb.z.es. For' mn:t of

the moi ,:iulei3 c.:n.i'.lderei the a :'--e'in-enr iF i-r.hin e.-.peri talent-]

error. For lii0:,. C-O anrrld I Ci I the ai -..:rrrient i. r ':.:t rm.!'.r ,,.:. G.

but for CHsCi and ( iCHn i CO the c 'ir'. atuii- of cal.uiaL.- i i:ui'.es

seems 9 little 1irgr tghan i that cf e';;.p'rii-nt.





































. 1-











hi '












I00 I I I I 7 I

T"K


Figture 7 Scon Virial Tc':ffic: intni fo1'

IJH?, FC-2 and H20














/-' CH:,CH:






' -H3 1 2


1100 -

?C







/ o
iC i /








14000
O














2500 -
C I I I C
2 230 ..00 C.5.0 00 ., .,,:

T`K
Figuie- E, Second Vi'ri>i C'-jeifici,-nts For
CCH3'HO, ICH ,':' ) an.i CIlhCIl


I 1 I I











4' II










/ /




















80 i
00 r250 300 '350 00 4 50

Figure Sec,-d V iriFl CoeffiiclenritS or CHa71 and C -HI.C1









Tn0-- v'aiu.. of '-:' i.: obt ainei '.: ir m the- :.,:ecor Ini '.i Lc!i

.oel'f icie:ints :i r-.o 1i -,s : lar er th.-an r h.Lse. f'.-.-ii :,.i2 i s.

A : i be,. E, e :--c .i 0' .Alue-. a'e 'imall.-r i n 1n 1.i. :. :'

''lha.pter III e;: pti. Ha'' 'Ot- .'rhih bcr r ''.: n.i.I r'' ,3 ;

is'r e,' cihn tho.:, r.-tain-,.-] firn-.n .'i ti:.: .ies. in T.-.l-: 1 1

tihe-1 r tios o-f -iipirical t tl-i::- 'e tic :-l *.ili..e t:cli:] int r. 1.-io,.n'

'-;on a t ar'e il o gi ive T t 'I e, ,reti- ali r, n.: .. mi: .:6

i,: the L] -r h ',- of Ifla, 0-'.'aiI'_i' anit" l: .t rih in 'f E I '- 4. L It

i iintr esTrinC t. n'ot-e that l.:--p f: il -0 ri-, r[ i, .:- 3a-

smalle-1 thaLi rtiijih rf ,na.r:l er III. This ti -e: is c intrir ',

tC. t e *xl: 1 .: t 1 iein :.a0 fa1 b:t tih i t e irt.: g 'l'hic

of l-e I o,:,:Cti .1 i.*rial oe: 0 ffi ei.- .an.l1 tiaiar poiD i 1: ri re ',

p 'i --2 : .riai-.ii.; on t I a r 'T, ti.', a'i.i '- 1 J i'.'. ?e t .tl.in Cf

th-c i.Oten ti' l, :'es e. ti"-el:,. hcu ve'.-ir th1- i.pari t e r-c r

1cn3i. t-rt *: ,:impared 'ith l't'.I-, t .' f. r t rh t .:i Ti.ea; ei' .r i:.: r i t l.. -

In :h latte r r ,ac o cr CH-i J l and j C'l! 0 as- ,tr.i 1 llemi trh ia'

th.aL fCi' C'il4 L'hich is mos L .: jniil:- I -;.

Tl-e merican e'.'i ci.n in a-e c:Cl. iul 'atir' i'. of tIh.: Joule-

Thomrrson --oeffi,-'ie- L at s- r re. sur'e i7 1 .. I .. For H.'I'.

11H-5, ani,.i ..-':, the 0. 'ia lorn a t.:- :.. 16.4 an- 16. -

respectiv -ly, ;,hl- h Ieni-s t quite -.atis-factory. 'T-, e ..ot'rir.u-

ti,:n of t1lh e c 'r tE.iI i- Eq. 5. I 'arg-,.i f-cr about 10 '

up to abcut ': in this calculit ioI- Tl-.e ag,?., m--t f r

Hi:O is excellent but for IIH-M anid 50; thie ,.i evilatit-,n :sems

rather sa.te'rnatic:. The zeco'i '.irial c'- :f fi cient nii hI 'i

capacity are irepr'duce..i thin .5 ] with the cor-' lat i:ons

used for these moi-ecules. In this respect the jev'.'i'ati' ns






4-.







E o *'r l.otn Cr in.i- 'r At l.: .t Vt ri n i ry:.1V.;tl el:',

lo nLi"tent .

T 1- a ;.1-2-. r.;' .-: r t i:l it ah fa .....a-J to n p1 laI





' a i'a ,ii t er: .-l : ri re in l rrr.t. Unf .-1r I't LrI' e Il i It

'pparS j ~ ii 1,- : il o e'-:-lai.'- 'Jath pr'.i er ic.l., ith a in. le

et of nC l aalrml et" r .1.















C'HA'TER VI


ESTIIIlA''TOil 'FP 12- 6 POTENTIAL ElJE,.'- FUJJiJ.CT.'I!
F'ARAI'"ETER FRFOi.i 'F CRITICAL TEiFERATIIRE 7
U11T PiT.ARITAEBTI..ITIEL


In t-e pi cedjingi chapter rI-i- ariie-gIe- t.2ei igto pir-

pot tential e-er .r- fr'u.c t i r as bee: n i.r,'v :t r.lgit d t: *C -r'el ait

proi.periez of p.tla giZes. The mridei ilt r r, Lp):er:t.it .-

lependI: nt [:-3ami -r'y i-o pro. -cd to be SiT':.: :- .L2 ii. Tr'i. :":t: rtI

pararni ter.5i ar d-rt iri ni-d fr'-lO e-[:::,.r iren t-i i si i,:

.in.d ,eco-l '.Ir al :oeffi..i t a.i this is ,.ii 1: ..-- rh- ,..-

iith other; pot.ent. iali -Ho'.aer-. r, i r .i .In-,- pct-.ir. i. l r,:,1:i l

to b-e Lriulv useful ini lrP:-.i:tiag prope r.L'es .-f Ni13a:+.it i.,

thli e P m.ust be a methc'd of zest i:iar ing rtIe i:par ?t; .r-rz .,- it.h

confidi-rn:e froir so:mei simip le, esily aci:essable pO!lpeties.

in flr L t :'c'r ti': Le-: ar,_-,.J n.:.- 1 -6 pr.' r T.nil rh -ei h-if

be-rin ae-.eral merhocds of i=ztin.air irn tlh plar.amnrr r-r, i..- ,

from criti,..al c:'.nstitnrt f1 .;i [o a i abi' lit 1- 1 ri

fo-on saturated liquid drenities ai t lowi re:.rc.'-. Ir

this chapter r tk.he iang-1.-averag.e pot.-nt.Jia ,l ya'3riet ar-

esr.inar.ed fo-o.t L r iti;. telpeFp-t-',rure, and pl.lar'l 'i.:bilir ie .

The pr'incipi- f crr.pondirg 3tatec h-as beer, .sed

to predict the porte.tial parameters:. for 12-4. i-ittil~-

model. (3) This principle i. bi.-cd on e.'er'l assrptio-,'








rimhn;" wrhic, h r, t.e .f ll- :i-. i ri *' imp i:rr t to. t 2i- L- ; ieri lt

JL.~.:- .. io.-, ( ,) -1he mol.::,+'. i ,.:. ph'Leri*.-1- l1 .' C;,m -. tric,-.,

(' the pC r-irenit ial entr: -i- i i s only a fu ':tion of intc-ri t .i:le. : r

.etpa-r'jtini T u.:, with th- i2-6 C o.-..rntit model r.hiii'h it.

,.,o,:i for .iIpl:-, ,ph r ic~l. 3i-. c' rn'im t.i- .: o : .l.- l.ie.:l l ,

:ol-: '.-:es thou i J. t i tin. if onlum th h Crpr r po ,r Qiri r.?

the.:r,' i I'd .C l. beL t e:ted I t iffe r- til "i h A:. for

Ihe i::. I mI l]e C:.ul th I- o'. 3 ,. rrpt .: rin cinnI:- t b. trie.

The p re.setiL model, Eq. i.2'), -.?.s rather ,uc :3 .f l i 'ith

[ci:,.l. rni.:, o. nj pe'i ri m le i ':ilcu : .-. .: 'a3 oCn in r l-i.,

chartr. s. 4 i,:,r e-.- th,:. .:ten..: i ene?,-' i, onl, : C c i r-n

,f ignite, 'ri .lec iulr i c -:ir:t.ior in .t e f icm :i Eo. ( ) althi:,uh

it 1: 1.,: .ri implit fu nc:tion of te, .r3 ture, rdipole

-ic-m.:nts. .an,- pc-lari abilitie:. E:j. ()', il,, :,-...tt., fiez the

' rqiL-nrt :.f uni .i.' : S l fin .:. ti v.,al 'c-7L for th-e pot '.ntiaai

c ri e -'r' Tier-fur ,' c-n f.: o.i j th deri'.'.iZ ' 4 f

the-. pr1in.-ip[-i of' corr'- Fpor:li.n- g -T.teS t Inl-eedl th-h *iepeinderi...e

0o t-'he p- 'r met-: !"' tho- proIC r-'c.-tie, c'do' C Iot hiti-d-CI the

in-?e iP-.-ation c.-'. ,' Iom-rInta iAn the t.rti' tii:i r, fuUi ncLion. F"r.Cm

the Conldirion. for the :ri ticai a .tat-s it follows that at

the c rii. al strtt t i:T E nd r '.'Z/ C hoi 1d be uni-versal

c Cn-r intc H:r- we usC-d the c1ubs-cript A eo clenIote critical








C, .'
For og with r'.iticlt i u tp fr t -rts. -In it i cr and ratre oni

.: ** dn-'jd -lnc,'',.-irt Uizl'v; che pa .am.t '-rr.z: in ,:'1hapt,. III.

., ll ; ofil r.' /ikT are :ll':tlaI:--. r gi'.-,'i) in Table, I

airing uiw-th ,eri.ic;- tenpor-ii s. In vih- <.*' thm- nratire of









.Jta I u a n lei i C t .n te a. VZ" It U.ta. ft 3 L b tir

tnfe r.iart.or-ii-lip,











n'n.t:, r ':' "ic.l ti *: '.' i.t i.:i :.-, .:. n rI r h .: t .:- .

Th,- th.,: ,: .Of i n'.'n,, o ni-i-ijiZ an..t -..I-hel r l-J i:- .:r .i,:.i n

3a.tt;ra i .i -L .vei. ii Er'. ( ll '. ;, tl':. l i iI the r,-

f Luric io_-jial foIinTi as r-ot ':f Sl tr-.ir : Ln .i

T'lE t ta:.. j rIl.TIl'be. f .l r: : 1 i'- a T l rtI- r t4n- :-

iincrert .t in b ler L-f '.3al: 'i -.;t'n I' I-.- i i th I- .

It ': i i'rl- in 'il"L ti-- IlII ti : t e L d' -i.'-lt I f i :t

*.ialc il'L '-d *.';li.i- O .f c'' r :,' te .- i mp -ii ..:al .3il.ies

Le:' lmhl i ,'i' e f: ai : mol -cu.il .:. ( 1 1 .: ei-;.'. ;? ti t

E're *' I t plot te 3 a''-.irin t : Ci-. full l .:tg r iri-Lii.

.sc jlc, i t s3h l.: :,.:L.i a : rai t li ine .:f :.1--,7l 0re In

Figure 1', tl-.i 1::nd ,-i f c i r.l t ,:i. rrLiade F:i the p:.t' r- r ,n:ri :u eI-

all rih- infol-rm, tion 12i takl:n fr'm : rn p1>:.'.,-c-dinj ._ -. .

The i-1o-enr line- calcular, ed 1-.:, Eq. ( 1 1, ,J,-s n-:t itl.:.f'y

t.ho-e e-'mpi.i:al points By th- m-- thid of lese.t square -

an er.i:. rical eq-luatio-) .i.r obtained for-i th-- moliecule-

20on il er :-:i -'-:.


.r 4r.r -10 I '-10-'.?t -c p- (5i


The empirical line i al.o shown in Fig,.i e 10.












I1







I i






_- C \ i '














F-I
,\ \ \ ,I







'. \, \,
",o \ ^

,. \












..-LT- \










--U










Fti m Eq. I' t n.] i g i !K anri r- ':"- n I ca .lcul t:.:.

Then by Eq. (a ,- I: rI b. .-l i. ui. h -.r:n i.n dip:.

iriI.icnt and pc 'iricabili t The vale .-,f r-' fi: i .-re:

frro, n h -alu,- *.u f -. In h-c i .ia- trh- a -.in 4 1

inI TableCi -"cireo.
adrl A ar c Ac lc la d ind 'ic lli ei j .*iin er l,.i : i l i'ie :

in Taci l e 14. T e average 3 .i ri.tiL f the ,:al :'-.il at, .

v;a3.ui:-.T f .: .1: and- r' are 14 ., 3awd 5.7 r p:t..e t i I.

uhichl .s-ee: qil ice c.-.ticfai :t a r aror nd c '.i: f- ,.- -.ibl. 'itr

hcc,.se :f 1 .' -'" a -nd ,.4 f' Br i'rid t ; )

Tc. :h;.k ri: ap lici bi i f.- f Eq.:. ( .) i r,.. Iq e

.eco .nd viiial .-,.,.e ffiG _;.cnt. e arnd "i .:',:,itiez ':' 1 :

Freac. rs ar'e c alctilate.i The est i.a te .-i i'- at re r i'e"-n

in the l .cier pa rt .:,f rbole 14. Dip':'ole nm mern t aind p'1lai P -'i

oilir.tiem a3 r. aken fr .m Larvi:ol t-B.r, r tcein T.ar.. i T

'.'alu:-s of 'ipole lir-rtr' c i ]ely:- u.niG a'e 0. ., t. .1:nd

1.2'9 and polari.abtliici in A- f .. ?4, .. .ni ,'

f~or Fre.r.n-11. Frec.-i-1?, and Fre.:,n-21, rexpe;mc ively. The

polariz..,ility of F-eori-2 .2 l :: i.iIte by Er- nd-

Fr-mr the bonrid pari2a1:.ilities.

The ,calc latc'i :U!,xrC:i '.i'ii l : C,.f fic ie-tc ,nd .t-L : .:,'irt iC-.

,ith the .a i.im.a:-td p r'a.netere.- are cc.mpar'e i /i i -: ,pe r :!ir.,::r!ic

itL Tables- 1. ard 16. Tr.e agre-rm.-rit is ci.i:-r-i ir-ig ,'l .:jrod

for borh properties. Hoe'.'er, the '..arerall ag rueeIent in

Fre.jn-21 c altxlation- is 0 .onlv' _lair Sin:ic thi- pola i_-abil it;

comes in ever" .ztep of rIhe ca.:_iI- latio n, t we i;iw-uld li r

suspect the accuracy of the :t-icuiar.xd p,:la.srizability :,f Frl'en- 2'1.








Ac. f:r Eq. f:.' the c: f ici: t :.f ,''.T i. :m iier

thi i C it .-,f I'- ,;O F :"- i i- m 1,-,.. LI -. ?.:ri "c t:. C'.Cl .- '

1r ..'i.l ,'.11 Ot' ;. r i.hiiant. : f ."11ilpti : 1 ati,] i.01"-5 m:' l ll d .-..

t- e f :: t of a.Z mr -.t a ', i pil.O : In.:,ii-,', ri Ea-,'. r : i ti, : ~1

t j raiF.' trt...r hif. :'. r I h't I:'T 1: ni'-r. . r ,po r-.li i t" p o h eihei ,ic-.- ,

n pOi'i'I P i iol ,:, i...'".. to p F o-A oi.:.i u .e : the; s ,t. inedl

thie i- t r :.,'Lon ,i- p,:


*T -= T 1 4 5,


Si!' -iere '.u b ,lip-t e ii e- r, t i C i t .? '.s1 V lue: d ti LtCer- ,? i tel ..

d ,' d jeiote ii-oialr 'i .d- th.-0.tr e'tic a i i'r: po,;'ir,- Lr I l.C-e,- I .e .

The; *.bts. inr -. n 1 1' i ,cf Pt-r thi : .?t.ii3 r. ?,i r I rc

:Cr.: E ':i-i- g, tl.eT. pitiri1i1 e ':- -I -t:O:.' p1 s

f 'll'-, : ,',. l2,i- for I-m ,. "2', f.p i .1 :' .,,1i2 for riEr.

1,-h an .-ei d 'ae 1 .- .': = 1. 72.i 7;. u i h iL turn gr '.-:

T = 1 T -. Fr-om Eq. an iJ that f :.r inp l. .

S.e. = ' T. as u eiJ them, ,.e obtain

T- = 1 7 T u' iJ'l in oiMe -ense '.nonfl ni,. ci-e .*lid it.'

*f Eu. :

I .-j
'T',ni iing t to i'e L mr pirj.ial r quation fo c. I f. r pIple

.:3 b-; :ome e.*:plana i on' th- c >'*: : -"nt T-at i.,

"Je orrmi.i-i or' iier dipFole-dlipole interact. ion termsr

o.ild beC countierbal3anc-d ,by t rio- use o hi;her e-poent..

The .'*l.~of 1 -.9 5 lie:-. betwc'n theo.Ec tical valie of 1:1.5

a.,d '( br ,ni.it '-. alue o:f i .'2 HoJ e'.'e Br.-n,.t u.'-d 3 nater-

Kirl-wood' 7, fl'muia itn. ta, of ivrc'aniri.s-.te h?n IIn













Ir c c lii L : iS f-ltr t t t I: r.-ii .i

- -.stim it ira,' t, -r: fr :'' i .: . i,' Ir

] l..1ari1abiliiri,- s.e;nt s-ti fait.r y.:. i!e..r-ti,.iri ,3. iV

th.fe -i .- : iri- p : a.=T -- ' 1 -! f,. i l..: 0.,.e

t Tref .-- 'i d to P:,:,. e-i,-ir, ted.














I I.J i' F, VII


,:',:F,FPEL _F,,,irI li'. .'T..T E ,.*',, F.EL." i ,'.,l' h, .,F.







..t,:, e.:lljli i lr t I: -i_"l:,,-. 1- i ,- t-
S tCl'OT P






p. 'Ti p ih iciO of c'. :p ii g.:.l ,-a .a I er.
''it I,; ai :i icr tie .:c reltti n.r -. i- i-ri i.:-jiii '.i i.ii



in-'I:''ii j lir iui- -l f .i ; I l ii. i i: -t 'r .' .





.rc n oe the cyriti c:r l *::; .;t:-nt tIl por on ia.:. i l p ~ a'tnler

:.or c -L.iITrhL in 1 l ,-. "Ih--. tih- ii -f.J:.Iir;.. I'. i:ter tial

1Z. WMI a: the uln"-.; pC;iittil rr-. flzl. -,

the -, irrmp. -: :pl L-i. -. i 1 norp :..-. riclcc-tile: foll. .; e:.ZActl:,'

r-e :.ii,-i._i e : f -: -JC g i..:. l-]i g -S- ?es. F'i-r pc'i : trr i.:

r'ait"-:u:i.-l- . 'l'dappe '- i s f i:.,- Iater. -.-] a -c- :Priri ,ipl:- ,f

,i,-r e.--. .n:,rd.ing .-t.- b irr:.- -:o -i2 he C L.i zp.-lse ., l

a!::.-i'..:imc' ion for the p' ter: i l liel, Cc'' "a ho''lii'isZ'

t' :te.:l th-: -llipJ tiC.:l aId !:'liar mfic. i-,ules b,- th- usE' of"

agie-- .epecndient p.roerntiail r.odJel .:uggerinheir: anr'd O-r:naildJ

L 1cou`-e:'L for :S,-' .';;* :t -erTatic rCe-iAtio 1s of hyI',rccarb c:.n

fr:.mri ti-e rii2- l.: :f ..?ri 2 '7r. ponding [atei s b iy inor. :lducin -

.:ri a i'- i :io -,al p r.-'r tc: Tir'ad .s arid c,:'-'.Io i:: :. ,' ''- '}

.eNi 'a:- .'i .;r-j ti .n" forr tI ar pr- t p.'ro' rti.. . '.--.. h









,dir"tZior, i .rialy-.i.. : i h r.t e .: itic.a c.rL. t .,r I-0i-._i

r'c lt i. -e z cc,: C'ul for Cimpl: rzl: .i ;- .

.Ac'C i d iir f- c th- e L : it',i:: .le .: 'i pl- :' I.j.. i- t:.. .-

the r Ju.; et p '. np ;r'ti: ,i_. 'i m ,-riail L .,l'cL i '0 ,- 1 ..-l:. '

furji tion c.f i e.i-ut c tempv.ra m ir: ,an i pi i 1 '. -

.-: -1I, L cs -Il rrilc-'- ,ic 2. W.i i tl' .:..e rti al e h._. far. .: ir3 I

parr- iet'r. a3 dLuc .C vari- abi,-. ;: h .- the i 3e,.ie.

vi 0.co0i t a d i Ifus-;i OF, co l f ic ir- 1 .7 ': .1 .



r = !r 1 1


D = t 57


'. i'- l : he f'.: c',:mbo: it ,- l. e i''for3- i. -.zed. 'ITh r-ai.i

,ra.Jbi; cl: in the atbo'v-e snchere i:. th..i he h_ pC ti Lt 1l

ia:ram te n-.nuld ,e :i .'n fo the mr ,ife.:, e. ce_ ..:.JLiie_ -

tiori. nfriort ur ciitly, p. eit ial t ri [i-:-rr-n r U e -2r:a 1 '

kncutin. Th'i., z lti : e or theri th- c: i ic.. l hC 1:'i:, t. : a:e

ir'eue tyi used.

In thi: chtri'. r r e -.ar nr.t.l-J liqui..d dJern ,_ c 1 arn-m t .-

a: lci pre',cure ai' 3!e ,.t _d thue 'e'.iu.:ing + t l .ai ol- _. e '

ha: sh:.'-ir r hat ti, d:er c.7eri crle1c o0- :3t ur 1at td ii' 1.i.dJ :i]e

oi terpe'-atl r- for T .0. '.' c.a be e::pr-ez d .az:


J A = T


..'here i, i. ne 1o r .er it,', 'ar)d ] ar n"c' i e. '.-, ...' -

heed and i.' icKin e/ nI hav':e .'houni at rh--z.e paI-n.imti : v'-

i'ela 'tej. t t r-he par am er- o1'- f r : th. n i: ia li z -d i.-m i.,otI ntfit: il








I. c .:nrl: .,-i Lg t. he -mcor p I- ce L ti C 1ie 1 U.-dei-l for l iqui'

ahase 5z- "nd rin-m poterti 13 I'oi- ': pjht.2. ThIfuis tie r lat:i.n-

'"s ij.l :


A

i-". ':"-


a o = C= a I- .2 1 r .C:, I








l.-. : 1 Ci
;i rc C' an h.: c r i i .: t.5 n t C r Ci.-Ateri: to tr7 *.- .

1- combU ni: g Eqsp I I t.) a-- i r oi t n e -I .

(C 1 t_ re -lu : -d pCr.pI t i -'l asI-.: .r- c t.i nei .



1 -- i -' L '-



1 *, 1 1 r
S F= .- 1 2.- i I : ) '6?)


Th l- reduce. i '..iscic ,"y aiI di fuLsion n oJ 'lli:'i.r"it 3 r-e 1r_,'

fl',icti) J.n o, I-f i I e e't+P .:1,,:t. P2111 r ia L. es.L, e. Thei

,redcLec d r-em rpeaa tur.e, T is tcere 'T''A.

Thre e::.p-r-iin:-l vicosit ies of .simi!:le mriecules

are re:idur:-.cd bt Eq. (i6 i. TheseF a-e at iP;r, ure' one

tr,.: lr:- ; les.. 'T'he values ,f' 1. and F: i.-i ar-e given

i'r T.able 17 Il -ZLej- the sourc-cs i:. e:.pn'riintal Jersit data

i-e also .eni. the le-ast- 3,:1uares method the- reduced.

'.iC.- itie: are ,,btairnd in term' of' r-educed3 temperatures

-, j e'l i-ht n..li-,?i.aes.










r '.CT, +- 114'9.T .l '-.T

+ 4. -1..T - C ., ;2-, T i ,


TIhis~ -]ati .n i.. Obr in .d r :p l i-' e ten: -r.n.ti,-c t ;. i

*.4' T ~ 1i.1 j:.cig r at r-c.:|. .'.t viz ..... ii .: .:-f

Ar, KP, arn. [42 fail i D, to e3:n D.r et a ..tifii. f i.

e;lag tiJOr 1r ', ,t'ail ,'j for rth i :i ::li 3,


= --T8 + 1-,4 .2 j-7"- -.... -. .. -

4 1.477'- vT C.64ll.T :(


ifo the tre'npe-atu ran.-tg : 0.' T '. .

Th,-: e:.perinren:t:il ,-iiff..<.-sion .:.,:,ffi'ileni ; .i. one

tri tfO.ph vr. ar. al..o ra:-' ed b,.- F..:i. '-.- h'

re-liu d :'-,l -liffu. c oef ,.ie t are pl,. d t ,: ig:,irt

Pre'I ..-C temri:..e pai tire i, appe1'ar',. tht: t-,ei ,;.: ,l.: I b .e r Iest

r-.pur -ented I.; two :ra,-iit li :e.. bi lb.e i- E- ,11re.-

fit tLn fColl uii'u ti'o q'., ti,':r are- ontr.A ir.'. 4.

:.: ,2,'0 = .--. T ''' -. *' T - -. .i


D -' .0 T T .


'T Ie r Se al : ''F '.'ic, L t : it, l IlhtiC'ion ,r- -. I V '-i inl

Table I': i ;er-e ttihe u.i' r c'f dci ..: p ,'in ?., tei-i t'T- ii' 'cur it'i e,

per.--etF 'r Lct i.:,atii ,on ai-nd. tfe .G'u,'.o. ouf :-:'.. -rj..i.r t:il d.a.-:

are al oi ~iv. For h'-hr r: -: .fira p i)'ii -.L ,T ir., o rul.-.'

ts-, ir n the c: :i".'r agc d'.". r i ; .r, .








i a ,-eri l he ,0*:'.i .:it ..r -.e:. ..;:e 1 '- :. th.- r.I .: i':

L ..c r-e rr,,:. .:c.ngple::. T'h r. i.. :..: .:o iti:-L .z ',--* ..

A;- n( :-i -r/ 1 cr'! *i r,t:: .:t '-': --i i .' i : ...r C.t, ic r.:- -hi. -

S fall i

tre.:io hi. been n.ti.:ed. Fpr ".' .:'i t ,- *.:;j-,r '-' In

tris ca.il:uli.:i -: n re-ji.c .i c 'ol- iiZ O:f 1i N ., i- '-,

"e- :." .::-1,o, .: t i :'. : cf Ar. Tiere.? f,'r*'- ., t'.n: :.r, ?;...,-: ,i C il

cd3:. ," c [f lic hi h :- E p,. .iur .5 ar,. r r _';er ;u.1. r L .1 in

l.-r cI' .,- cncilu::icr ,f r.17 a& ,:- ...-lI ,iC, t"-..., ri-.t

, "- :-i ,io...:si jcSie re I.,- :i t ,i ,h t,-..:i-'.rat' ur' n *;F i.r--

Af the ie- ...ilr .:.f :-ri : ,- l. -:C;it Sm c riteri,'i c::-t_,_'in:rI tcr Thle

Ji.i ; ir epar-: e in L he tle 'ic -'.id '- ,.. S ri ? .r .ran-..' .

Sr-:. j1.c, ncr-ed .:, thcin.

cr1. n orl Ax, rI, 'C' arin li] e I r .- n in ,i'- t- Ei-:

'.e -i .1 .-iti:- i. t. -1.1 1 for li. ; t..a p'. ointsr Here

ir i-c.E ti- 1 r' ': vi:.T io %mo :n the- i all.

Th :1'.u'i:' .: f c:iffi -ior. c-.: ffi:i,:'c t r :lcuiri t i

is iiv 7n t i-J Tabie 19. I tr '.1 .atc. p:.in-.: -f so v.-n ir iol-ecaies

th: ,: i l d-eiarir.n is ".2c The .gr'eemenT: i ; goo...

for. ;-i.ipl-: .: lc-.ile: sacch as A.r, mr. a' K 0 and Qi1. Ho:'.?'ver,

it is po).-r f- r CH4 and. .'.F It shuil b-. nWctcd that the

-,- cter cI tG he e.-.p-r-inent?. daa; : z. qL; ite 1: 0 r'g3- -or '. Lt

Of th-i m,-,lecuies c,.)sii-'red heire. Thu;., rhe devi-ation seen i

_*itk,:- sat i. f a tc.-. ;.








In r iL C :'Jltr..,, ..I r ia: L'-: r i, ll -. l t t :I L

niitlli.:II.1-.: "* ,1 . r 0 t i'2 :'Y 12'! ni-In :, .t n rt i:1 e ,- '.:: fun i.'i, .

-.:-t it. i. : .,'9 ll-!-.:n ,Jn fac i" -. tthl 1.. f'1 t a ...

Th,-t i.,. t e 12-, e tae.ial i : g.o. ,r ll i-E i al

r.:.l--,1.1u-' -;-3 u ilj i -7 p- .'".-r1- ra.t i:i better' f :'r ,: ':. t-:r. _.:

m l:.l-'L.l]- ?, a t-,l-l .i- 12--. mr :,] 1 T' -_U :, -:.h, ir--: :, :',. ;. :..:,i
. -rr.id. :'i -,i:.r. it l1, a -i:l : -:- e:.p -._ r eh-.t ri.-- ,i:le if'::,

cr:.na,.p eredf. here a h:.:,l,'i ,:, ,. I i:i)e :aue .:-. ,-- *jt.i a t.2..







cc,.nFpr I f...,'.-r. abl;.' Ii or ers.. 1- 1 .








1-
L-


1 -



L L. L"


L- 1- L - : -


L. DX. -T


*-i ,'* ( J .


*[-
L -T


,_* ,-" J


i-
i' i


-- P' .- ,- -
r.,N k-j -


-S.
L" 2 ,






rI L











Li~.

,- Lir'


L.' ,U, >



I' -T








0' 0i
ui, i:_






c' -
u-', ,ia


C1 ['-

*r ^3


Lr- io -a- i.' -. :.

C' f ( T r-D I r- C. CO
4c .-i c L- 0
.- H L'| -- c'.i r-- -r LP. Cr' u'








L in C
S U -- r T 3 3 f .
-





-. C -. cu C.
ca C U L U C -, C Ct C


CL


.-'
























ii













--T
















o C)
: ,T



5
00



.' .


L1-
[ -




*:.I




I.
I-

s c.








u <: r

ir
[,-











Potential Farjmetr


M lecule Pt ent til


Ar L- i

lic. se
I. ic. r',e

I'cP L.- J



CO2 L.-J

SF5 L-J

CF4 L-J



CiHf L-J



Ca H,5 L- J






CaH1 L-Jb

Morse

IJeoC His L-J


Table. 2

er's ':r Jl'npr la li'i,-.i c lle e


S 1; : ',A


192.24



167 .7

151.5














410. .



23.5


3.. 07
R4









I54
2. -'-'7





.* (4'l4










4 ,-
;-.7'l7



4.;212

,. ':':T.

5.o0 5

T. 'ih5


r.


1'.
i.





1'

i'-'



1"**









17
21 17








51 ] T
l I,











Critical VO\'clses anrd


Fa larizabil iti e


V ..:: "n- ie




*^.2

4- '

1995

i38

C'G

2'0.2



2-55.1
23.o;.


A:'





C .'


C -








li0c.sH
ih'. 511.


.62
2 ,A~








S. .:1


,.03



, 29




1.:,. ;..6


o RFef.

-.4



,4

3.4







4.4
A4

-.4



^4






















rl I'- a, . C .7 C 'C '
I ''' Z, J "' ,-, '.L, u. Tr

CJ u'. L ii [- I-, i-r --
.-- + + + + + + + +















-1)
,*jC u- : r ,. : ',
rj'- r'.j *-i ~', O? C :, -T L*- 'EC'











. **r -


i + + + + '+ + +






--








* . -

', .~7 I- C -s ,I I*
r r- : .- , '
r* i [- -1 CC- .-I i- i- -4 *
















I - I I --" r l I. .--, I .-- I
.r iir -r [-" '. .:.- .:- -,"














c. ,- r- r- r-- .- r-i r-i C-


4T.

C) +
.'i
C" a


[,j
,1.















*-t




01
C'





-r--
. *1


















C,
E-










*i






4*


U,)



r'-


l-- I+- .I I- -1








-r r , ,- i,'


,--
t + + +















I'l
I I + I I







































.4., .' [ :1), ':
i-r





Q, [' r i
















Cf
X,















u u",











- [ I j j



- I c L.: L- u i
















C' a. "
-J .--i C -
i' I I i i i


a-' I'\J LI.i,
r -. .. [






a-:
[-1


L'4






a'F Cu '








'_'










r .:
' u
'1j
-*
'*;


ril

















v~ Zr a












'a.,


U

+1
2


Ll,








--,
j i i .- i









S r- r- [C- r-


l -, +, i




































,- -r .






aJ' 0 -- '











C.




'+
L..



-t
'-r


Lii 3i-





.2
























-r r-- r-





















1 1
-.r C' -












iX ul .".
i~rI Li L -r P .


Cu CO C, 0i.


S ", u'. .-
E r-' r' 1.'.


+ + + + +






















I I I i i I











uLI. ,:, cj ,:, r.", r'. ,Cx,
S r-. r-i ,- C C r -


J ..".J C\J ..".J .J J 'J


Ic -- K. .








ri


L'

. 7
- L J
S I



, T,














Lr.











l.l














-1



2=j


'. j J uC '., Cj LI", 3.I,

-. ,- -- [I-- = [ -- 0
o -I -= [- [- r-1
r r*'. f a a L.


a -r a -. '
'**" -'T -r .' '", "'uJ 1",
-"- ,- -t- -t- -'

















GX, *'J l ," ."j ,-. ;.

-r Cij 0 7 c'- i"- .0'
.- r^ .-





i I I I I I I



:1' -- -, -' -a

L rc. c"." r-


[- C^' ' .- --r *
-r L [T- I Cl ri-

,I [- [- [.- '. CS ,'r. L ,















CC L. C *D u L-

-- L+ D ["- -i

LC, u Ii. LI. T -" -

-+ -- -- T -r Zr







I- L:0 "3' "' .-i r' C. r'-


rI Oj ". U '- r', :0












t- ,0 "J a CA IC
j r". "'. r'














c
.U




















C
'2' -:- .-T '.j L
u' =r ~:C]
-. -. -l C I U. .~
t + + + +


1-- u`





Ci :







I I I" `


. r r.









. A .- .:i;,


:. r' C r* '. j r". r'.
o r- *'J -7 [- r J
t- -r -sr L u". i f-L


u.- -* ..j 1 .' -+T I"

':u ," L 'l' 'i '-' 'C,


r- [-






4 -- +




r~. 1-


Ii- C.~ -.













I- 'C C, i


2~ C I-C ^ 3. ftJ i'.

D. -r [-- 0 -r i- C
- a r [ -
V.. V. Nt r -T Li


U



21























,-i [1- Cu -

i, r Li- .






















*ilj C. 7 + +















V .T -- CJ

L4 r .- .,J

*- :-















- S
* L"- ,













Ii
C
1-

,'LJ +



1,"j 'L


+ + + +




















4-,





I r + --












0 0 LI
.', ,' *:































C.
,'- r, ,'




























r i


+

'r
1- 1
I: :i





















.-'













-.r -

7j *L c








'1 7
-I r- .










0 ,. I.


















-" .r :'- -.





,: -T :-- .'

r,, r, -'i ,









[- C J J -j(J


Li





'. .4


Kb L-- *&











=i ~ LiT Cr u`


11
1)



S1)






14

-4


















'1'


I'-.1 I'


-` -1 *-4(






.: J




r-. 0j V


(1



p. *, C, ti C' a a
cm a rr i-, r a- a ~ i
- -J - ..L .i -. -4 )


2*-









Table 6

-.e,?o:.-.:i ina ,'.:eff1ic lien, for F.olar i,:,es



E *:. je 1.


S'I.'



261

19'

i4'


S103


-B c,:- 'i,:,le


-.:*-. 2:: 4




15:1 112

92S 72


I- c











iccl:


-I

ici I


4~1








Table 6 (Cont inued')


-2 B c. cie
S _toc.C. alc. e:.:ot.





'0 28; 404



50 24: 3;;. 2S
5 212 279

100 1 4 232.

125 1iGO 20.0

150 141 171.1

175 124 144.1

200 110 125.,



-B c, mile
CH3C1 ti C. ,_c0 cext.

-3.4 505 754

-2) 457 665

-18 436 b37

+10 344 500

27'9 401

65 232 320

93 194 265

121 164 214

149 140 164

177 120 155








Table 7

Empirical and Threoretical Dispersion
Attraction Constants


E 0ro1, erg. x A6

Equation 12

67.6

36.2

255

114

587

312

672

1131

155

427

566


Polai
Molecules

NHH3

H20

SO2

HCi

HI

CH3C1

CH2CI2

CHCI2

CH30H

C2a1sOOH

(CH3)aCO


lonpolar
Molecules

lHe

Ar

Kr

Xe

112
He

02

CH4

CC14


.-: I 12
Empirlc al
Theoretical

1.105

1.26

1. 50

1.11

0.727

1.50

1.93

1 1

1.89

1.97

2.54


1.03

0.99

0.50

0.76

1.17i

1.04

1.46

1.86


4.38

55.36

115.3

569.9

55.75

49.09

88.2

2004


Empirical

74.7

45.7

3583

127

427

468

1295

2160

294

843

1436


4.50

534.6

116

281

62.8

51.1

128.9

3731







Table 8

Potential Parameters and Molecular Constants
for lNonpolar molecules


Molecules E /k.,'K r.A a .A3 ef.

H2 57.0 .2B7 0.79 0

2 91 .? 4.132 1.76 7O

O2 1130- 3..5 1.60 30

CH4 14 ,0 4,261 2,60 30

C2H4 205.0 4.750 4.26 30

CO2 190.0 4.485 2..,. 30

CC14 327 6.601 10. .0 30

He 10.22 2.869 0.204 3:'

IHe 35.7 .131 0.393 .0

Ar 124.O 3.837 1.626 30







Table 9

Viscosities of Binary fixtures


calc.-expt.
System TOK X polar* rL~alO7 4 dev. Ref.

IHa+H2 293.16 0.9005 1005 -0.1 86

0.-7087 1045 -0.2

0.5177 1080 0.0

0.2975 1088 +0,1

0.2239 1073 +0.1

0.1082 1013 +0.2

373.16 0.9005 1355 +2.8 86

0.7067 1361 +2.1

0.5177 1372 +1.5

0.2975 1338 +0.7

0.2239 1503 +0.5

0.1082 1207 +0 ..2

473.16 0. 005 1726 +4.0 86

0.7087 1750 +5.0

0.5177 1711 +2.1

0.2975 1627 +1.1

0.2239 1572 +0.8

0.1082 14)8 +0.4

523.16 0.9005 1906 +4.4 86

0.7087 1900 +3.43

0.5177 1865 +2.3

0.2975 1756 +1.1

0.2239 1690 +0.7
X = mole fraction








Table 9 (Continued)


System

JHJ3+1J2







































NIH3+02


TK X polar

293.16 E .8 88

0.7147

0.5638

0.2920

0.1111

373.16 0.6888

0.7147

0.5638

0.2920

0. 111

473.16 0.858

0.7147

0.563

0. 2920

0.1111

523.16 0.8883

0.7147

0.5638

0.2020

0.1111


293.16 0.8755

0.7079

0.4786


n x107

10'?4

1261

1392
1592


1 RQH

1434

16:11

1731

1 53
19350

203 3





2115

2306

2409

2015

2169

2291

2480

2583


1159

1343

1602


calc.-expt
tdev .

+0. 2

+0.5

+0.7

+-D 6
+0.6

+0.5


+2.0

+1.2




+2.0




+1.2
+0 4
+3.5

+2.5

+1.4

+0.4

0.0

+-.8

+2.7

+1.3

+0.

+0.4


-0.3



-0.1


Ref.

86









86


















S6










86







Table 9 (Continued)


calc.-expt.
System TOK X polar "x107 i dev. Ref.

C0.2'-8 175 0.0

0.1551 1927 +0.2

375.16 0.8755 1489 +2.1 86

0.7079 1707 +1.0

0.4786 1982 +0.5

0.29 c 2174 +0.2

C0.1351 22'32 +0.1

473).6 o.t755 1896 +3.0 86

0.7079 2123 +1.I

0.4786 2409 +0.8

0.2986 2611 +0 .3

0.1351 2778 +0.2


1H3+CH4 287.66 0.9 990 -1.8 100

0.8 1019 -1.9

0.7 1043 -1.7

0.G 1063 -1.)

0.5 1078 -1.2

0.4 1087 -1.1

0.3 1092 -1.2

0.2 1090 -1.3

0.1 1083 -1.5








Table ,a ( '-ontn iiied!


1Syt +C H4
;IH-,+i'H4


T": :; plar





C' cD 1



S C,


37). 16 0.'f67



I .?C 41






0.5.17











CI IC'17i
475.16 0.-m,.



i i I -






1. 2993




0C 3961
0,5172

0. 2995


ri xl 7





1:47


1 i:




i So











1712

173' '
13 42










1512
17047





1609
15,,31





ir'48
Io5



1747


c a .:. -expr.
, de ..

+1 .

+1.7





+2.1
+2.1




+5.2

+.2


+2.7

+1.






+,I.. 6
-I- .









+ 0.

+4.3
'+5.







+2.,







+0 .


hzi

:9 ~








Table ? Co 'ntrinue.l)


3ystitc
HCt+H
HC1+H.


calc. ;ipt.
r, x1C dev-.


T.E; X polar

294. 0;.322,:i



0 .042

S.20:13

527.16 0.;22(i

0. 7179



0.201 i

372.16 ,..822,

0.7179

C'. 3042
0 5002

0.203 i

427.16 0.9417













0.2409

5?5.i C0.7947

C0.6312

5 2175 4

0.2991


145 l


14 r6)



1459







13.59
1531
1617

16250
1t.2-4
20C'!I4

1 14 1-,

1.S,9



















2451
2,-'99

200(-







2 52':







24 c,:
2057







24855
2296

2245

20,;,8



2489

24:46

2256


- I i









-0.7
-0.3













-0.3
-1.4

-u .7






-0.5
-0 .

-1.4












-0.7


-0.3


-0.7

-0.5


e f.

94







C 4


94









94









Siiih m

04 iiii








Table .: C: cntinu,: )


calc -e.pt .
System 'T' :E pOcl r ::i0 '. d hef.

HC1+CC0 291 16 0, 142,5 -2. .* '100

0.3 14.7 -2.A
-,1- i

0.5 14 5. -2. '

0.6 145 -2.7

5o."-' 123 -2.t'?

0.54 1459 -2.'

0. 1460 2.

o,. 2 1459' -2.7

0.1 T,7 -12."


SO2+H9 290.16 0.8215 1273 -1.5 '-'

0.5075 13.3 -i.

0 .29 .0 1 346 -1.7

0.22.56 .13-3 -i .'

0.1676 1294 -'.

;10.16 O.S02S 140o -1.1 go

G.5075.. 1 ,62 -0.9

0,2C6,3, 64 -I.4

0.22.?6 1441 -0.,

0.1076 1397 -0.9

34. 16 0.8028 1527 -0.? 90)

0:. 999 I1. .1*

0C,. ~17 f5 -l.0

0.4823 1577 -0.6








Table 9 (Conrinuedj


3ys -.tem


TK: :*o polar

0.29 .

0.2306

0. 1676

0C 657

565.16t 0.502



S. 2. Si Ci
,1. 6175

0.4025

C,.2306



0.1657

59 7.16 0.67, 60

0 4 '1r2

0.5265
'J 1;6:

432.16 0.6760
0 69.Q

:0.3265

0.1676

0.1512

472.16 0'.6760

0.4905

0.5285

0.1512


Ref.










Cil0


n4 E

i56l.
15 LI


1457





164

1659

1674

1624

15 64

1562

1;79



1797

1-675


1916




17.7

1769

2115

2123

20 85

iljS


*a1 ex.pt.
: de.

-1. 2



-0.4
-0 9

-1.3











-1.






-II .2,
-0.1


-0.1
-0 .







-0.5

+-3.
01.0





-01.2

-0.1
+0.1

-0,6

-3.1









Table lCLtinu' ,JI


;.'," temn


P: il. -e:-:pt.
X Poliar : ,:.:i,, .e..


302a+C 20:. .. '- ,",. ..:
..c'


0.-
















;121 21-U14 23.f15 4. ?42.
114
0 314









0.1 i
C;-IaCia-rCC14 29-.. 5 .5425








0.14Z 4

3 5.16 ',. 67}).




,7,. i -4 '.


0..201



1.12G1


ef .


Ilr



15 16



1364



14"i4

1421




















1401

1401jl

1796



i 3c0


- .0

-2.1
-1.l








-1.4
-1.





















-i


-1.5
-i,
























-I I'
-1.*






+3j. -'








TaLLe l1

Diffusion Coefficients of Binary I'l x:tues


iHaO Ci+H











HzOi+ Or


T' K

293.11




;,T2.5o:


>07.2,;





-J7 .16'

)28. 6


'7 C .5


I C -. 1 i.


532,. 96




;o:3.06





400.00

5. 'O L


900.00


1050.00


]"12

1-1 1 "I,



1.221
1.201

0 900

1.013



0 .9'?0

1.4

.o. o "

0.2:.4

--




0..21




0.292
J 1

c .31

0. 417

. 621

1.11

1.718

2.23,0


cale. -e;: t.
3 .iev.

-2.<


-i .
-1.'
-I.4


-11 .;




-1.6


+5.5


-0.a




.0


-9.G




-y.2



i-.1
-6.0

-a.

-6.6

-6.7


Ref.

102







105





104




103





104




103








Table 10' Contii.e.l I


li- .-e;:; 0.
y.T m T' D : .. Re f.


Hal.,'+ 2.*--.6.il :i.i75, +E.T 102

.. .:'.2gi +:..2
112.5 .C02702 +4.2

2c, Z. I+

52S. a *.21 +0.



2'c,. i. 21 +7 . 1,,


Ha')+CH.; ':.7. -12.1 'r

2'.7 .7291 -12.1

';,2.O .: 2,! .l 1 1


HaO+CaH4 307.76 :.13- "* : 105

:.e23. -46 C.211 4

>52.5' 0.21 2.


H20+He ;T07.' 6 c.C 2.4 10:

.,2_:. ,,: ".:. -4 2.7

2 1. i .: 1 .1

29o 8.l, J. -7 7.8 1:15


IJH3+H2 2"-..16 0.75 + 0.. ,

2 .16 0.927 1.-



52 ..0u Cl. V+10. 1.






T1biC
Table 1i 1 C ..ntinuedI


System







;JH3+:i
























CSHOH+ Ha



C-H=OH-COa


Ca2HOH+He


(CH3a ICO+>H


T"K


395..0






-'2 ic

358.16











_;I. 1C1


S6J..j'

343.00


3'.0.0




340.16


2 .16


296.16


.C... -e..:t.


Ref.


1. 734

1 .276


0. 272

0.118


0.52-

I', 45 6s



1 .0 '


0.10i




o Ac.

0.2i2


0. 623


0C.107


0.45.9


0C .4i





''2


Tabl 11

Potetwnial 'Parar.ters for the 12-a-6 F,,tcential
Determined 'rorm thle ecc:rnd Vir l3l C:.-ffi:ients


CHNI-
t{2'.)






CII- CI


CH3-CHO

(CH3)aCO


23 4.



24 ,)



157. 7

167.,:

264.1
ici;T. j

2.:0 .


3.6 01

3.670.

S. 5. ,'



4 .7 85

5.447

5.040

5,. 2'1


''r'' Thre.




2.1 i3









1.322

1.3')5


;.
o '.







Tacble 12

Joule-Tho;:sirn Ocefficiientc at Zero Pr:'esu


System T 'C.


50.7

101.

150 .5

200 .2


E::t., K 'tm.



4. f





2.5'1

2. 1,,

1. 725

1.224


1. O20





1 .45

1. 515










1.20,

0.91

0. 73

0.595

0.4 90

0.415


Ex:pt. -C&al .


-1.5 4;



-1. 54

-0 3T;



-0 .221









-0. 3 50
- .0.55




-0.15
O .270

-3-0.350




-0.52

+0.15

+0.14

+0.06

0

-0.02

-0.01

-0.013

-0.016

-0.012


Expt. -Cal-2.
5 de'v.


-32.1



-74. IS







7.

a.5




5.2

+12.5

+21 .

+28.3











Em ir:,i ic r l .1 ;.-d


T -, ]':
T_. t



647 .0



47'
5;8.7



I I- -
32A4.







536..6
51;"5 .

51,3.3

i .'e-rage


Table 15-

Estinmi ctd ":ilucs






47 .8
"5;,. "




247 .4






.2.- I '


579.5


37,5.7
32o.9


ct' : LI


C' .:T.'




1.37
1 ; '3





7Cl




C0.7',

0. 7:4-



C, 621

7 27


HaO





HC1i

HI

CH Ci
,H2CI 2

CHC1-,



CH-OH
,2H aH= OHi


C:iC.-LJR.



-i5




-45






-I+ '

-1.7



+11

+17

15.























ri


L.












Ct
'4j






Li









A



'N~?


Cr" [ ., LC. *. ,

- '- I I I


SI,
-i:



-r









C4


[- '3 .J

?" c. .- r,
+ .-= +



U. -r L



CCi C, fC '
S ,.-' U*- C,

r[' ]*r 3 -1






J C'C]
-r r-', C. .-'
cr. r [ 0










C [r- [-


r, u". CJ








i J i I

-0 '. .,-i
L' O uL. C.
r-i J C*J









13C, O r (
-j 0 r. L,

rH- OJ Ci i Ci


.- Lu cj

r1-' -r .-I c'

S -r I + +







.-1 [- -Il 0 OJ

C' rI' l- .-r
C. OJ --. ,'3 .
r'. CJ ''. r,'. OJ







,-0 CJ ,-1 (C1

, fr, C, -

*. J r f, (Cu


-1 -J r-
I I I


o 0 0


r. r


cj

Sr -- .-- n
c n 0O ruj .3 .
2 : O c' C -H C -' 2r S
2: 2 CA E X ) U j (3


I I I


I i I


V.. ~.,

Li.




V. -



2. a
V.' P


7. ,J ['-

'. r," 0

UL. -r L .






0 Cu, [-

C' L-, 'J

u". -- L.





















SJ i L- .". ,. i s

-r I C .3 l' .- '
.j j". CuJ ( Cu'J -1 -i







'; I I J- L' .- u -
[- [^- r; u'. -- ;- i, P. ;U


CI
ci











T
r1


SI 0 I
.





I U.-

iS -- -


'J O,


-. I i.
-T --7 L,.
Oj OJ .-


I F







I I


Ci'





(A,

ci






01





ii i
. In


') u f" 'X L r-P
,. ir. -u- U --







r-. i if "- bi -r
j r LT. L, .. ,


.--, ,7 ,- i I ,
u". -" i 1. : "J ['- CI
'4' r4 uL. -r -- .





'J N" C. .-i .-i
. CJ Oj f. :. C: C
S r- - a r.". i. e


C.,

T .- ..
.-- Cr -r C. -

J . r C. ,1. i C C' a, I
Cu r*' ." ,-'. r.' --r -




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