AN APPARATUS FOR VAPOR-LIQUID EQUILIBRIUM MEASUREMENTS

UNDER PRESSURE

by DONALD JAMES WHITTLE

B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1956

Ay THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE

i n the Department of CHEMICAL ENGINEERING

We accept t h i s t h e s i s as conforming to the required standard

THE UNIVERSITY OF BRITISH COLUMBIA September, 1958

ABSTRACT

Equipment and methods used to measure v a p o r - l i q u i d equilibriums at

pressures above one atmosphere are reviewed, and the methods of t r e a t i n g

the r e s u l t s obtained from such equipment are also discussed. An appara­

tus s u i t a b l e f o r the study of v a p o r - l i q u i d e q u i l i b r i u m at pressures up

to 3000 pounds per square inch and temperatures up to 550°F. has been

designed. P r o v i s i o n i s made i n the apparatus f o r measuring the volume of

each of the two phases and f o r removing samples of the i n d i v i d u a l phases

at constant temperature and pressure. Recommendations f o r the c a l i b r a ­

t i o n ... and use of the apparatus and f o r the p u r i f i c a t i o n of the solvents to

be studied are given.

In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree'at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.

Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver Canada.

TABLE OF CONTENTS

TITLE PAGE

Introduction 1

H i s t o r i c a l Review 8

Methods and Equipment 8

Treatment of Vapor-Liquid E q u i l i b r i u m Data 21

Material s 48

Benzene 48

Mercury 54

n-Propanol 55

Apparatus 62

Procedure f o r Making Measurements 72

Bibliography 83

TABLES

1. Table of Symbols 46

2. Physical Data f o r Benzene from the L i t e r a t u r e 58

3. Physical Data f o r Propanol from the L i t e r a t u r e 61

LIST OF ILLUSTRATIONS AT END OF TEXT

Figure 1 - Freezing Point Apparatus

Figure 2 - Mercury Transfer Flask and Sample C o l l e c t i o n Flask

F i t u r e 3 - Transfer Apparatus

Figure 4 - Tubing Diagram

Assembly Drawing 1 - Assembly of Equi l i b r i u m C e l l

Assembly Drawing 2 - Assembly of Measuring Head

D e t a i l Drawing 1 - Equi l i b r i u m C e l l

D e t a i l Drawing 2 - Mercury Storage Bomb

Det a i l Drawing 3 - Cap and L i d f o r Bomb

D e t a i l Drawing 4

D e t a i l Drawing 5

D e t a i l Drawing 6

D e t a i l Drawing 7

TABLE OF CONTENTS (cont'd.)

Packing Support Rings

Gland Nut and Guard Ring

Measuring Head D e t a i l s

D e t a i l s of Magnetic S t i r r e r

ACKNOWLEDGEMENT

The author wishes to express h i s appreciation f o r the constructive

c r i t i c i s m and the encouragement given by Dr. L.W. Shemilt, under whose

supervision t h i s research was c a r r i e d out.

Acknowledgement i s also made of the Standard O i l Company of B r i t i s h

Columbia Limited f o r t h e i r f i n a n c i a l help during the winter months of

1956-1957 and of the National Research Council f o r t h e i r assistance

during the f o l l o w i n g year.

INTRODUCTION

When a l i q u i d composed of two or more chemically pure substances i s

heated, the composition of the vapor given o f f w i l l normally be d i f f e r e n t

from that of the l i q u i d remaining. This change i n composition with change

i n phase forms the basis of such separation processes as d i s t i l l a t i o n and

absorption, and therefore a qu a n t i t a t i v e knowledge of the change i s essen­

t i a l f o r the a n a l y t i c a l treatment of these processes. Although i n a d i s ­

t i l l a t i o n column the vapor evolved i s not generally i n phase e q u i l i b r i u m

with the l i q u i d i t leaves, corrections can be made f o r t h i s f a c t and

equ i l i b r i u m values are used as a basis f o r c a l c u l a t i n g the composition

d i f f e r e n c e s . Since v a p o r - l i q u i d e q u i l i b r i u m values are used, i t i s impor­

tant that extensive tables of these be a v a i l a b l e , and the determination

of such values has become an important f i e l d of study.

As w e l l as being of p r a c t i c a l importance, the determination of vapor-

l i q u i d e q u i l i b r i u m values i s of t h e o r e t i c a l i n t e r e s t . Many of the studies

made i n recent years on the theory of solutions have been made from a 78

"molecular" viewpoint . With t h i s method of treatment, expressions are

found f o r bulk properties i n terms of molecular properties and intermole-

cular forces. In order to determine the v a l i d i t y of such expressions and

thus of the molecular theory on which they are based, the calc u l a t e d

values must be compared with experimentally determined ones, and one of

the basic sources of data f o r such comparisons i s from v a p o r - l i q u i d equi-

l i b r i u m measurements .

A considerable amount of v a p o r - l i q u i d e q u i l i b r i u m data i s a v a i l a b l e 83

i n the l i t e r a t u r e , as exemplified i n the compilation of J u Chin Chu ; but

much of i t i s f o r systems composed of s i m i l a r or re l a t e d compounds, f o r

12 5 167 example, that of Banks and Musgrave , Ainer et a l , and Woodson et a l .

Mixtures of t h i s type often form nearly i d e a l solutions, and many of the

problems associated with an understanding of the more general non-ideal

s o l u t i o n s do not a r i s e . Although some experimental values are a v a i l a b l e 90 99 159

f o r non-ideal systems ' ' , most of these are f o r systems which are

at or near atmospheric pressure where again the mixtures often approach

i d e a l s o l u t i o n s . For these reasons i t i s obviously of i n t e r e s t to study

a system i n which the components would form a non-ideal s o l u t i o n and to

make measurements over most of the range of temperature and pressure where

a l i q u i d and vapor phase can co - e x i s t .

Some valuable work has of course been done at pressures above one

atmosphere and with non-ideal systems. Comings**^, S m i t h * 4 5 , and Newitt^^^

have compiled l i s t s of workers who have made measurements at elevated 37

pressure,and Comings has also discussed the theory, apparatus, and t y p i ­

c a l r e s u l t s of these workers. Among the we l l known workers i n t h i s f i e l d 127 128 129

are Sage and Lacey, ' ' who have studied a large number of systems which are important i n the f i e l d of petroleum at elevated pressures. „. 8 5 , 8 6 , 8 8 . , 4 8 , 9 2 , 1 6 3 . , + + i . i Kay 1 and Katz have also studied s i m i l a r systems at elevated

123

pressures. Prigogene has attempted to predict the behaviour of mixtures

at conditions up to the c r i t i c a l ones from molecular structure and i n t e r -

molecular forces.

Several sets of measurements have been made at t h i s u n i v e r s i t y on the

va p o r - l i q u i d e q u i l i b r i u m of the normal alcohols with benzene and with t o l ­

u e n e 2 9 ' 5 2 ' 5 4 ' 7 5 ' 8 1 ' 1 5 7 ' 1 6 2 . Since a mixture of polar and non-polar mole­

cules of t h i s type forms a non-ideal s o l u t i o n i t was decided to extend the

measurements f o r one of these, the benzene-normal propyl alcohol system, to

- 3 -

the c r i t i c a l region. The p a r t i c u l a r system benzene-n-propanol was chosen

because the c r i t i c a l values of the two components were not too high f o r

convenient measurement and because there i s a reasonable diffe r e n c e bet­

ween the two c r i t i c a l temperatures and c r i t i c a l pressures.

A second f a c t o r which influenced the choice of t h i s system was that

some measurements have been made on benzene-methanol mixtures at elevated

pressure****. Since r e l a t e d systems often lend themselves to group c o n t r i ­

bution p r e d i c t i o n s , that i s pr e d i c t i o n s i n which each element or group of

the system contributes a set value, i t was thought i t might be worthwhile

to obtain information on another s o l u t i o n of t h i s type.

Many types of equipment have been used to experimentally determine 133

v a p o r - l i q u i d e q u i l i b r i u m . Robinson and G i l l i l a n d have c l a s s i f i e d these

under the headings of

(a) C i r c u l a t i o n Method

(b) Continuous D i s t i l l a t i o n Method

(c) Dynamic D i s t i l l a t i o n Method

(d) Dynamic Flow Method

(e) Bomb Method

( f ) Dew and B o i l i n g Point Method.

The c i r c u l a t i o n method consists of pl a c i n g the mixture to be studied i n

an evacuated v e s s e l , c o l l e c t i n g the vapor from above the l i q u i d and c i r ­

c u l a t i n g i t back through the l i q u i d u n t i l the composition of both phases

becomes constant. Although t h i s method i s b a s i c a l l y very simple, several

precautions have to be taken to obtain accurate r e s u l t s . The system con­

t a i n i n g the mixture must be leak-free or the amount of material i n i t w i l l

p rogressively change and cause corresponding change i n the eq u i l i b r i u m

- 4 -

p r o p e r t i e s . Not only does the t o t a l quantity of material i n the system

have to be kept constant, but the t o t a l q u a n t i t i e s of each phase must also

not change. In order that the volume of each phase does not change,it i s

necessary that the apparatus be kept at a constant temperature and that the

displacement of the pump used to c i r c u l a t e the vapor remain e f f e c t i v e l y con­

stant. An inherent error e x i s t s i n t h i s type of measuring equipment caused

by the f a c t that the pressure at the bottom of the l i q u i d phase where the

vapor i s reintroduced,is d i f f e r e n t from that at the top of the phase, where

the vapor leaves,and thus the e q u i l i b r i u m composition i s d i f f e r e n t at the

two l e v e l s . However, at most t o t a l pressures the change i n composition

with t h i s small change i n pressure can be neglected.

The continuous d i s t i l l a t i o n method i s a le s s accurate but simpler

method of measurement. The vapor i s c o l l e c t e d from above the l i q u i d , con­

densed, and returned to the s t i l l as a l i q u i d . This method has been quite

generally used but has the disadvantage that there i s some doubt as to

whether or not the vapor formed by the b o i l i n g l i q u i d i s i n eq u i l i b r i u m

with the l i q u i d . Another d i f f i c u l t y a r i s e s because the vapor returned as

a condensate i s not of the same composition as the s t i l l l i q u i d . I f any

of t h i s condensate i s vaporized before i t i s completely mixed, the vapor

produced w i l l not be i n eq u i l i b r i u m with the l i q u i d phase.

In order to eliminate some of the d i f f i c u l t i e s a r i s i n g from t h i s method

of c i r c u l a t i o n , the condensate i s often vaporized before returning i t to

the s t i l l . In t h i s case the r e s u l t i s equivalent to r e c i r c u l a t i n g the

vapor but the equipment i s sometimes easier to operate. Care must be taken

that the condensate i s completely vaporized and that i t i s super heated only

enough to make up f o r heat losses,or the s t i l l w i l l not operate under steady

state conditions.

- 5 -

The dynamic d i s t i l l a t i o n method i s a very simple one f o r obtaining

approximate v a p o r - l i q u i d e q u i l i b r i u m values. I t i s based on the d i s t i l l a ­

t i o n of small q u a n t i t i e s of vapor from a large quantity of l i q u i d . The

l i q u i d mixture i s placed i n a s t i l l , a small quantity vaporized, and the

composition of both phases measured. The procedure i s then repeated u n t i l

several samples have been obtained. The average composition of each of the

phases i s p l o t t e d on a graph versus the amount vaporized,and the curves

obtained are extrapolated back to zero vaporization to obtain the e q u i l i ­

brium compositions. The values obtained by t h i s method, of course, w i l l

only be the true values i f the b o i l i n g l i q u i d produces an e q u i l i b r i u m

vapor.

Another approximate method of determination i s the dynamic flow method

i n vhich a vapor i s bubbled through a s e r i e s of vessels containing l i q u i d

of constant composition. As the vapor passes through each v e s s e l , i t s com­

p o s i t i o n changes u n t i l by the time i t reaches the l a s t one i t i s assumed

that the vapor i s i n e q u i l i b r i u m with the l i q u i d . The composition of the

vapor i s then measured and that of the l i q u i d i s known since i t i s that of

the o r i g i n a l mixture. A serious weakness i n t h i s method of measurement i s

that a pressure drop must occur i n each vessel,and thus the composition of

the e q u i l i b r i u m vapor i s s l i g h t l y d i f f e r e n t i n each one.

The bomb or constant-volume method i s an accurate one that requires

only f a i r l y simple equipment. A l i q u i d sample i s placed i n an evacuated

bomb,and the mixture then e i t h e r s t i r r e d or shaken u n t i l the two phases

come to e q u i l i b r i u m . Once the phases are at e q u i l i b r i u m , samples of each

phase are taken by displacement with an equal volume of some i n e r t material

such as mercury. Although accurate r e s u l t s are possible by t h i s method,

-6-

care must be taken i n order to obtain them. A very common error that

a r i s e s i s that some of the l i q u i d phase i s splashed or else condenses i n

the vapor sampling l i n e . Since the volume of the vapor sample when con­

densed i s u s u a l l y very small, a small amount of l i q u i d i n the sample l i n e

would represent a large percentage of the t o t a l sample and could cause a

very serious e r r o r . Because the equipment required f o r t h i s method i s

quite simple, i t i s often used f o r high pressure measurements!

The dew and b o i l i n g point method i s another method commonly used to

measure v a p o r - l i q u i d e q u i l i b r i u m at high pressures. A sample of known

composition i s placed i n a c e l l of v a r i a b l e volume which i s surrounded by

a constant temperature bath. The volume of the c e l l i s then varied u n t i l

the sample f i r s t s t a r t s to vaporize. The point at which the vaporization

f i r s t occurs i s found by p l o t t i n g the pressure volume isotherms or, i f the

c e l l i s of glass, by observation. The volume at which the vapor f i r s t

s t a r t s to condense i s found i n a s i m i l a r manner. Since the composition of

the mixture i s determined before i t i s placed i n the c e l l , no a n a l y s i s of

the phases i s necessary.

Two f a c t o r s were considered when choosing the design of the equipment

b u i l t f o r t h i s i n v e s t i g a t i o n . Since i t was hoped to obtain e q u i l i b r i u m

values of t h e o r e t i c a l i n t e r e s t , i t was important that the apparatus should

give as accurate r e s u l t s as p o s s i b l e . As w e l l , however, i t was desirable

that the basic design be kept as simple as p o s s i b l e , since the apparatus

had to be b u i l t to withstand elevated temperatures and pressures. On the

basis of these two considerations i t was decided that, of the various types

of equipment used to measure v a p o r - l i q u i d equilibrium,a m o d i f i c a t i o n of 134

the constant volume apparatus used by Sage and Lacey was most s u i t a b l e .

-7-

' The d e t a i l s of the design and construction of the apparatus, along

with the proposed operating procedure and d e s c r i p t i o n of the methods of

p u r i f y i n g the solvents to be studied are presented here. Included as w e l l

i s a b r i e f d e s c r i p t i o n of some of the equipment used by other workers to

measure v a p o r - l i q u i d e q u i l i b r i u m at elevated pressures and temperature,

and, since i t i s important from the standpoint of the structure of l i q u i d

and vapor solutions,the method of t r e a t i n g and u t i l i z i n g data obtained

under these conditions.

-8-

HISTORICAL REVIEW

Methods and Equipment

Of the various types of apparatus mentioned above, those that have

been used f o r measurement at pressures above one atmosphere w i l l be d i s ­

cussed more f u l l y . The majority of measurements obtained at elevated u v -+u i 4.- • ,11,92,134,135 pressure have been with n o n - c i r c u l a t i n g equipment, ' 7 ' such us i s

used i n the constant-volume method or dew and bubble point method,but some

important r e s u l t s have been obtained with equipment where e i t h e r the l i q u i d + u u • • i * ,71,119,120,134 . , . , . „ , .T or the vapor phase i s c i r c u l a t e d ) ' ' ' and a d e s c r i p t i o n of both

types w i l l be given.

The constant-volume method has been used extensively f o r the deter­

mination of v a p o r - l i q u i d e q u i l i b r i a at elevated pressures. This method of

measurement i s advantageous i n r e q u i r i n g simple equipment, making accurate

r e s u l t s t h e o r e t i c a l l y p o s s i b l e , and allowing any number of components to

be studied. One apparatus of t h i s type that has been used s u c c e s s f u l l y 134

i s that of Sage and Lacey . Their equipment consisted p r i m a r i l y of an o o

e q u i l i b r i u m c e l l with a working temperature of from 0 to 460 F. at press­

ures up to 10,000 pounds per square inch.

The temperature i n the e q u i l i b r i u m c e l l was c o n t r o l l e d by immersing

i t i n a w e l l agitated o i l bath. Mercury could be added to or removed from

the c e l l through a high pressure l i n e connecting i t to a storage vessel,

and the pressure on the c e l l was c o n t r o l l e d by regulating the pressure

applied to t h i s v e s s e l . A v e r t i c a l rod extended into the c e l l through

the bottom and c a r r i e d a mercury l e v e l i n d i c a t o r at i t s upper end. The

i n d i c a t o r consisted of an e l e c t r i c contact p o i n t i n g downward, and i t and

the e l e c t r i c lead wire which extended from i t through the rod were i n s u l ­

ated from the rod and c e l l . The contact and the c e l l were connected

-9-

through an i n d i c a t i n g c i r c u i t so that a si g n a l was given when the contact

point touched the mercury surface.

The height of the va p o r - l i q u i d i n t e r f a c e i n s i d e the c e l l was measured

by means of a hot wire anemometer which was also supported by the rod.

The anemometer consisted of a short length of platinum wire stretched

across two insulated pins. A small current was passed through the wire,

and since the rate of d i s s i p a t i o n of heat from the wire was d i f f e r e n t i n

each phase, the temperature and thus resistance was also d i f f e r e n t i n each

one. The l o c a t i o n of the i n t e r f a c e could therefore be found by determin­

ing the l e v e l where the resistance of the wire suddenly changed.

The lower end of the rod extended into another c e l l which was f i l l e d

with mercury and connected to the top one so that no change occurred i n

the free volume of the top bomb when the p o s i t i o n of the rod was changed.

The rod was raised or lowered by r o t a t i n g a worm which engaged a gear

attached to a nut threaded on to the rod. The gear and thread were con­

structed so th a t , a f t e r i t was c a l i b r a t e d , a counter on the worm shaft

in d i c a t e d the p o s i t i o n of the rod.

Two valves were b u i l t i nto the c e l l , one at the top and the other half­

way down the maximum working volume of the c e l l . The top valve was con­

nected to a vacuum pump and to an apparatus f o r adding samples to or with­

drawing samples from the bomb. Samples could also be added or removed

through the lower valve.

Excellent mixing of the material w i t h i n the c e l l was achieved with

a s p i r a l a g i t a t o r which was designed so that the free cross section w i t h i n

the c e l l was the same at every p o s i t i o n where l e v e l measurements could be

made. This a g i t a t o r was driven by an electromagnet which revolved around

the outside of the c e l l .

-10-

The composition of each phase at e q u i l i b r i u m was found by withdraw­

ing samples through the two valves b u i l t i n to the c e l l . As the samples

were removed, mercury was added so that i s o b a r i c conditions and thus equi­

l i b r i u m were maintained.

Other workers have used d i f f e r e n t forms of t h i s apparatus to measure 92

phase e q u i l i b r i a . Kobayashi and Katz have used an e q u i l i b r i u m c e l l at

pressures up to 2800 pounds per square inch and temperatures to 300°F. i n

which the i n t e r f a c e between the two phases was determined through a glass

window. The c e l l was immersed i n an a i r bath f o r temperature control, and

the c e l l contents were s t i r r e d with an e l e c t r i c s t i r r e r mounted e n t i r e l y

w i t h i n the c e l l . C e l l pressure was varied by changing the amount of mat­

e r i a l present. Samples of the e q u i l i b r i u m phases were obtained through

four posts set at d i f f e r e n t l e v e l s . The l i q u i d sampling posts and l i n e s

connected to them were f i l l e d with mercury to prevent accumulation of

material i n them. When samples of e i t h e r phase were taken, mercury was

i n j e c t e d into the c e l l at the same rate as the sample was removed, thus

preventing any change i n the e q u i l i b r i u m conditions. 2

Aktrs, A t t w e l l , and Robinson have made eq u i l i b r i u m measurements i n

a bomb-type e q u i l i b r i u m c e l l at pressures up to 5000 pounds per square inch

and temperatures up to 300°F. A g i t a t i o n of the mixture i n the c e l l was

accomplished by rocking the e n t i r e e q u i l i b r i u m c e l l i n a constant tempera­

ture bath. Samples of the vapor were obtained by cracking a needle valve

on the top of the c e l l . A constant pressure was maintained during the

sampling by the i n j e c t i o n of mercury from a mercury pump. Sampling was

continued u n t i l three samples of the gas had been obtained, a f t e r which

the remaining vapor was forced out of the c e l l . The point where the l i q u i d

i n t e r f a c e reached the e x i t valve was detected by a sudden jump i n c e l l

-11-

pressure. When i t was c e r t a i n that only l i q u i d remained i n the c e l l , the

pressure was increased by about a thousand pounds per square inch and l i q u i d

samples then withdrawn. 39

Copeland, Silverman, and Benson have designed an apparatus which

has been used f o r the sampling of one phase of a v a p o r - l i q u i d e q u i l i b r i u m

system at pressures up to 300 atmospheres and temperatures up to 400°C.

The e q u i l i b r i u m c e l l consisted of two chambers, a sampling chamber and a

valve chamber, which could be i s o l a t e d from one another with a spring valve.

Normally the valve was i n the open p o s i t i o n and was held there by a small

shear p i n . When i t was planned to close the valve, an a l i e n screw on the

outside of the valve was tightened. The screw operated through a diaphragm

on the valve stem and when tightened, broke the shear p i n and closed the

valve. When a sample was to be taken, the equi l i b r i u m c e l l , which could

be rotated, was placed i n such a p o s i t i o n that only one phase was present

i n the valve chamber and the valve closed. The eq u i l i b r i u m c e l l was then

c h i l l e d , the valve chamber opened, and the sample removed with a small

p i p e t t e . 51

Drago and S i s l e r used a s t a i n l e s s s t e e l e q u i l i b r i u m apparatus at

pressures up to 100 atmospheres i n which a l l inner surfaces were coated

with t e f l o n enamel and i n which the eq u i l i b r i u m c e l l contained a glass l i n e r .

In t h i s apparatus no pro v i s i o n was made f o r e q u i l i b r i u m displacement of

samples. When a sample was required, a small amount of material was bled

o f f through a dip tube extending into the eq u i l i b r i u m c e l l .

The equipment described above i s representative of the types that have

been used to measure v a p o r - l i q u i d e q u i l i b r i u m by the constant volume method. 56

Many workers, i n c l u d i n g Evans and Har r i s , Ottenwelter, H e l l e r , and Wein-

r i c h 1 2 1 , De an and Took43 } a n a Benedict Solomon and Rubin 16 have used

-12-

s l i g h t l y d i f f e r e n t designs, but i n each case the general form i s the same

as i n those already described.

Many determinations of v a p o r - l i q u i d e q u i l i b r i u m at elevated pressures

also have been made by the dew and bubble point method. The p r i n c i p l e

involved i n t h i s method of measurement i s quite d i f f e r e n t from that i n

the constant volume method:, where actual samples of the e q u i l i b r i u m phases

are obtained. In a binary, two phase mixture, f i x i n g two degrees of f r e e ­

dom f i x e s the e n t i r e system. I t f o l l o w s , therefore, that f o r any binary

system at any p a r t i c u l a r temperature and pressure the. compositions of the

vapor at the dew point and the l i q u i d at the bubble point are f i x e d and

are equal r e s p e c t i v e l y to the vapor and l i q u i d compositions of any two

phase mixtures formed from the same components at the same temperature and

pressure. For t h i s reason, the determination of v a p o r - l i q u i d e q u i l i b r i u m

i n a binary mixture can be reduced to the measurement of dew and bubble

points of mixtures of known concentration. This method i s r e s t r i c t e d to

binary mixtures, of course, because f o r a mixture of more than two compon­

ents, f i x i n g the temperature and pressure does not f i x the e q u i l i b r i u m

l i q u i d and vapor compositions.

Probably the most generally used apparatus f o r dew and bubble point 126

determinations i s that of Ramsay and Young as modified by Bahlke and

Kay**. Their equipment consisted of a long s t e e l compressor f i l l e d with

mercury i n which the volume could be varied with a plunger f i t t e d i n to the

block through a pressure-tight j o i n t . The block was also f i t t e d with a

v e r t i c a l branch through which mercury could be forced. A t h i c k - w a l l e d

glass c a p i l l a r y was f i t t e d i n to t h i s branch and sealed o f f with a s t u f f i n g

box. The sample to be tested was placed i n the tube and confined there by

mercury from the block. To ensure adequate mixing of the sample, the

-13-

tube was f i t t e d with a so f t i r o n s t i r r e r which was activ a t e d by an ex­

t e r n a l electromagnet.

The experimental tube was also surrounded by a glass jacket through

which organic vapors were passed. These vapors were produced from a

ser i e s of organic l i q u i d s whose b o i l i n g points lay w i t h i n the tempera­

ture range desired. By b o i l i n g the l i q u i d under reduced pressure, a range

of temperature s u f f i c i e n t to overlap the b o i l i n g point of the next l i q u i d

i n the se r i e s could be obtained. The pressure applied on the sample was

determined from a measure of the pressure on the compressor block and a

s t a t i c head c o r r e c t i o n f o r the height of mercury i n the tube.

When a known weight of sample had been placed i n the tube and the

tube i n s t a l l e d i n the block, vapor at the desired temperature was bubbled

through the jacket and the pressure slowly increased. Measurements were

made of temperature, pressure, and phase volume at the dew point, bubble

point, and several intermediate p o i n t s . Since the tube was constructed

of g l a s s , the dew point, bubble point, and phase boundaries could a l l be

determined by d i r e c t observation. When the measurements had been com­

pleted f o r one sample, the tube was r e f i l l e d with a sample of a d i f f e r ­

ent composition and the measurements repeated.

From the measurements made on dew and bubble points,the v a p o r - l i q u i d

e q u i l i b r i u m was determined. The d e n s i t i e s of the unsaturated l i q u i d

phase, the co- e x i s t i n g l i q u i d and vapor phases, and the super heated vapor

phase could also be calc u l a t e d from the volume measurements and a know­

ledge of o r i g i n a l weight of m a t e r i a l .

84

Kay l a t e r modified the apparatus so that the pressure was applied

from a high pressure gas c y l i n d e r instead of the plunger, and Kay and

Rambosek 8 8 modified the pressure regulator on the jacket surrounding the

-14-

experimental tube, but i n both cases the e s s e n t i a l operation of the appara­

tus remained the same. 135

Sage and Lacey have used a s l i g h t l y d i f f e r e n t technique to deter­

mine dew and bubble p o i n t s . I f pressure-volume data are determined f o r

a system over the e n t i r e two phase region and p l o t t e d as pressure versus

volume isotherms, d i s c o n t i n u i t i e s w i l l occur i n the curves at the dew and

bubble points except where the data i s measured near the c r i t i c a l condi­

t i o n s . The apparatus used by these two workers at pressures up to 10,000

pounds per square inch and at temperatures up to 600°F. to determine the

pressure-volume data consisted, i n essence, of a U-tube. closed at each

end and p a r t l y f i l l e d with mercury. The sample was confined i n one arm,

while a i r under pressure was admitted to the other i n order to change the

volume occupied by the sample. The temperature of the arm containing the

sample was c o n t r o l l e d by surrounding i t with a constant temperature bath.

E q u i l i b r i u m w i t h i n and between the phases was obtained by means of a

s t i r r e r driven by a magnet r o t a t i n g on the outside of the bomb.

Since the t o t a l quantity of mercury i n the two c e l l s was constant, a

measure of the height of mercury i n the pressure c e l l gave the height

and thus free volume i n the e q u i l i b r i u m c e l l . This mercury l e v e l was

determined with a movable e l e c t r i c contact which extended down from the

top of the c e l l and gave a s i g n a l when i t touched the mercury surface.

The measuring procedure consisted of adding a known weight of sample

to the c e l l , s e t t i n g the constant temperature bath at the desired value,

and then varying the pressure u n t i l pressure volume measurements had been

obtained f o r the e n t i r e two phase region. The temperature was then i n ­

creased and the procedure repeated. When one sample had been completely

15-

investigated i t was removed, replaced with another, and the measurements

repeated. Once the f u l l range of temperature, pressure, and composition

had been investigated, the pressure volume data were p l o t t e d , the dew

and bubble points found, and the v a p o r - l i q u i d e q u i l i b r i u m determined. 18

Bloomer and Parent used a d i f f e r e n t method f o r varying the system

pressure. Their apparatus, used at pressures up to 750 pounds per square

inch, consisted of a graduated glass c e l l immersed i n a constant tempera­

ture bath. S t i r r i n g was accomplished by magnetically r a i s i n g and lowering

a s t e e l b a l l i n s i d e the c e l l . The contents of the c e l l were brought

through the gas phase region to the dew point and then through the two

phase region to the bubble point by the a d d i t i o n of measured increments of

the material being studied. The dew and bubble points were determined by

d i r e c t observation and checked from a pressure versus volume p l o t . 89

Katz and Kurata have used an e q u i l i b r i u m c e l l c o n s i s t i n g of a

glass-windowed s t e e l tube at pressures up to 3100 pounds per square inch.

A g i t a t i o n to insure intimate mixing was obtained by rocking the e n t i r e

c e l l . Pressure was applied to the c e l l by the a d d i t i o n or removal of mer- -

cury. The p o s i t i o n s of the mercury-sample i n t e r f a c e and v a p o r - l i q u i d

i n t e r f a c e were determined from a scale placed beside the window. 38 53 Many other workers, i n c l u d i n g Cook , Eaken, E l l i n g t o n , and Garni,

34

and Clegg and Rowlinson have used the bubble and dew points method to

determine v a p o r - l i q u i d e q u i l i b r i a i n binary mixtures. Although the appa­

ratus that these workers used d i f f e r e d s l i g h t l y i n d e t a i l from the ones

described above, the general features were the same.

Several workers have adapted atmosphere e q u i l i b r i u m s t i l l s f o r use

at elevated pressures. Although the equipment required f o r t h i s method

of measurement i s f a i r l y complicated, accurate r e s u l t s can be obtained

from a w e l l designed s t i l l . Scheeline and G i l l i l a n d have designed

such a l i q u i d c i r c u l a t i o n s t i l l from gauge glass tubing. The top of

the tubing was sealed with a packing gland and the bottom was f i t t e d into

a e t e e l base. Four tubes entered the s t i l l through the top gland: a

s t i l l sampling l i n e , a thermocouple w e l l , a vapor e x i t l i n e , and a l i q u i d

return l i n e . In order to prevent r e f l u x on the s t i l l w a l l s , the s t i l l

was surrounded by a pyrex jacket through which hot a i r could be blown.

A length of t h i c k walled glass tubing, sealed at the upper end,

was used as a condensate t r a p . Condensate from the s t i l l condenser entered

through a tube extending up nearly to the top of the trap and was returned

to the s t i l l through a s i m i l a r shorter l i n e . P r o v i s i o n was made f o r

removing samples from the condensate return l i n e .

The pressure i n the s t i l l was regulated by c o n t r o l l i n g the heat i n ­

put with a mercury switch which also operated as a pressure manometer.

The bottom of the condensate trap served as one arm of the manometer

so that when the pressure i n the s t i l l rose, the mercury l e v e l i n the con­

densate trap was depressed,and the l e v e l i n the other arm of the mano­

meter also rose. This r i s i n g mercury surface closed an e l e c t r i c a l

c i r c u i t which reduced the heat input to the s t i l l . When the s t i l l press­

ure dropped, the contact was broken and the heat input to the s t i l l was

increased.

Measurements were made with t h i s s t i l l at pressures up to 600 pounds

per square inch. A s i m i l a r one, modified s l i g h t l y by Griswold, Andris,

and K l e i n was used to pressures up to 1000 pounds per square inch at a

temperature of 250°C. 119

Othmer , S i l v i s , and S p i e l have b u i l t a l i q u i d type c i r c u l a t i o n

s t i l l of s t a i n l e s s s t e e l s u i t a b l e f o r pressures up to 1000 pounds per square

inch. Two small sight glasses were b u i l t i nto the s t i l l body to allow

observation of the contents, and one into the drop counter so that the

b o i l i n g rate could be determined. The temperature i n the s t i l l was

measured by means of two thermocouples which were placed i n we l l s i n

both phases.

The temperature and pressure were c o n t r o l l e d by adjusting the heat

input to the b o i l e r and the condenser cooling water flow r a t e . Heat

losses from the s t i l l body were prevented by i n s u l a t i n g and wrapping

Nichrome wire around the outside. The power supplied to the heating

wires was c a r e f u l l y c o n t r o l l e d so that the temperature on the outside of

the s t i l l was the same as that on the i n s i d e . Samples of the l i q u i d

phase were obtained through a l i n e from the condensate return l i n e . 120

Otsuki and Williams measured v a p o r — l i q u i d e q u i l i b r i u m at atmos-65

pheric pressure i n a s t i l l based on the one designed by G i l l e s p i e .

Measurements at pressures up to 500 pounds per square inch were then

made i n a copper duplicate of the atmospheric s t i l l . 9

Aroyan and Katz obtained eq u i l i b r i u m between the l i q u i d and vapor

phases at pressures up to 8000 pounds per square inch by c i r c u l a t i n g the

vapor from the top of a s t i l l back through the l i q u i d phase. Their ap­

paratus consisted of an equ i l i b r i u m c e l l placed i n a constant temperature

bath from which vapors were pumped with a magnetically operated high

pressure pump. Since the pump maintained a constant displacement during

the c i r c u l a t i o n , no pressure f l u c t u a t i o n occurred i n the system. The

vapor from the pump was passed through c o i l s i n the constant temperature

bath to bring i t to the equ i l i b r i u m temperature before returning i t to

the c e l l . Two b a f f l e s were placed in s i d e the c e l l to prevent any e n t r a i n -

-18-

ment of l i q u i d i n the vapor. Samples of each phase were taken d i r e c t l y

from the e q u i l i b r i u m c e l l when equ i l i b r i u m had been reached. The equi­

l i b r i u m pressure was maintained during sample withdrawal by the i n j e c t i o n

of mercury into the pressure control cylinfer.

Cines, Roach, Hogan, and Roland*** u&eola s i m i l a r apparatus f o r deter­

mining v a p o r - l i q u i d e q u i l i b r i u m at pressures up to 650 pounds per square

inch. The eq u i l i b r i u m c e l l was placed i n a cryostat which i n turn was

surrounded by a vacuum jacket to reduce heat t r a n s f e r from the cryostat

to the surroundings. C i r c u l a t i o n of the vapor phase was obtained through

the action of a mercury pi s t o n pump and two mercury valves. Fluctuations

i n pressure from the pumping were l e s s than one pound per square i n c h .

The vapor was passed from the pump through two p a r a l l e l l i n e s . With t h i s

arrangement i t was possible to obtain samples from one l i n e and allow vapor

c i r c u l a t i o n through the other. The vapor was returned to the l i q u i d phase

through a tube i n which four small holes had been d r i l l e d . The vapor

passing through these holes gave excellent mixing of the l i q u i d phase.

Samples of the l i q u i d phase were obtained d i r e c t l y from the s t i l l .

Most v a p o r - l i q u i d e q u i l i b r i u m measurements at elevated pressures have

been made using one of the four types of equipment discussed above. How­

ever, other types have been used by some workers. Ashley and Brown***

investigated v a p o r - l i q u i d e q u i l i b r i u m at pressures up to 220 pounds per

square inch with a c e l l i n which i t was possible to c i r c u l a t e e i t h e r the

l i q u i d or vapor phase or both. Samplers were provided i n the c i r c u l a t i o n

l i n e s so that a portion of the equ i l i b r i u m f l u i d could be i s o l a t e d and

analyzed without d i s t u r b i n g the e q u i l i b r i u m i n the c e l l . A magnetic pump,

with a displacement of approximately two per cent of the volume of the

- 1 9 -

system,was used to c i r c u l a t e the f l u i d s . A l i q u i d - l e v e l i n d i c a t o r , con­

s i s t i n g of an inverted bucket type f l o a t attached to a l i g h t i r o n stem,

was used. The stem formed the core of a transformer, and with a f i x e d

primary voltage, i t was possible to determine the f l o a t p o s i t i o n from the

secondary voltage.

The sample to be studied was charged to the e q u i l i b r i u m c e l l and,

with at lea s t an inch of l i q u i d i n the bottom of the c e l l , the two phases

were c i r c u l a t e d u n t i l e q u i l i b r i u m was reached. Both phases were returned

to the c e l l at the bottom, thus g i v i n g intimate mixing. An an a l y s i s of

each phase was then obtained by i s o l a t i n g the samplers and l e t t i n g a por­

t i o n of each flow through an analysis t r a i n .

Akers, Burns, and F a i r c h i l d have used a s i m i l a r apparatus at press­

ures up to 1500 pounds per square inch, except that each phase was analyzed

continuously. The gas mixture to be studied was passed through a compres­

sor and cooling c o i l i n to a separator. The vapor and l i q u i d were then

removed from the separator through d i f f e r e n t l i n e s , expanded to a pressure

s l i g h t l y above atmospheric, and passed through thermal conductivity c e l l s

f o r a n a l y s i s . The two streams were then recombined and fed into the com­

pressor. The c i r c u l a t i o n was continued u n t i l no change of composition

occurred i n e i t h e r c e l l . 33

Clark, Din, and Robb determined v a p o r - l i q u i d e q u i l i b r i u m at press­

ures up to 120 pounds per square inch by a batch d i s t i l l a t i o n method.

The mixture to be studied was placed i n a small copper c y l i n d e r immersed

i n a constant temperature bath. The vapor phase was then s t i r r e d by

means of a magnetically operated plunger. When eq u i l i b r i u m was reached,

a small sample of the vapor was qui c k l y withdrawn and analyzed. The wi t h ­

drawal had to be performed r a p i d l y or a change i n composition would occur

-20-

i n the vapor phase during sampling. The contents of the c e l l were then

allowed to return to e q u i l i b r i u m and the procedure repeated. When several

samples had been obtained, a graph of quantity removed versus composition

was p l o t t e d and the curve extrapolated to zero amount removed to f i n d

the composition of the vapor i n e q u i l i b r i u m with the o r i g i n a l l i q u i d . 112

Mertes and Colburn have used a flow type apparatus to determine

v a p o r - l i q u i d e q u i l i b r i a at pressures up to 100 pounds per square inch.

An e q u i l i b r i u m c e l l , b u i l t from a glass-windowed s t e e l c y l i n d e r , contained

the l e a s t v o l a t i l e l i q u i d of the mixture to be studied. A vapor of con­

stant composition was then continuously bubbled through the e q u i l i b r i u m

c e l l u n t i l the l i q u i d i n the c e l l was i n e q u i l i b r i u m with t h i s vapor. The

c e l l was kept i n a constant temperature bath,and the pressure i n the system

was regulated by passing the vapor from the c e l l through a condenser and

then to a condensate receiver where a constant back pressure of carbon

dioxide was maintained.

From the above discussion i t can be seen that experimental vapor-

l i q u i d e q u i l i b r i u m measurements have been made at pressures up to 10,000

pounds per square inch with.the s t a t i c type of equipment and up to nearly

that pressure with the c i r c u l a t i o n type. Both types have advantages and

disadvantages when used at elevated pressures. The chief advantages of

the c i r c u l a t i o n type l i e i n the f a c t that i t i s r e l a t i v e l y easy to obtain

e q u i l i b r i u m between the two phases. Samples of the c o - e x i s t i n g phase being

studied are also easy to obtain. However, because the equipment necessary

i s r e l a t i v e l y complex, t h i s type has, not been as generally used as the

s t a t i c one f o r pressure measurements.

Of the s t a t i c methods, the dew and bubble point one i s p a r t i c u l a r l y

s u i t a b l e f o r studying binary mixtures at elevated pressures because the

-21-

equipment required i s very simple. Unfortunately t h i s method can be used

f o r measurements i n binary systems only, a f a c t which l i m i t s i t s u s e f u l ­

ness very much. As w e l l , a large number of readings must be made to

define the e q u i l i b r i u m composition of the l i q u i d and vapor phases. The

constant volume method i s a more v e r s a t i l e one but s l i g h t l y more complex

equipment i s required. A second disadvantage i s that great care must be

taken to get a t r u l y representative sample of the l i q u i d and vapor phase

i n e q u i l i b r i u m . With both of the s t a t i c methods, of course, i t i s much

more d i f f i c u l t to obtain e q u i l i b r i u m between the phases than with the

c i r c u l a t i o n methods.

Treatment of Vapor-Liquid E q u i l i b r i u m Data

Since a knowledge of the e q u i l i b r i u m formed between l i q u i d and vapor

sol u t i o n s i s important i n modern i n d u s t r i a l processes, and since e x p e r i ­

mental values are d i f f i c u l t to obtain, t h i s f i e l d of thermodynamics has 15 27 105

been treated t h e o r e t i c a l l y at considerable length i n recent years ' '

131,164^ object of t h i s study has been, p r i m a r i l y , to obtain r e l a t i o n ­

ships from which v a p o r - l i q u i d e q u i l i b r i u m values can be c a l c u l a t e d from

a knowledge of the properties of the pure components or from a t h e o r e t i c a l

measure of t h e i r i n t e r a c t i o n s . Another, and also important purpose has

been to obtain methods of checking the i n t e r n a l consistency and accuracy

of experimentally measured values.

The thermodynamic basis of both studies i s the same and from t h i s

basis by empiricism or by a s t a t i s t i c a l thermodynamic approach the two

purposes have been achieved to some degree. From the point of view of t h i s

research, the more important of the two i s the checking of experimental

values and therefore the theory w i l l be discussed front t h i s approach. The development of the thermodynamic r e l a t i o n s h i p s given below i s essen-

-22-

+ - H + 1 . +u + • i *> i- i 45,74,80,133 . x t i a l l y the same as that i n a number of books 7 on the subject,

but has been rearranged to serve as a basis f o r the equations which

fol l o w i t .

In order to completely define a sin g l e phase i n which the t r a n s f e r

of material can occur, as i s the case f o r e i t h e r phase i n a v a p o r - l i q u i d

mixture, i t i s necessary to spec i f y the mass and the composition of the

phase as w e l l as two other independent var i a b l e s such as temperature and

pressure. Thus, any extensive property, such as free energy, w i l l be a

functio n of each of these v a r i a b l e s or, i n symbols

P - F(T,P, n i n 2 n3...) ( l )

For an i n f i n i t e s i m a l change i n the free energy the equation may be

wr i t t e n

c/f^iI)dT + (il)dP t(±F)dn, (2)

and since

- s / 2 £ \ =. V

lo>T/p 0 (^ \ o)P /r.n, Ad­

equation (2) has the form

jr-.-SilT

For the sake of convenience, the d i f f e r e n t i a l c o e f f i c i e n t s of free energy

with respect to mass are often represented by f*- and c a l l e d the chemical

p o t e n t i a l . Therefore equation (3) can be w r i t t e n

c/f = - S J T +V</P +• JUL,tin, / JUX<*\ t • (4)

dr.- -SJT + VdP iT^u- d%- ( 5 )

-23-

where

R J F

For a closed system composed of two or more open phases i t can e a s i l y be

shown that, at e q u i l i b r i u m under conditions of constant temperature and

pressure, the chemical p o t e n t i a l of a component i n one phase i s equal to

that of the same component i n every other phase.

Since by i t s d e f i n i t i o n , the chemical p o t e n t i a l , o r p a r t i a l molal

free energy, i s an intensive property, that i s , i t depends only on the r e l a ­

t i v e proportions or concentration of each component and not on the t o t a l

amount, and since the equation i s homogeneous and of the f i r s t degree i n

number of moles, equation ( 5 ) can be integrated by applying Euler's 7 4

Theorem to give under conditions of constant temperature and pressure.

Zf*. nL (6)

Equation (6) can now be d i f f e r e n t i a t e d to give

dFrt/u^dn- ( 7 )

I f t h i s equation i s subtracted from equation ( 5 ) the f o l l o w i n g r e s u l t

i s obtained.

S J T * VJP-TmdK =0 ( 8 )

This r e s u l t , known as the Oibbs-Duhem equation, shows the r e l a t i o n s h i p

between simultaneous changes i n temperature, pressure, and chemical poten­

t i a l . I t i s often r e s t r i c t e d to conditions of constant temperature and

pressure so that

r ni C//U:--<D ( 9 )

The equation may be expressed i n terms of mole f r a c t i o n instead of the

-24-

number of moles by d i v i d i n g both sides by the t o t a l number of moles to

give

Z A/c d/uL *0 (10)

In t h i s research the number of components i s r e s t r i c t e d to two and there­

fore equation (10) can be w r i t t e n as

/V,</y", f A/xdfl^--0 (11)

At constant temperature and pressure the chemical p o t e n t i a l i s a

function of composition only, and therefore equation ( l l ) can be w r i t t e n

i n terms of p a r t i a l molal q u a n t i t i e s as follows

/ K / M I ' - A ^ v / J / M = o ( 1 2 )

This form of the Gibbs-Duhem equation may be w r i t t e n i n terms of f u g a c i -

t i e s rather than chemica) p o t e n t i a l . By d e f i n i t i o n , the chemical poten­

t i a l and f u g a c i t y are r e l a t e d by the equation

d/U,-- RTd^nf, (13)

and the d e f i n i t i o n i s completed by the r e l a t i o n s h i p

j, ~v o A S P-'C ( 1 4 )

S u b s t i t u t i n g equation (13) into equation (12) and d i v i d i n g by ET gives

M ijAif, \ •+ ^ ( J _ M | , o (15)

Since NL + N = 1 and dN, = «dN , equation (15) can be rearranged as

Since the a c t i v i t y c o e f f i c i e n t Y f o r any component i s the r a t i o of the

a c t i v i t y and the mole f r a c t i o n f o r that component, i t can e a s i l y be shown

-25-

that equation (16) can also be w r i t t e n i n the form

N, /cJ A Y, ) , A/z (IAlL ( I 7 V dA/, ' V d Nu ) V /

which i s perhaps more useful f o r l i q u i d s o l u t i o n s .

Equations (16) and (.17), when applied to the l i q u i d phase under con­

d i t i o n s of constant temperature and pressure, can be used i n the d i f f e r ­

e n t i a l form or can be integrated to t e s t experimental v a p o r — l i q u i d equi­

l i b r i u m data f o r thermodynamic consistency. When the d i f f e r e n t i a l form

of the equation i s used, the values of Ad^kJj and j^?.Xj- or i f x i s used

f o r N i n l i q u i d mixtures, and y f o r N i n vapor mixtures, a n t*

4-^?lX<- are found by measuring slopes from a graph on which ^ and

Vu are p l o t t e d versus mole f r a c t i o n . I f the data are thermodynamically

consistent, the r a t i o of the two slopes at every value of ~X. w i l l be equal

to the r a t i o — at the same X . I t should also be noted that i f i t i s not

convenient to p l o t the logarithm of a c t i v i t y c o e f f i c i e n t s equation (17)

can be rearranged to give

j^l. Jjd ^ J K (18)

In t h i s case the a c t i v i t y c o e f f i c i e n t i s plo t t e d versus x»and the r a t i o

of the slopes must equal -' J-

In order to use equations (16), (17), or (18) to t e s t v a p o r - l i q u i d

e q u i l i b r i u m data f o r thermodynamic consistency, the f u g a c i t i e s or a c t i ­

v i t y c o e f f i c i e n t s must be re l a t e d to experimentally measurable q u a n t i t i e s ,

As stated e a r l i e r , the fugacity i s rel a t e d to the chemical p o t e n t i a l by

d e f i n i t i o n as follows

d/u, -, Rl 4&-f (13)

-26-

D i f f e r e n t i a t i n g both sides of equation (13) with respect to pressure at

constant temperature and compositions

In an analogous proof to the one showing t h a t / — ^ ) 5 V , i t can be

proved that - V, wh ere 17 i s the p a r t i a l inolal volume. Substitut-

ing t h i s r e l a t i o n into equation (19) gives

- % ( 2 0 )

Under conditions of constant temperature and composition

dA /, - 2 d P (21)

I f i s subtracted from both sides of t h i s equation, then dAf. -d&,(x,P)-- X dP x,.P

m

I - RT I '

Since conditions of constant composition were s p e c i f i e d d£n?t, = o a n a

Integrating (22) under conditions of constant temperature from

A 0 r P--P P

2.P

Since at P- O , /, - z., P , the equation becomes "

<e~ t -foP(iL-±)dp +J*px, ; ( 2 3 )

I f the value of V, i s known as a function of pressure at constant compo­

s i t i o n and temperature, t h i s equation can be integrated and the value of

found.

I f the values of the p a r t i a l molal volumes are not a v a i l a b l e to a

s u f f i c i e n t degree of accuracy to allow the use of equation (23), then some

other method of evaluating the fugacity must be found. I f the temperature

and pressure are not too near the c r i t i c a l values, the need f o r p a r t i a l

molal data can be eliminated by assuming that Lewis and Randall's*^^ rul e

f o r an i d e a l s o l u t i o n i s true f o r the vapor phase. This rul e states that

the f u g a c i t y of a component i n an i d e a l mixture i s equal to the mole f r a c ­

t i o n of that component i n the mixture m u l t i p l i e d by the fugacity of the

pure component at the temperature and pressure of the mixture. Expressing

the r e l a t i o n s h i p i n terms of symbols

(24)

I f the fugacity of a component i n the vapor phase can be cal c u l a t e d using

t h i s r u l e , then the desired quantity, the f u g a c i t y of the component i n the

l i q u i d phase, i s known, since at equ i l i b r i u m the two are equal. In order

to use Lewis and Randall's r u l e , the f u g a c i t y of the pure vapor must be

known at the temperature and pressure of the mvxture. This f u g a c i t y i s

found by in t e g r a t i n g equation (23) w r i t t e n f o r a pure substance.

''Jo ( }R1~?^P (25)

The value of the molar volume f o r a pure vapor i s much easier to f i n d than

the p a r t i a l molal volume, since i t can be ca l c u l a t e d from an equation of

s t a t e . I f no p a r t i c u l a r equation i s a v a i l a b l e , the i n t e g r a t i o n can be

performed using the generalized c o m p r e s s i b i l i t y chart or one of the more

recent generalized methods. Once the i n t e g r a t i o n has been performed, the

fugacity i n the mixture i s calculated from the product of the pure compon­

ent value and the mole f r a c t i o n or

. (26) Writing the Gibbs-Duhem equation f o r t h i s case gives

or i n terms of a c t i v i t y c o e f f i c i e n t s where the standard state f o r a c t i ­

v i t y i s chosen as the pure component at the temperature and pressure of

the mixture

(28)

The value of the f u g a c i t y of the pure l i q u i d f o r use i n equation (28)

may be found i n two stages. F i r s t the fugacity of the l i q u i d at tempera­

ture of the mixture and the vapor pressure i s c a l c u l a t e d from an i n t e g r a ­

t i o n of equation (25) between the l i m i t s of P = 0 and P = vapor pressure.

The value at the pressure of the mixtur'e i s then found by i n t e g r a t i n g

equation (21) w r i t t e n f o r a pure component between the vapor pressure and

the s o l u t i o n pressure. The value of the l i q u i d volume as a function of

pressure can be found from a generalized chart i f experimental values are

not a v a i l a b l e . The two equations are now

tJop ' I ( </W -') dpi stn . (29)

-30-

and

- ... V'f (30) ruq p

At low values of temperature and pressure, assumptions can be made

which furt h e r s i m p l i f y the fugacity and a c t i v i t y c o e f f i c i e n t c a l c u l a t i o n s .

I f the pressure i s low enough that the vapor phase obeys the perfect gas

law, then the. f u g a c i t y i n t h i s phase i s equal to the p a r t i a l pressure, and

equation (27) s i m p l i f i e s to

(31)

or J A ^ B -o/x,

And equation (28) becomes

- ^ ^ ( M )

The c a l c u l a t i o n of the fugacity of the pure l i q u i d at the temperature and

pressure of the mixture i s also made much simpler since the f u g a c i t y of

the l i q u i d at i t s vapor pressure i s equal to i t s vapor pressure. Equa­

t i o n (30) can therefore be w r i t t e n

a™ f - / J^Lln t Pf-vp (33) J Pvnp Rt

Very often i t i s assumed that the pressure change from the vapor

pressure to the pressure of the s o l u t i o n has a n e g l i g i b l e e f f e c t on the

fu g a c i t y of the s o l u t i o n and that the fugacity of the pure l i q u i d i s equal

to i t s vapor pressure. When t h i s i s don# the a c t i v i t y c o e f f i c i e n t becomes

-31-

or a measure of the devia t i o n from Raoult's law. Under these circumstances

equation (28) i s w r i t t e n

yt, \^^A = ^SZll^J^sA (35) c) A, c U t

When the above assumptions are made, i t i s also possible to express

the Gibbs-Duhem equation i n terms of t o t a l pressure rather than p a r t i a l

pressures. Rewriting equation ( l l )

~° (36)

Rearranging

T 3 C'-3> J

I 'T (37)

Experimental data can now be tested by p l o t t i n g P vs. y and comparing {^pj~>

with

Up to t h i s point the methods given f o r t e s t i n g vapor l i q u i d e q u i l i ­

brium data have a l l been based on the d i f f e r e n t i a l form of the Gibbs-Duhem

equation. In order to use t h i s form of the equation, the d e r i v a t i v e s

must be obtained by measuring slopes or from an equivalent procedure.

Since the measurement of slopes i s u s u a l l y subject to a high degree of

e r r o r , an integrated form of the equation i s often used.

The most accurate type of integrated equation i s the one i n which the

value of one a c t i v i t y c o - e f f i c i e n t i s cal c u l a t e d from the measured value

of the other and the calculated and experimental values then compared. 47 /

One such method i s suggested by Dodge . Equation (11) i s w r i t t e n i n the

-32-

f orm

7-j c6^i Yt + ( ) d s&t " C (38)

Rearranging the equation

Integrating between x^ = o and = x

At x^ = 0 the a c t i v i t y c o - e f f i c i e n t =/ and the equation bee

(39)

omes

^ h-- -f*"(-7=krU^r, J X - f%

A graphical i n t e g r a t i o n of (39), using values of w i l l y i e l d values

of Xx. , to compare with the measured ones. > • ' •

Although the value obtained f o r the a c t i v i t y c o e f f i c i e n t from equa­

t i o n (39) i s exact under conditions of constant temperature and pressure,

i t can be calculated only i f a measured value f o r the other a c t i v i t y co­

e f f i c i e n t i s a v a i l a b l e , and the equation therefore i s of l i t t l e value f o r

the p r e d i c t i o n of v a p o r - l i q u i d e q u i l i b r i u m . For t h i s reason, many approx­

imate solutions of the Gibbs-Duhem equation have been proposed. M a r g u l e s * ^

suggested a s o l u t i o n of the form

J-fx*- " ( 4 9 )

•Vr 4 - ( 4 1 ) .

I f enough terms are included the s o l u t i o n w i l l be exact but generally,

to avoid undue complication, only the f i r s t three terms are used. When

-33-

the two equations are substituted into the Gibbs-Duhem equation, the

f o l l o w i n g r e l a t i o n s h i p s are found

27 Carlson and Colburn rearranged the constants on the basis of these"* e q u a l i t i e s to give

• Jn t, = (Z8-n)0-zft Z(»9-0)(!-^) 3 ( 4 2 )

X * Y V , ( Z A - e ) * 1 - + 7.C 6-19) z 3 ( 4 3 )

I t can be e a s i l y seen that at t £m /ft and that at T-^i

I f graphs of s&nYi , and VV. are p l o t t e d versus mole f r a c t i o n * - , then

the value of the two constants can be found from the end values of the

curves. To check the thermodynamic consistency of the experimental data,

the a c t i v i t i e s are cal c u l a t e d using equations (42) and (43) with the meas­

ured constants A and B, and the. r e s u l t s compared to the experimental

values.

Since the constants i n the Margules equation are functions of temper­

ature, the values ca l c u l a t e d f o r one temperature can not be used at any

other temperature. To extend the usefulness of the equation, Robinson and 133

G i l l i l a n d suggest that the constants be taken as proportional to the

one-fourth power of the absolute temperature. Thus i f the values of A and

B are known at one temperature, the p r o p o r t i o n a l i t y constant can be c a l ­

culated, and the values found at any other temperature. Probably the best known s o l u t i o n of the Gibbs-Duhem equation ,is that'

97 -I;

proposed by Van Laar . The s o l u t i o n was o r i g i n a l l y put forward as the

r e s u l t of a'theory based on the Van der Waals, equation of s t a t e d and

-34-

although the theory i s probably i n e r r o r , the equation i s a useful empiri­

c a l representation of the data. The equation has been rearranged by 27

Carlson and Colburn into the form /• y ft

^ }' ' (I + ft*, (44)

X n r v = _J> (45)

As with the Margules equation, the constants can be evaluated from the

values of the a c t i v i t y c o - e f f i c i e n t s at x = 1 and x = 0. Experimental data

i s checked f o r thermodynamic consistency with t h i s equation using the pro­

cedure described e a r l i e r . A f t e r the constants are calc u l a t e d from the

end values of experimental curves, the equation i s solved f o r a c t i v i t y co­

e f f i c i e n t s using these constants, and the experimental and calculated

values are compared. Because of the form of the Van Laar s o l u t i o n , a very

quick q u a l i t a t i v e check of the data can be made. When the mole f r a c t i o n

equals .5, equations (44) and (45) can be w r i t t e n

A^n r, . ^ K ; . AQ_ ( 4 6 )

I f A equals B then ^ ^ j ^ j ' - equals while i f A = 2B or B, the r a t i o de-2

creases Thus the half-way value on one curve should equal approx­

imately \ of the end value on the other curve i f the data i s consistent

and i f the Van Laar equation a p p l i e s . 133

Robinson and G i l l i l a n d have modified the Van Laar equation to i n ­

clude a temperature term and thus extend i t s usefulness. When t h i s i s done,

the so l u t i o n s have the form s^K ~- B'/T (47)

-35-

<&»X = BloiZ. (48)

Using a s i m i l a r development to that of Van Laar, Scatchard and 138

Hamer have developed solutions of the Gibbs-Duhem equation i n v o l v i n g the molar volumes of the pure components. The constants have again been

27 rearranged by Carlson and Colburn to give

where v^ and v^ are the molar volumes and i, i s the volume f r a c t i o n of

component one given by

/ = „?/ • (51)

The constants i n t h i s rearranged form can be found from the end value of

the curves and the equation used to check thermodynamic/ consistency i n

the same manner as the Margules and Van Laar solutions are used. 164

Wohl has shown that the Margules, Van Laar, and Scatchard and Hamer solutions are a l l p a r t i c u l a r cases of a more general s o l u t i o n hased

ID on the excess free energy. The excess free energy, F , has been defined

138 by Scatchard and Hamer as the difference between the free energy of

ot an

mixing f o r a r e a l and Aideal s o l u t i o n . The free energy of mixing 4/>, , i s

the difference between the free energy of the pure components and that of

the s o l u t i o n . Thus 4 F m c ^77; F[ - T Hi (52)

Now

-36-

A

Therefore

T

From the d e f i n i t i o n

z A. Ffy, r c o ( - >a (do/

F€ -- RT Z 77< XR,YC (55)

The free energy of a mixture can now be w r i t t e n as

F= T71i F; i RTT-n; *L / Fe

and the chemical p o t e n t i a l as

(53)

(54)

(56)

Rearranging

Fi " K - R T X , , ^ -f- JF~

Rearranging again

<JF': - RTsCr* Yi (57) o> 7)-

164

The fo l l o w i n g general equation i s used by Wohl to express the excess

free energy

_Fl - T. iL ih bih t J 2; i ij 1>L>,- , (58)

where « e f f e c t i v e molal volume of component

2 i = e f f e c t i v e volume f r a c t i o n

6 = an empirical constant

and each summation represents molecular i n t e r a c t i o n s .

D i f f e r e n t i a t i n g with respect to ?7, and ^ f o r a three s u f f i x equation

where fl= 9, V * 3 and 8 ^ ( ^ 6 , ^ + 3 ^ , 1 ^

(60)

^ ( R T ) ^ ^ C< L ^ - v . ^ - o y ^ j ( 6 1 )

I t can now be shown that i f - then the two equations reduce to those

of Margules. I f ®lB the Van Laar solutions are obtained and i f

9</9 = the equation becomes that proposed by Scatchard and Hamer. 130

Redlich and K i s t e r have developed an expression based on the

Gibbs-Duhem equation r e l a t i n g the composition and temperature. The d e r i ­

vation assumes that the changes of volume accompanying the isothermal mix­

ing of the l i q u i d components and of the gaseous components are n e g l i g i b l e

and that the equation of state of the gaseous components can be repres­

ented i n the form J p

where B depends only on temperature. When these assumptions are made

they have shown that SLL S (62)

where "s" the slope f a c t o r i s given by

-38-

^ O' • H 3 U 3

or t d t

The pressure terms P^ and P^ are f a c t o r s to take into account the change

of f u g a c i t y of the components i n the l i q u i d phase with temperature and t o t a l

pressure,and a method i s given f o r evaluating them. The authors believe

that the equation i s considerably more s e n s i t i v e and more convenient to

use than the usual forms of the Gibbs-Duhem equation. 131

The same two authors have also derived a thermodynamically correct

equation r e l a t i n g the concentration and a c t i v i t y c o e f f i c i e n t s i n an i n ­

tegrated form of equation. As shown i n equation (55) f o r a molar s o l u t i o n F e- ATE xt X , ft

By d e f i n i t i o n

(64)

F K

For ajbinary misure

d Q - s&x* £• dx i -x,d ^ K t x^d ft ( 6 6 ) J h

From the Gibbs-Duhem equation

and therefore

Now at i = 0, ^ = 1, and Q = 0 and at x = 1, Yf = 1, and fi = 0, and i n ­

t e g r a t i n g (67) between x = 0 and x = 1 gives

I /6»<j d x = o (68)

-39-

I t follows from equation (68) that a graphical i n t e g r a t i o n of

with data obtained at constant temperature and pressure must equal zero

i f the data i s therraodynamically consistent. 19

Broughten and Brearly* have developed a s i m i l a r expression to that

of Redlick and K i s t e r with the change that the Gibbs-Duhem equation i s

w r i t t e n as

•X, d ( T,£yj X, ) + 7L d C T Joy JfJ =0

to t r y to correct f o r non-isothermal data.- When t h i s c o r r e c t i o n i s applied

the i n t e g r a l becomes

/

/

TA^j *1 dx -O (69)

These authors, on the basis of t h i s equation, have derived a r e l a t i o n s h i p

f o r c o r r e c t i n g inconsistent experimental data where the inconsistency i s

caused by conditions i n the equ i l i b r i u m s t i l l such that

<*co*- = ^ o b i (70)

where c^C o Y. i s the correct r e l a t i v e v o l a t i l i t y , c / 0 ( ) s i s the observed

r e l a t i v e v o l a t i l i t y and s i s the s t i l l f a c t o r . Combining equations (69)

and (70) gives

0:(\T^ £)dx ~-ij'(r^h)d* + Lzs 7 - ^ 7 ^ ( 7 1 )

JO <Iu'Co>r -O 'I obi 3

The equation i s solved g r a p h i c a l l y and the value of s to make the equation

true c a l c u l a t e d . 15

Benedict et a l have derived a r e l a t i o n s h i p f o r c o r r e l a t i n g vapor-

l i q u i d e q u i l i b r i u m data of the f i r m

p RT ~ where if^ i s the molar volume of the i t h component i n the l i q u i d s t a t e .

-40-

The r e l a t i o n s h i p i s dependent upon the assumption that the equation of

state of the vapor phase i s

and that there i s no change i n volume on mixing the constituents of the

l i q u i d phase. The authors recommend evaluation of the a c t i v i t y c o - e f f i c -164

i e n t s by the four s u f f i x equation of Wohl and the use of t h i s r e l a t i o n ­

ship f o r multicomponent systems. 105

Marek and Standart have found that an attempt to c o r r e l a t e vapor-

l i q u i d e q u i l i b r i u m data of mixtures containing a aibstance which p a r t l y

associates to form a diiner i n both phases leads to thermodynamically i n ­

consistent r e s u l t s i f the a s s o c i a t i o n i s not taken into account. The

authors have developed an e q u i l i b r i u m r e l a t i o n s h i p , analogous to Raoult's

and Dalton's law, f o r such a case which states that f o r the a s s o c i a t i n g com­

ponent

and f o r the non-associating one

*z.^L P ^ 'I ^ (76)

where

2( i s a c o r r e c t i o n f a c t o r f o r vapor phase a s s o c i a t i o n of 1

t i s a vapor phase non-idealty f a c t o r f o r 1 o

P, i s the hypothetical vapor pressure of pure monomer 1

C i s a c o r r e c t i o n f a c t o r f o r l i q u i d phase a s s o c i a t i o n of 1

X i s a l i q u i d phase non-idealty f a c t o r f o r 1

Equations are given f o r evaluating each of the c o r r e c t i o n f a c t o r s . When

equations (75) and (76) are used f o r the e q u i l i b r i u m r e l a t i o n s h i p , the

thermodynamic consistency of the data can be checked i n the usual manner

-41- "

except that and fu !fL are used f o r a c t i v i t y c o - e f f i c i e n t s .

Many authors have attempted to c o r r e l a t e v a p o r - l i q u i d e q u i l i b r i u m

data by means of e n t i r e l y empirical equations. These equations generally

have no t h e o r e t i c a l basis but have the advantage that they are e a s i l y

applied and are often used f o r engineering purposes. 32

One of the best known of these empirical equations i s that of Clark .

He suggests that the r a t i o of the mole f r a c t i o n i n one phase i s a l i n e a r

function of the r a t i o of the mole f r a c t i o n i n the other phase when the r a t i o s

are u t i l i z e d such that the component inthe largest amount appears i n the

numerator. Thus, when component one i s present i n the lar g e s t amount

J*. " ^ and when component two i s present i n the lar g e s t amount

2i r '3= -f B' (78)

The point at which equation (78) i s used instead of equation (77) i s

given by

3- = J^B/AB' (79)

95

Kretschmer and Wiebe from t h e i r work on the ethanol-toluene and

ethanol-iso-octane systems have suggested a r e l a t i o n s h i p f o r alcohols i n

hydrocarbons or other symetrical non-polar molecules such as carbon t e t r a ­

c h l o r i d e . Their equation i s of the form ' /?:8v

z A d M = ( ^ y - c ) ( / - z c + c *,) (80)

122 Prahl has proposed using the equation

The three empirical constants can be evaluated using a graphical method

-42-

r e q u i r i n g one experimental point of known accuracy. 55

Eshaya studied the p o s s i b i l i t y of representing the data i n a power

se r i e s of the form

He found that normally three but sometimes four terms were necessary f o r

accuracy to a few per cent. 169

Yu and C o u l l made use of an expression of the form

J L a P (JL\e i (83)

This equation has the advantage that the empirical constants can be simply

evaluated from a log-log p l o t of the molar r a t i o s . However, the f a c t

that molar r a t i o s are involved makes the equation i n v a l i d f o r d i l u t e s o l u -

tion£>. 77

H i r a t a found that most e q u i l i b r i u m data could be represented by u x

three s t r a i g h t l i n e s on a log-log p l o t . He p l o t t e d -pL versus 7^ on l o g -u

log paper and found a s t r a i g h t l i n e of c h a r a c t e r i s t i c slope over the cent­

r a l portion of the curve and l i n e s of slope one at each end of the curve. 82

Johnston and Furter developed a s i m i l a r expression to that of Yu 169

and Coull except that only the numerator rather than the e n t i r e mole „*

f r a c t i o n i s raised to some c h a r a c t e r i s t i c power. Expressed i n terms of

symbols, the r e l a t i o n s h i p becomes _ i = (84) /'J /-*•

Norrish and Twig have proposed a r e l a t i o n s h i p f o r binary mixture

where water i s not one of the components. The equation recommended i s

K k * x> I C (85)

V where K i s the r a t i o of the molar volumes, M i s an a r b i t r a r y constant and

C i s a known function of the laten t heats and b o i l i n g points of the pure

components. A r e l a t i o n s h i p i s given from which M at one pressure can be

found from the value at any other pressure. 131

Kedlich and K i s t e r have developed an equation of the form

The r e l a t i v e importance of some of the constants has been re l a t e d to the

degree of a s s o c i a t i o n of the components.

I t can be seen from the discussion to t h i s point, that i f an i n t e ­

grated form of the Gibbs-Duhem equation i s used to t e s t experimental vapor-

l i q u i d e q u i l i b r i u m data, there w i l l be some question as to whether any dev­

i a t i o n i n the data from that predicted by the equation i s due to inaccura­

c i e s i n the data or to the f a c t that the equation does not apply. For t h i s

reason the integrated form has i t s chief importance i n the p r e d i c t i o n of

data. However, before using one of the equations f o r the p r e d i c t i o n pur-

poses, some check must be made to s e e A i t f i t s the system under considera­

t i o n at l e a s t reasonably w e l l and t h i s check i s most e a s i l y made by using 133

the equation to t e s t experimental data. Robinson and G i l l i l a n d have 155 109

given the r e s u l t s of Tucker and Mason of a t e s t of four of the i n t e ­

grated forms f o r the benzene n-propanol system. The data used, which was 99

probably that of Lee , was f i r s t screened to see that i t gave good agree­

ment with the d i f f e r e n t i a l Gibbs-Duhem equation. To give a q u a n t i t a t i v e 109'

estimate of the agreement, Mason defined the percentage d e v i a t i o n as Percent Deviation = I IzJ^llt 1 <3-

He c l a s s i f i e d the agreement as good when the average percent deviation was

l e s s than 5f>, f a i r f o r a d e v i a t i o n of from 5 to 11^ and poor f o r a devia-

-44-

t i o n of greater than 11$. The r e s u l t s of the t e s t s are given as f o l l o w s :

C l a s s i f i c a t i o n

F a i r

Poor

Poor

Good

Shemilt and S i n g h h a v e found the percent d e v i a t i o n i n values c a l -81

culated from the Van Laar equation from that measured by Howey f o r the

va p o r - l i q u i d e q u i l i b r i u m of the benzene-n-propanol system at 740 m i l l i -

l i t r e s of mercury t o t a l pressure. They obtained, using the d e f i n i t i o n

proposed by Mason, a maximum devia t i o n of 31.8$ and an average deviation

of 10.3$ when the constants f o r the Van Laar 4equation were evaluated from

azeotropic data. The agreement between the data and the equation, accord­

ing to the above c l a s s i f i c a t i o n , i s only f a i r .

Shemilt and Singh have also tested the data of Howey and the i s o t h e r ­

mal 40°C. data of Lee with the equation of Broughton and Brearly (equation

7S|). They found a slope f a c t o r of .9688 f o r the former's data and one of

1.0092 f o r the l a t t e r ' s . 159

Weke and Coates have also measured the v a p o r - l i q u i d e q u i l i b r i u m f o r

the system benzene n-propanol at a pressure of one atmosphere. The data

was checked f o r thermodynamic consistency by comparing the values of ^

consistent with-^Jf, , to the values measured f o r ^ 1 ^ t The two sets of

values are plo t t e d on the same graph, and although no f i g u r e i s given f o r the average deviation the agreement between the two seems very good.

96

Kumarkushna et a l have measured the v a p o r - l i q u i d e q u i l i b r i u m of

the benzene-propanol system at elevated pressures. Measurements were

made at eight pressures ranging from 44.7 to

Equation Max. jo Dev. Avg. $ Dev.

Margules 53.3 8.6

- Scatchard 68.4 11.6

Van Laar 18.8 17.8

Clark 16.3 4.7 141

-45-

309.7 pounds persquare inch and the data obtained was co r r e l a t e d with a

three-constant E e d l i c h and K i s t e r equation.

-46-

Table of Symbols

A, A 1 A r b i t r a r y constants i n various equations

a a c t i v i t y

B a r b i t r a r y constants i n various equations

B* a r b i t r a r y constants i n various equations

b empirical constant i n Wohl's equation

C arbitrary constant i n various equations

D a r b i t r a r y constant i n various equations

F free energy

F p a r t i a l molal free energy

excess free energy F*

/\ F^ free energy of mixing

f f u g a c i t y

f° fu g a c i t y of pure component

K molar volume r a t i o

M a r b i t r a r y constant i n various equations

N mole f r a c t i o n

n number of moles

P t o t a l pressure

P vapor pressure vap p p a r t i a l pressure

p. K e d l i c h and K i s t e r function

q e f f e c t i v e molal volume

E gas constant

S entropy

s E e d l i c h and K i s t e r slope f a c t o r

s Broughton and Brearley s t i l l f a c t o r

- 4 7 -

T temperature

V volume

V p a r t i a l molal volume

v molar volume

x mole f r a c t i o n i n the l i q u i d phase

y mole f r a c t i o n i n the vapor phase

Z e f f e c t i v e volume f r a c t i o n

Greek Symbols

^ r e l a t i v e v o l a t i l i t y

% a c t i v i t y c o e f f i c i e n t

4 a r b i t r a r y constant i n Margules' equation

£ a r b i t r a r y constant i n Margules* equation

/U chemical p o t e n t i a l

Subscripts

I component I

2 component 2

3 component 3

h component h

i component i

J component j

c a l c a l c u l a t e d

cor correct

exp experimental

i d e a l i d e a l f l u i d

l i q l i q u i d phase

obs observed r e a l r e a l vap vapor

-48-

MATERIALS

Benzene

A reagent grade of benzene, supplied by Baker and Adamson, was p u r i ­

f i e d f o r use i n t h i s research. The manufacturers c e r t i f i e d i t as being

thiophene-free and meeting ACS s p e c i f i c a t i o n s . Lot properties were given

as f o l l o w s :

B o i l i n g range 0.5°C. max.

B o i l i n g point at 760 mm. of mercury 80.1°C. max.

Freezing point 5.2°C. min.

Maximum Limit of Impurities

Residue a f t e r evaporation JOOlfi

Substances darkened by H^SO^ to pass t e s t

Thiophene to pass t e s t

Sulphur components (as S) 0.005^

Water to pass t e s t

The i n i t i a l p u r i f i c a t i o n of the benzene was based on methods reported

by Gilmann and G r o s s ^ , Gornowici, Anick and H i x o n ^ , and Tompa*^. One

l i t r e of benzene was shaken f o r 10 minutes i n a 2 - l i t r e separatory funnel

with 250 m i l l i l i t r e s of Nichols reagent grade s u l f u r i c a c i d* The purpose

of t h i s acid wash was to sulphonate and remove any thiophene or t&iophene-

l i k e substances present i n the solvent. A f t e r t h i s mixing, the acid was

allowed to s e t t l e out f o r 20 minutes, and then drained out through the bot­

tom of the funnel. Since the ac i d turned a pale yellow color during the

shaking, the above procedure was repeated. The second volume of a c i d ,

which was l e f t uncolored by the benzene, was also discarded, and the s o l ­

vent washed twice with 500 m i l l i l i t r e .portions of d i s t i l l e d water. In

each case the mixture was ag i t a t e d f o r at l e a s t 10 minutes and allowed to

-49-

s e t t l e f o r at le a s t 20. The benzene was then shaken with two 500 m i l l i -

l i t r e portions of 0.1 normal NaOH. The caustic s o l u t i o n , which was made

from Baker and Adamson's reagent grade sodium hydroxide, was used to remove

the l a s t traces of s u l f u r i c acid and also any weak acids such as hydrogen

sulphide or mercaptans which might be dissolved i n the benzene. A f t e r

the benzene was washed twice more with d i s t i l l e d water, i t was shaken with

100 m i l l i l i t r e s of t r i p l y - d i s t i l l e d mercury to remove any remaining s u l f u r

compounds. The mercury was l e f t i n contact with the benzene f o r several

hours to allow ample time f o r reaction before i t was poured o f f through the

bottom. I t was found that a d u l l grey«»colored powder formed oh the mercury-

benzene i n t e r f a c e and much of i t remained i n the funnel a f t e r the mercury

was removed. F i n a l l y the benzene was washed four times with d i s t i l l e d

water, but even a f t e r these washings some of the powder remained i n the s o l ­

vent. A f t e r the fourth washing,the benzene was poured through the top of

the funnel into a glass-stoppered f l a s k . The solvent was poured from the

top rather than the bottom to prevent contamination with any water that

might remain i n the funnel stem. Care was taken to see that the grey pow­

der from the mercury treatment was l e f t i n the funnel and not t r a n s f e r r e d

as w e l l . In order to remove any water dissolved i n the benzene, calcium

chips were added and the solvent allowed to s i t f o r a week. The stopper

on the f l a s k was l e f t p a r t l y open to l e t evolved hydrogen escape.

The glass ware used i n the drying and i n a l l subsequent operations was

f i r s t c a r e f u l l y cleaned and d r i e d . I t was immersed f o r 24 hours i n chromic

a c i d , then rinsed f o r 24 hours with tap water, and rinsed again 3 or 4

times with d i s t i l l e d water. A f t e r cleaning i t was d r i e d , e i t h e r i n an oven

set f o r 220°F. or else i n a stream of a i r which was f i r s t passed through

a glass wool f i l t e r , then a s i l i c a gel dessicant, and f i n a l l y powdered

phosphorous pentoxide.

-50-

The s t i l l used f o r the d i s t i l l a t ion of the dri e d benzene was an

"Ace Glass" 25 m i l l i m e t r e vacuum-jacketed column packed to a depth of 35

inches with 4 mi l l i m e t r e glass h e l i c e s . The glass h e l i c e s were packed 28

into the column a few at a time as recommended by Carney . The s t i l l

pot consisted of a 2 - l i t r e roundbottomed f l a s k connected to the s t i l l

through a ground glass j o i n t and heated by a "Glass-Col" e l e c t r i c heater.

Heat supplied to the s t i l l pot was c o n t r o l l e d by means of a small v a r i a b l e

auto transformer. The r e f l u x r a t i o was controlled with a "Galena" brand

vacuum-jacketed s t i l l head which was also connected to the column with a

ground glass j o i n t . With t h i s head, condensate flow was supposed to be

con t r o l l e d by means of an electromagnet and timing device. When the timer

turned the magnet on, the condensate was to go to the d i s t i l l a t e receiver,

and when the magnet was o f f the flow was to return down the column. How­

ever, i t was found that t h i s method of control did not work s a t i s f a c t o r i l y

because vapor passed continuously out of the head to the d i s t i l l a t e r e ­

cei v e r . Best control was given by adjusting the p o s i t i o n of a stopcock

placed i n the l i n e to the d i s t i l l a t e r e c e i v e r . Since benzene picks up

atmosphere moisture very e a s i l y , a l l parts of the s t i l l which were open to

the atmosphere were sealed with a s i l i c a gel dessicant.

Two l i t r e s of the p u r i f i e d benzene were charged to the s t i l l pot with

f r e s h calcium turnings. This benzene was b o i l e d at t o t a l r e f l u x f o r at

leas t 12 hours and then c o l l e c t e d at a r e f l u x r a t i o of 20 to 1. The f i r s t

300 m i l l i l i t r e s were discarded and at le a s t 300 m i l l i l i t r e s were l e f t i n

the s t i l l pot at the conclusion of the d i s t i l l a t i o n .

The purity'.of the benzene Avas checked i n three ways. Measurements

of the b o i l i n g point, the fr e e z i n g point, and the r e f r a c t i v e index were taken on the d i s t i l l e d solvent and compared with values taken from the

-51-

l i t e r a t u r e and shown i n Table I I . This table does not represent a com-149

plete compilation, but i t does contain those values that Timmermanns 132

and Riddick and Toops selected as most r e l i a b l e as w e l l as many s e l e c -7

ted by the American Petroleum I n s t i t u t e Project 44 . Since the American

Petroleum I n s t i t u t e gives a less s e l e c t i v e l i s t of references than e i t h e r

of the other sources, references were taken from i t only f o r the period

of time not covered by the other two workers.

The b o i l i n g and condensation temperatures of the benzene were meas-148

ured with a Swietoslawski d i f f e r e n t i a l ebulliometer. The ebulliometer,

which i s s u i t a b l e f o r measuring e b u l l i o m e t r i c degree-of-purity as w e l l as

b o i l i n g and condensation temperatures, was constructed according to the 14

standard s p e c i f i c a t i o n s of Barr and Anhorn . I t consisted b a s i c a l l y of

a b o i l e r with a thermometer we l l and drop counter, an unpacked r e c t i f y i n g

column, a condensation temperature element with a thermometer we l l and drop

counter, and a condenser. As with the d i s t i l l a t i o n column, the top of the

condenser was sealed with s i l i c a gel dessicant. The ebulliometer, except

f o r the drop counter and l e v e l i n d i c a t i n g bulb, was covered f i r s t with

asbestos rope and then with wet powdered asbestos f o r i n s u l a t i n g purposes.

The b o i l i n g tube was wrapped with a length of nichrome wire and the heat

input was c o n t r o l l e d with a v a r i a b l e auto-transformer. The thermometer

wel l s on the ebulliometer were f i l l e d with mercury to a depth s u f f i c i e n t

to cover the thermometer bulb and then to the top with o i l . These wells

were b u i l t up with cork and i n s u l a t i o n so that the thermometer was immer­

sed to the bottom of i t s s c a l e , e l i m i n a t i n g the d i f f i c u l t y u s u a l l y found

i n making stem corrections i n Beckmann thermometers.

The Beckmann thermometer used with the ebulliometer had 100 d i v i s i o n s

per degree. I t and a l l other mercury-in-glass thermometers used were

-52-

c a l i b r a t e d i n a constant temperature bath against a Leeds and Northrup

platinum resistance thermometer with a 1955 NBS c e r t i f i c a t e . The constant

temperature bath consisted of an o i l - f i l l e d glass vessel covered with min­

er a l woo} i n s u l a t i o n . I t s temperature was maintained with two heaters

c o n t r o l l e d by v a r i a b l e auto—transformers. One heater was on continuously

and was adjusted so that the hea t input was s l i g h t l y l e s s than the heat

loss while the other was operated by a mercury thermoregulator and r e l a y

combination. The heat input from the second heater was kept as low as

possible to give the best control of the bath temperature. The bath was

kept at a uniform temperature by means of a small v a r i a b l e speed s t i r r e r .

During the c a l i b r a t i o n , the Backmann thermometer was kept immersed to the

same depth as i t was i n the ebulliometer.

Since the b o i l i n g point of benzene i s s e r i o u s l y affected by traces

of moisture, care was taken that as l i t t l e contamination as possible occur­

red between the d i s t i l l a t i o n and the b o i l i n g point t e s t . The d i s t i l l e d

benzene was c o l l e c t e d from the d i s t i l l a t e r eceiver i n a 500 m i l l i l i t r e

f l a s k which had f i r s t been flushed out with dry a i r and which was kept

sealed with a tube of s i l i c a gel dessicant while the solvent was stored i n

i t . The benzene was transferred to the ebulliometer by d i s p l a c i n g i t from

the f l a s k with a i r which had f i r s t passed through the dessicant. To be

c e r t a i n that a l l moisture had been removed from the benzene, the b o i l i n g

and condensation temperatureswere measured; then 5 m i l l i l i t r e s of the ben­

zene d i s t i l l e d o f f and the temperatures measured again. I f there was a

s i g n i f i c a n t amount of water i n the benzene,some of i t would be removed and

the change i n composition r e f l e c t e d i n a change i n the b o i l i n g point.

Although the Beckmann thermometer used can be read to j^oo

ne i t h e r the b o i l i n g point nor the d i f f e r e n c e between the b o i l i n g and con-

densation temperature can be determined that accurately. In order to

correct the b o i l i n g temperature measured to that at one atmosphere, the

pressure at which i t i s measured must be known to the nearest .01 m i l l i -

l i t r e of mercury. Since the pressure i n the b u i l d i n g can be measured only

to the nearest .1 m i l l i m e t r e , the temperature can be corrected only to the 1 o

nearest -JOQ C. A s i m i l a r although l e s s serious d i f f i c u l t y occurs with

the determination of the differ e n c e between the b o i l i n g and condensation

temperatures. The two temperatures are determined with the same thermo­

meter and thus cannot be measured at the same time. I t i s assumed that

the atmospheric pressure remains constant during the ten minutes that are

required to determine the two temperatures, but i t i s l i k e l y that the pres­

sure does change enough to cause a s i g n i f i c a n t e rror i n the d i f f e r e n c e .

The f o l l o w i n g are the r e s u l t s obtained with the ebulliometer described

above:

B o i l i n g point 80.07°C.

Difference between b o i l i n g and

condensation temperatures .005 C.

Af t e r d i s t i l l i n g o f f 5 m i l l i l i t r e s of solvent

B o i l i n g point 80.08°C.

Difference between b o i l i n g and condensation temperatures .004 C.

The f r e e z i n g point of the benzene was determined with a f r e e z i n g 104

point apparatus s i m i l a r to that used by Rossini and co-workers and i s

shown i n Figure 1. An unsilvered double-walled dewar f l a s k which could be

evacuated through a stopcock was centred i n a brass c y l i n d e r by means of

cork c o l l a r s placed at the top and bottom of the f l a s k . The c y l i n d e r was

supported i n s i d e a glass vessel by a metal stand. Heat t r a n s f e r through

the glass ware was reduced by 2 inches of mineral wool i n s u l a t i o n . The

-54-

temperature i n s i d e the dewar was measured with a platinum thermometer held

i n place by a cork s e a l i n g the end of the f l a s k . Heavy wire, bent i n the

form of a s p i r a l around the thermometer, was used to s t i r the benzene when

readings of temperature were made.

When the f r e e z i n g point of the benzene was measured, the space bet­

ween the brass c y l i n d e r and glass vessel was f i l l e d with crushed i c e .

Benzene was then added to the dewar f l a s k to a depth s u f f i c i e n t to cover

the c o i l e d portion of the resistance thermometer. Care was taken that there

was as l i t t l e opportunity as possible f o r the benzene to absorb moisture

while i t was being poured into the f l a s k . I t was found that a s a t i s f a c t o r y

rate of cooling was obtained with the f l a s k l e f t unevacuated. The benzene

was cooled at approximately ,06°C. per minute, and readings of resistance

were started about 40 minutes before the benzene began to freeze and taken

f o r about 20 minutes afterwards. The f r e e z i n g point, determined by ex t r a ­

p o l a t i n g the cooling curve f o r the f r e e z i n g benzene back to the one f o r the

l i q u i d , was found to be 5.49°C.

The r e f r a c t i v e index of the p u r i f i e d benzene was measured with a P u l -

f r i c h RefTactometer. This refTactometer, supplied by Adam Helger L t d . , i s ,

according to the manufacturers, accurate to one u n i t i n the fourt h decimal

place of the r e f r a c t i v e index. The temperature was maintained by water

pumped through the prism and around the benzene from a constant temperature

bath. The temperature of the water stream was measured with a mercury-in-

glass thermometer c a l i b r a t e d against a platinum resistance thermometer.

The value determined f o r the r e f r a c t i v e index was 1.4879 at 25°C.

Mercury

A t e c h n i c a l grade of commercial mercury was p u r i f i e d using procedures 79

recommended by Sanderson 1 3 6 and the Handbook of Chemistry and Physics .

-55-

The f i r s t step i n the p u r i f i c a t i o n was the removal of surface d i r t by

passing the mercury through a funnel i n which the stem.had been drawn out

to form a small j e t . The cleaned mercury was then placed i n a f l a s k and

f i l t e r e d a i r bubbled through i t f o r 24 hours to o x i d i z e any dissolved mat­

e r i a l s such as the a l k a l i metals, z i n c , copper, or lead. The surface of

the mercury was kept covered with a frequently changed 1$ s o l u t i o n of n i t r i c

a c i d during t h i s operation to a i d i n the removal of the i m p u r i t i e s . The

oxides formed rose to the surface as a scum, and were removed by again

passing the mercury through a small j e t . The mercury was*next washed three

times i n a 10$ NaOH scrubber to d i s s o l v e any grease. The scrubber consis­

ted of a column of glass tubing 3 centimeters i n diameter and 110 c e n t i ­

meters high,which was sealed at the bottom with a mercury t r a p . The mer­

cury was poured into the top of the column through a length of c a p i l l a r y

tubing so that i t f e l l through the caustic s o l u t i o n i n a f i n e spray. A f t e r

being washed i n the NaOH tower,it was passed through a s i m i l a r one contain­

ing 10$ HN0o to remove the l a s t traces of the base metals, and f i n a l l y o

through one containing d i s t i l l e d water. The mercury from the water scrub­

ber was b l o t t e d with f i l t e r paperto remove any surface water and t r a n s f e r ­

red to a vacuum s t i l l i n which i t was d i s t i l l e d three times to remove any

traces of the noble metals or t i n .

n-Propanol

The n-propanol that w i l l be used i n t h i s research was supplied by

the Fisher S c i e n t i f i c Company. I t was c e r t i f i e d as being of reagent grade,

and l o t properties were given as f o l l o w s : A c i d i t y (CHgCOOH) 0.002$ B o i l i n g Range 96.0° - 97.5°C. Non-Volatile Matter 0.000$

Substances p r e c i p i t a t e d by H20 None

-56-

Th e procedure recommended f o r the p u r i f i c a t i o n of n-propanol i s based 93 17 91 on techniques used by Kertschmer , Berner , and Keyes and Winninghoff

Kretschmer found that the p r i n c i p a l impurity i n commercial n-propanol was

a l l y l alcohol and that i t can be removed by shaking each l i t r e of the s o l ­

vent with 15 m i l l i l i t r e s of bromine. I f a separatory funnel i s used f o r

t h i s operation, the l i q u i d s can be separated by running the bromine out of

the bottom of the funnel and pouring the n-propanol from the top as was

done i n separating the benzene-water mixture. The propanol should be

stored i n glassware cleaned and dried as previously described, and l e f t

over anhydrous potassium carbonate f o r several days to remove any dissolved

water.

The alcohol can be furt h e r p u r i f i e d by d i s t i l l a t i o n and the same pro­

cedure and column can be used as were i n the benzene p u r i f i c a t i o n . When

changing the alcohol to the s t i l l pot,fresh anhydrous potassium carbonate

should be added as w e l l . Since pure n-propanol i s e a s i l y o x i dized to the 22

aldehyde , nitrogen must be bubbled through the column during the d i s ­

t i l l a t i o n . Commercial grade nitrogen can be p u r i f i e d f o r t h i s purpose by

passing i t f i r s t through two bubblers containing a l k a l i n e sodium hydro-

sulp h i t e with a trace of sodium anthroquinone -sulphonite (Fieser's s o l ­

u t i o n ) , then through one containing concentrated H^SO^ to remove any water

vapor or caustic s o l u t i o n entrained i n the gas, and f i n a l l y through a

glass wool t r a p . The deoxygenating s o l u t i o n i s prepared by d i s s o l v i n g 150

grams of caustic soda i n a l i t r e of water, adding 2 grams of sodium anth­

roquinone -sulphonate and allowing the mixture to cool i n a stream of

nitrogen. A f t e r i t cools 100 grams of sodium hydrosulphite are added and

the s o l u t i o n shaken w e l l . The middle s i x t y percent of the propanol i s c o l l e c t e d and any moisture

-57-

s t i l l remaining i n the solvent i s removed by s t o r i n g i t over magnesium

ribbon f r e s h l y polished with s t e e l wool. Any aldehyde produced by the

bromine treatment and not removed i n the d i s t i l l a t i o n , a s w e l l as any formed

subsequently, can be removed by adding a l i t t l e 2,4-dinitrophenylhydrazine

to the a l c o h o l . A f t e r the a d d i t i o n of t h i s compound*samples of n-propanol

must be removed from the storage f l a s k by vacuum rather than atmospheric

d i s t i l l a t i o n because of the explosion hazard. The solvent can not be t r a n s ­

ferred by pouring, of course, because of the danger of also t r a n s f e r r i n g

the 2,4-dinitrophenylhydrazine.

Both the b o i l i n g point and the r e f r a c t i v e index of the n-propanol

should be measured as a check on the p u r i t y . The equipment f o r and the

method of making these measurements was described e a r l i e r . Table I I gives

recently-measured values f o r these two q u a n t i t i e s which were obtained from

the same sources as the corresponding values f o r benzene. The values 132

Riddick and Toops recommend as best are indicated by un d e r l i n i n g .

-58-

Author

Barbaudy

Timinermans and Martin

Zmaczynski

Lowry and Allsopp

Puschin and Matavulj

Deffet

Davies

Cohen and B u i j

Wojciechowski

Smith and Matheson

Grosse and Wackher

Scatchard, Wood, and Mochel

Linton

Maryott, Hobbs, and Gross

Smith

S t r e i f f and Rossini

Davison

F o r z i a t i , Glasgow

Gibbons, Thompson

Glasgow, Murphy

TABLE I I

Physical Data f o r Benzene from the L i t e r a t u r e

B o i l i n g Point Freezing Date at 760 mm.Hg. Point R e f r a c t i v e Index Reference — ^ ^_ nD nD

1926

1926

1930

1931

1932

1935

1936

1937

1937

1938

1939

1939

1940

1940

1941

1944

1945

1946

1946

1946

80.106 C.

80.105 C.

80.07 C.

80.098 C.

80.08 C.

5.50 C.

5.50°C.

80.094°C. 5.51°C.

80.094 C.

5.50°C.

1.5009

1.5010

1.50115

1.5011

1.49795

1.4979

1.49807

5.530°C.

5.496°C.

80.103 C. 5.533 C. 1.50110 1.49790

5.50 C.

5.533°C.

1.5011 64

13

151

171

103

125

44

41

35

165

144

72

139

102

108

143

143

147

60

68

-58-

TABLE I I (cont'd.)

Author B o i l i n g Point

Date at 760 mm.Kg.

Harrison and Berg 1946

1946 Marschner and

Cropper

Simonsen and Washburn 1946

Campbell and

M i l l e r 1947

Fenske, Braun 1947

Coulson, Hales 1948

O l i v e r , Eaton, and

Hauffman 1948

Tomps 1948

Dew and Smith 1949

F o r z i a t i , N o r r i s , and Rossini 1949

F o r z i a t i and Rossini 1949

Steinhauser and

White 1949

F o r z i a t i 1950

Waldichuk 1950

La Rochelle and Vernon 1950

Al-Mahde and Ubbelohde 1953

Chang and Moulton 1953

Trew 1953

80.1°C.

80.099 C.

80.099 C.

80.2°C.

Brown and Smith 1954

80.1°C.

80.07°C.

Freezing Point Refractive Index Reference

n. 20

*D

1.5010

1.5009

n 25 D

5.53 C.

1.49797

1.5012

1.5011

5.511 C.

5.54°C. 1.4981

1.4981

1.50112 1.49792

1.4979

1.50112 1.49792

5.454°C. 1.5010 1.4979

5.454 C.

5.53°C.

1.4977

1.50119

1.4978

1.49803

76

107

1.49807 142

24

58

40

118

152

57

61

62

146

59

98

4

30

153

21

-60-

TABLE I I (cont'd.)

Author B o i l i n g Point Freezing

Bate at 760 mm.Hg. Point

Dixon and Schiester 1954

Grunberg 1954

Sandquist and

Lyons 1954

Week and Hunt 1954

Brown and Jungk 1955

Neff and Hickman 1955

L i c h t e n f e l s , Fleck, and Burow 1955

White and K i l p a t r i c k 1955

Canjar, Horni, and Rothfus 1956

Whittle 1957

80.10°C.

80.12°C.

80.1 ° C .

I.10°C.

80.07 C.

5.34"C.

5.492 C.

5.49 c.

Refractive Index Reference "2TT

nD

1.50110

1.5009

1.5012

1.5009

n "25" D

1.4975

1.4979

46

73

137

158

20

115

101

161

25

This research

-61-

TABLE I I I

Phy s i c a l Data f o r Normal Propyl Alcohol from the L i t e r a t u r e

Author

Young and Fortey

Dorochewsky

Dorochewsky

Mundel

Brunei, Crenshaw, and 'fobin

Brunei

Grimm and P a t r i c k

Trew and Watkins

Timmermans and Delcourt

Wojciechowski

Zepalova-Mikhailova

Addison

Vogel

Carley and Bertelsen

Mumford and P h i l l i p s

Howey

McKenna, Tartar, and L i n g a f e l t e r

Wetzel, M i l l e r , and Day

Pu r n e l l and Bowden

B o i l i n g Point Date at 760 mm.Kg,

1903

1909

1911

1913

1921

1923

1923

1933

1934

1936

1937

1945

1948

1949

1950

1951

1953

1953

1954

97.19 C.

97.20 C.

97.26 C.

97.1°C.

97.19 C.

97.15°C.

97.19 C.

97.15 C.

97.209 C.

97.15 C.

98.0°C.

97.19 C.

97.2°C.

97.2 C.

Refractive Index -h^2D npZ5-

1.3833

1.3833

1.38343

1.3856

1.38556

1.3862

1.3858 1.3838

1.3837

Reference

168

49

50

114

123

22

70

154

150

166

170

1

156

26

113

1.3841

97.2°C. 1.3840

111

160

124

-62-

APPARATUS

The apparatus designed i n t h i s research c o n s i s t s , b a s i c a l l y , of two

pressure bombs, ( l and 2)*, placed one above the other. The top bomb,

( l ) , which serves as an equ i l i b r i u m c e l l , ' i s machined from s o l i d 304

s t a i n l e s s s t e e l bar stock and i s 2 inches i n inside diameter, 3 inches i n

outside diameter, and 9 inches deep. The volume of t h i s c e l l i s about

450 cubic centimetres. The bottom bomb, (2), which i s used as a mercury

storage c e l l , i s s i m i l a r i n design but i s 2 inches shorter and has a v o l ­

ume of about 350 cubic centimetres.

The two bombs are placed, the top one i n a constant temperature bath one

and the bottom Abelow i t outside the bath, so that the open end of one faces

the open end of the other. Each of these ends i s sealed by means of a

cap (3) and a s t a i n l e s s s t e e l head (4 ) . The caps are machined from hexa­

gonal stock and are tapped to thread over the ends of the bombs. Each one

i s also d r i l l e d and threaded f o r s i x y j ~ i n c h set screws (13) which are

used to apply pressure on a hardened s t e e l r i n g (10). This r i i g , i n turn ,

presses the head against the end of the bomb. The seal between the head

and the bomb i s completed with a standard 0-ring (12) which f i t s i n a

groove machined into the end of the bomb according to manufacturer's s p e c i -

f i c a t i o n s . Since the 0-ring used i n the top bomb i s subjected to elevated

temperatures, i t i s made of t e f l o n . The one used with the bottom bomb,

which i s located outside the constant temperature bath and kept at room

temperature, i s of synthetic rubber.

The head sealing each bomb i s d r i l l e d to allow a -£-inch s t a i n l e s s

s t e e l rod (14) to pass from one bomb in t o the other. A s t u f f i n g gland 1 The number which follows each part r e f e r s to the part number on the

d e t a i l and assembly drawings included at the end of the t e x t .

- 6 3 -

T 3 1 o i s also d r i l l e d i n each and i s packed with -r x -r- x — x 90 t e f l o n Vee-o o 16

r i n g packings to prevent leakage around the rod. The packings are supp­

orted on s t a i n l e s s s t e e l packing r i n g s , ( 5 , 6 , 7 , 8 , 9 ) , the ones ( 5 , 6 , 7 ) i n

the top bomb placed so a-s that the Vee-rings w i l l seal under e i t h e r press­

ure or vacuum and the ones ( 8 , 9 ) i n the bottom bomb so that they w i l l seal

under pressure. The packing support rings and the packing glands are 53

designed according to the Vee-ringj& manufacturer's s p e c i f i c a t i o n s .

The two bombs are joined by means of pressure tubing -J—inch i n out-

side diameter and g^-inch i n ins i d e diameter. This tubing i s connected

to the bombs by means of standard f i t t i n g s , which thread into wells tapped

into the sides of the bombs, and extends from the bottom of the eq u i l i b r i u m

c e l l to the bottom of the mercury storage c e l l . The top of the storage

c e l l i s also connected with s i m i l a r tubing to a nitrogen c y l i n d e r . Apply­

ing pressure from t h i s c y l i n d e r to the lower bomb t r a n s f e r s mercury from

i t to the eq u i l i b r i u m c e l l . In t h i s way both the pressure on and the

volume of the eq u i l i b r i u m c e l l can be c o n t r o l l e d .

The pressure i n the e q u i l i b r i u m c e l l i s measured with a "Barnet"

dead weight t e s t e r . This dead weight t e s t e r , which w i l l measure from

0-4000 pounds per square^with an accuracy of greater than 0 * 1 $ , i s connec­

ted through a l e v e l i n d i c a t o r to the tubing j o i n i n g the two bombs. The

l e v e l i n d i c a t o r consists of a length of glass pressure tubing i n which

the p o s i t i o n of the in t e r f a c e between the o i l from the dead weight t e s t e r

and the mercury from the bomb can be seen. An accurate determination of

the p o s i t i o n of the inter f a c e i s necessary i n order that the s t a t i c head

between the dead weight t e s t e r and the eq u i l i b r i u m c e l l can be determined,

and thus a pressure c o r r e c t i o n c a l c u l a t e d . This c o r r e c t i o n i s p a r t i c u l a r l y important at lower values of the t o t a l pressure.

-64-

In order to determine the e f f e c t i v e volume of the e q u i l i b r i u m c e l l ,

the height of mercury i n i t must be known and t h i s height i s measured

with a resistance c i r c u i t . The rod extending from the storage bomb to

the e q u i l i b r i u m c e l l i s divided i n t o two part s , the lower part c o n s i s t i n g

of a s o l i d rod and the upper part,of a hollow tube. A measuring head

(assembly drawing 2) i s f i t t e d on to the end of the tube in s i d e the equi­

l i b r i u m c e l l . A wire, sheathed i n t e f l o n , passes up the tube and through

a t e f l o n seal (16) i n the head, into the bomb. The head i s designed so

that t i g h t e n i n g the cover (15) over the top of i t compresses the t e f l o n

seal and prevents vapor from leaking out, e i t h e r along the wire or around

the edge of the t e f l o n . The pressure from the cover i s transmitted to the

seal through a s t a i n l e s s s t e e l c o l l a r (17) which i s held from r o t a t i n g by

a small key (23). The wire which i s sealed i n to the measuring.head i n

t h i s manner i s made of two mate r i a l s . The upper end,that passes through

the seal and i n t o the head, i s of 22 B & S gauge platinum, while the length

i n the tube i s of the same s i z e copper. The two pieces are joined j u s t

below the t e f l o n s e a l . g Two T - - ~ i l l c n holes are d r i l l e d v e r t i c a l l y i n the measuring head cover* 16

and into each hole i s f i t t e d a t e f l o n sleeve (19 and 21). The sleeves

are kept i n place by a flange at the bottom and a wire clamp (25) at the

top. A s t a i n l e s s s t e e l p i n (18 and 20) i s f i t t e d i n s i d e each sleeve i n

such a manner as to be e l e c t r i c a l l y insulated from the head and held there

by a- nut (24) threaded on to the top. The wire passing up through the

measuring head i s joined to one of the pins (20) so that*when the wire out­

side the c e l l i s connected through a resistance bridge to the bomb,the p i n

may be used as mercury l e v e l i n d i c a t o r . Since the resistance of the c i r ­

c u i t i s d i f f e r e n t when the pin i s i n the mercury than when i t i s not, the

-65-

point where the contact j u s t touches the surface i s indicated by a change

i n the bridge balance.

The p o s i t i o n of the measuring head,and thus of the mercury l e v e l i n

the bomb,is determined by measuring the height of a graduation on the rod

extending between the two bombs. A zero p o s i t i o n of the graduation i s

defined by having the contact touch the bottom of the bomb, and heights are

measured with a cathetometer from t h i s p o s i t i o n . Since the rod extends

into both bombs, and since the bombs are connected by pressure tubing,

r a i s i n g of the rod causes mercury to flow from the top bomb into the bottom

one and lowering of the rod causes the reverse flow. This t r a n s f e r of mer­

cury means that the e f f e c t i v e volume of the c e l l remains constant despite

the p o s i t i o n of the head.

The measuring head i s ra i s e d and lowered by r o t a t i n g the rodil extend­

ing between the two bombs. A length of rod equal to the length that the

head w i l l be ra i s e d or lowered i s threaded through a c o l l a r which i s held

r i g i d l y i n a permanent p o s i t i o n . Since the c o l l a r cannot move, r o t a t i n g

the rod causes i t to go up or down. The c o l l a r i s formed from a threaded

brass cone which i s s l o t t e d v e r t i c a l l y to allow i t to expand or contract.

This cone i s forced into a s l i g h t l y smaller s t e e l one by a cap, causing

the brass to close t i g h t l y around the rod and thus preventing any play bet­

ween the two threads.

Since, i f the top h a l f of the rod were rotated, i t would break the

wire extending from the i n t e r i o r of the bomb through the measuring head,

the rod i s divided into two sections. These sections are joined by a

r o l l e r bearing which allows any v e r t i c a l force to be transmitted from one

section to the other but no ho r i z o n t a l one. to be, and therefore r o t a t i n g

the bottom h a l f of the rod gives only v e r t i c a l motion to the top one.

The bearing also allows the top half to be rotated s l i g h t l y f o r s t i r r i n g

purposes, without changing i t s l e v e l . A h o r i z o n t a l length of §-inch rod

i s threaded into a c o l l a r on each section so that each i s e a s i l y turned.

The l e v e l of the liquid-vapor i n t e r f a c e (and thus of the volume of the

two phases) i s measured with a hot wire anemometer, s i m i l a r to that used 134

by Sage and Lacey . A length of .003-inch diamter platinum wire i s

spark-welded on to the mercury l e v e l i n d i c a t o r p i n , stretched across the

end of the second p i n , and spark-welded to a t h i r d p in (22) threads! into

the measuring head cover. The post extending down from the second p i n i s

placed a l i t t l e o f f centre so that by r o t a t i n g t h i s p i n the tension i n the

wire may be varied. A current s u f f i c i e n t to heat the wire a few degrees

above the temperature of the surroundings i s passed through the wire,using

the measuring head rod as one of the leads. Since the conduction of heat

away from the wire i s d i f f e r e n t i n the l i q u i d phase from that i n the gas

phase, the temperature and thus the resistance w i l l also be d i f f e r e n t i n

the two phases. The resistance of the platinum wire i s measured with a

Wheatstone bridge. I f the bridge i s balanced with the platinum wire i n

the gas phase and the measuring head i s slowly lowered, the point where

the wire passes into the l i q u i d phase i s indicated by the bridge suddenly

being out of balance.

The resistance bridge used i n the l e v e l i n d i c a t o r c i r c u i t i s made up

of three wire-wound r e s i s t o r s each of approximately the same resistance as

the platinum wire and leads. A d i a l resistance box i s placed i n p a r a l l e l

with each r e s i s t o r f o r f i n a l balancing of the bridge. The current f o r the

bridge i s supplied from a 6-volt storage battery, and the balance measured

with a s e n s i t i v e b a l l i o f r i c galvanometer. For coarse balancing of the bridge the galvanometer can be protected by a 33000, a 2200 or a 270 ohm

-67-

s e r i e s r e s i s t o r . Since only the change i n resistance and not the actual

resistance of the platinum wire i s desired, the bridge has not been c a l i ­

brated. Once the p o s i t i o n of the i n t e r f a c e i s found, the volume of each

phase can be calculated i n the same manner as the e f f e c t i v e t o t a l volume

i s found from a knowledge of the height of mercury l e v e l .

The temperature of the e q u i l i b r i u m c e l l i s c o n t r o l l e d by immersing

i t i n a constant temperature bath. The bath i s 28 inches i n diameter and

30 inches high and i s constructed of — - i n c h s t a i n l e s s s t e e l p l a t e . In

order to reduce heat losses from i t , the sides are covered with 4 inches

of glass wool, ^ - i n c h of a powdered asbestos and water glass mixture, and

wrapped with cotton canvas. The top and bottom are covered with 4 inches

of glass wool held i n place by a plywood frame. The bath i s f i l l e d with

"Mobile super c y l i n d e r extra hecla mineral o i l " , which has a f l a s h point

of 600°F., f o r high temperature use, and with a l i g h t straw o i l f o r lower

temperatures. Pressure tubing, valve stems, and the measuring rod are

brought out of the bath through glands packed with g r a p h i t e - l u b r i c a t e d cot­

ton.

The temperature of the bath i s c o n t r o l l e d by three immersion heaters

and a cooling c o i l . Two of the heaters, both of 2500-watts power, are

tapped into the bottom of the bath and are used to supply enough heat to

almost balance the heat losses. A t h i r d 500-watt one, which i s suspended

from the top, i s used i n an off-on control c i r c u i t . A l l three heaters are

c o n t r o l l e d by variacs from a common panel board and the larger two are

connected to voltmeters and ammeters so that the heat losses from the bath

may be c a l c u l a t e d . The 500-watt heater i s c o n t r o l l e d by a r e l a y operating

from a magnetically adjustable " P h i l a d e l p h i a Roto-stat" mercury thermo-

regulator. This thermoregulator extends from the top of the bath 4 inches

-68-

down past the top of the bomb, and thus controls the temperature at the

bomb l e v e l . I f necessary, the bath can be cooled by means of cooling

water passed through a c o i l of -§—inch copper tubing wrapped around the

ins i d e of the bath. The bath i s s t i r r e d to ensure constant temperature

throughout with a £ h.p. "Greey" constant speed s t i r r e r suspended from

above the bath. Since there i s some danger that the o i l may smoke, a vent

of 3-inch stove pipe i s connected from the top of the bath through a win­

dow to the outside. The bath i s maintained at a pressure s l i g h t l y l e s s

than atmospheric by means of an a i r j e t placed a few feet from the end of

the pipe which operates from a 15 pound per square inch l i n e .

The temperature of the bath and thus that of the eq u i l i b r i u m c e l l i s

measured i n three ways. A continuous record of the temperature i s given

by a "Leeds and Northrup" thermohm. This thermohm, which measures tempera­

ture by means of a platinum resistance, has an accuracy of ±0.5° up to

250°F. and + 1° up to 1000°F. I t i s tapped into the bottom of the bath

and connected through a transformer to a Micromax recording Wheatsbone

bridge. The transformer i s needed to reduce the resistance of the thermohm

to a value which the bridge can measure. I t has three taps on the second­

ary winding to enable the recorder to cover the e n t i r e range of tempera­

ture over which the bath w i l l be used. The transformer i s kept i n an a i r

bath, the temperature of which i s regulated by a b i m e t a l l i c thermoregulator

coupled to a 15-watt heater. I t s temperature i s c o n t r o l l e d to ensure rep­

roducible bath temperature readings regardless of room temperature.

This continuous record of temperature, although very convenient, i s

not accurate enough f o r measuring the eq u i l i b r i u m c e l l temperature. For

t h i s reason two other measuring devices are used, a "Leeds and Northrup"

platinum thermometer and an iron-constantan thermocouple. Since the temp-

69-

erature can be read at only one l e v e l using the thermometer, i t i s used

i n conjunction with the thermocouple which can be raised or lowered to

read the temperature at various l e v e l s . In t h i s manner the uniformity

of temperature throughout the bath can be checked.

In order to determine the composition of the l i q u i d and of the vapor

i n e q u ilibrium i n the upper bomb, samples must be obtained from each phase.

A method by which t h i s sampling may be done under conditions of constant

temperature and pressure has been devised f o r t h i s apparatus. Pressure 9 5 tubing, y^-inches * n outside diameter by y-r-inches i n in s i d e diameter and

17 inches long,has been i n s t a l l e d i n the bath p a r a l l e l to the axis of the

equi l i b r i u m c e l l . This tubing i s connected to the equ i l i b r i u m c e l l i n

three places with inch tubing. Oneelength of the -^-inch tubing connects

the top of i t to the top of the c e l l , another j o i n s the bottom of i t to

the bottom of the c e l l , and a t h i r d connects a point 3^ inches from the

bottom of the c e l l to a point 7 inches from the bottom of the large tubing.

The sampling tube i s placed so that the point 3^ inches from the bottom of

the bomb i s l e v e l with the point 7 inches from the bottom of the tubing.

A valve i s placed i n each of the ^ — i n c h l i n e s and each valve i s positioned

so that i t i s at a s l i g h t l y lower l e v e l than the corresponding connection

to the bomb. The valves are placed i n t h i s manner so that once the l i n e s

connected to the bomb have been f i l l e d with mercury, the mercury w i l l r e ­

main i n the c e l l and not run into the bomb as long as the valves are closed.

In operation, the sample tube and - i n c h l i n e s are f i l l e d with mercury and

pressure i s applied from a nitrogen c y l i n d e r u n t i l i t i s the same as i n

the e q u i l i b r i u m c e l l . When a sample of the gas phase i s to be c o l l e c t e d ,

the valve to the top of the eq u i l i b r i u m c e l l i s opened and then the one

to the bottom. Mercury flows from the sampling tube into the eq u i l i b r i u m

-70-

c e l l , d i s p l a c i n g vapor from the c e l l i n to the tube. The two valves are

then closed^and the vapor c o l l e c t e d from the sampling tube by vacuum d i s ­

t i l l a t i o n . In order to sample the l i q u i d phase, the sampling tube i s

r e f i l l e d with mercury and the procedure repeated using the two lower valves.

In order that the mercury i n the sampling tube may be replaced a f t e r

the removal of a sample, the bottom of the tube i s connected to the bottom

of an a u x i l l i a r y storage c e l l . This storage c e l l i s inches i n in s i d e

diameter, 2-| inches i n outside diameter, and 3 inches deep. The top i s

sealed with a cap and plate i n the same manner as f o r the other two bombs.

Two l i n e s are connected to the top of the c e l l through a tee; one f o r the

ad d i t i o n of f r e s h mercury, and the other f o r applying pressure from the

nitrogen c y l i n d e r .

In order to assure that e q u i l i b r i u m i s reached between the gas and

l i q u i d phases, the contents of the e q u i l i b r i u m c e l l are agitated with a

magnetic s t i r r e r . A plate (25), which i s 2 inches i n diameter, -f-inch

t h i c k , and made from 304 s t a i n l e s s s t e e l , i s held i n s i d e the e q u i l i b r i u m

c e l l near the upper end. A l l but the minimum area required f o r mechanical

strength has been machined out i n order to allow c i r c u l a t i o n of the vapor

phase around i t . I t i s held i n p o s i t i o n with a tapered screw (27) which,

when tightened, expands the edge of the plate t i g h t l y against the wa l l of

the bomb. Three small pins (31) are screwed into the upper face of the

p l a t e . Since these pins are the same length as the distance that the

plate i s to be held from the top of the bomb, i t i s positioned by pushing

i t up u n t i l they butt against the top. The plate i s used to support an

"Alnico" permanent magnet. The magnet seats on a t e f l o n washer (30) and

i s held i n p o s i t i o n by a shaft (28) which extends from i t through the p l a t e .

A s t a i n l e s s s t e e l s t i r r i n g arm (26) i s bolted to the bottom of the shaft,

-71-

on the underneath side of the p l a t e , so that r o t a t i n g the magnet rotates

t h i s arm. The magnet i s turned by means of a much stronger one suspended

from the top of the bath to the top of the bomb. This magnet i s rotated

by a small v a r i a b l e speed motor and i s encased by a thin-walled copper

c y l i n d e r so that i t does not have to operate i n the bath o i l . The use of

the copper c y l i n d e r also allows the magnet to be positioned e a s i l y . A u x i l -

l i a r y s t i r r i n g , p a r t i c u l a r l y of the l i q u i d phase, can be accomplished by

moving the measuring head back and f o r t h . Because of the r o l l e r - b e a r i n g

connection on the measuring head rod, r o t a t i n g the head does not change

i t s l e v e l .

-72-

HIOCEDURE FOR MAKING MEASUREMENTS

Before any measurements can be made with the equ i l i b r i u m apparatus

described above, a c a l i b r a t i o n r e l a t i n g the height of the mercury contact

on the measuring head to the volume of the eq u i l i b r i u m cell,measured must

be obtained. This determination can be made by f i r s t evacuating the equi­

l i b r i u m c e l l and then completely f i l l i n g i t with mercury. ^he measuring

head i s raised as f a r in s i d e the bomb as i t w i l l go, and the mercury then

allowed to run out of the c e l l u n t i l i t s upper surface j u s t touches the

t i p of the mercury contact. The volume of c e l l measured i n t h i s manner i s

the minimum volume which can be determined with the measuring head. The

mercury removed from the c e l l i s c o l l e c t e d i n a weighing bottle,and i t s

volume determined from a knowledge of i t s weight and density. A ho r i z o n t a l

l i n e i s machined on the measuring rod i n such a manner that, regardless

of the p o s i t i o n of the measuring head, i t i s always v i s i b l e between the

bottom of the bath and the top of the mercury storage c e l l . The v e r t i c a l

distance between t h i s l i n e and a s i m i l a r one on the bath frame i s determined

with a cathetometer. The measuring head i s then lowered a quarter of an

inch, and mercury again removed u n t i i the contact j u s t touches i t s Sur­

face. This procedure i s repeated u n t i l the bottom of the eq u i l i b r i u m c e l l

i s reached. This l a s t p o s i t i o n i s the zero p o s i t i o n of the measuring

head and the distance between the l i n e on the measuring head rod and the

one on the bath frame defined i n t h i s manner i s subtracted from the other

readings to obtain the height of mercury i n the c e l l . The values obtained

i n the above manner are then p l o t t e d g r a p h i c a l l y with the volume of c e l l

as ordinate and the p o s i t i o n of the rod as abscissa. The volume of c e l l

above the liquid-vapor i n t e r f a c e wire can be determined from the graph

and a knowledge of the distance between the wire and the contact point.

The c a l i b r a t i o n determined i n t h i s manner, of course, i s v a l i d only

f o r the temperature at which i t was made. However, i t can be corrected

f o r use at other temperatures from a knowledge of the temperature co­

e f f i c i e n t of expansion f o r the bomb bath and measuring head rod. The

c a l i b r a t i o n should be made at at lea s t one other temperature, such as

200°C, to check the accuracy of the corrected values.

When the measurements of mercury l e v e l i n the eq u i l i b r i u m c e l l are

made, care must be taken that, at at lea s t one p o s i t i o n , the height of

mercury i n the glass l e v e l i n d i c a t o r i s determined as w e l l . This deter­

mination i s necessary i n order that a s t a t i c head c o r r e c t i o n f o r the pres­

sure measurements can be ca l c u l a t e d .

The next step i n the use of the apparatus i s to introduce both the

mercury and the sample to be tested i n an a i r free c o n d i t i o n . The mercury

i s d i s t i l l e d , under vacuum, into the f l a s k shown i n f i g u r e 2 and, while

s t i l l under vacuum, the stopcock on the f l a s k closed. This t r a n s f e r f l a s k

i s then removed from the s t i l l and connected through a ground glass j o i n t ,

shown i n fi g u r e 4, to the mercury storage c e l l . Once the eq u i l i b r i u m

apparatus has been evacuated, the stopcock on the f l a s k i s opened and the

mercury allowed to run into the storage c e l l . I f i t i s necessary to add

more mercury, the three-way stopcock, ( f i g u r e 4), on the t r a n s f e r l i n e i s

positioned so that the f l a s k i s i s o l a t e d from the rest of the system.

The f l a s k i s then removed and r e f i l l e d with mercury from the vacuum s t i l l .

When f i l l e d , i t i s replaced and the three-way stopcock positioned so that

the tubing between t h i s stopcock and the one on the f l a s k i s connected to

the vacuum pump. Af t e r the tubing i s evacuated, the mercury i s allowed to

run into the storage c e l l as before.

- 7 4 -

The method of t r a n s f e r r i n g the solvent to be studied into the e q u i l i -87

brium apparatus i s based on the procedure used by Kaye and Donham , and the apparatus used f o r the t r a n s f e r i s shown i n f i g u r e 3. The p u r i f i e d

benzene i s displaced with dry a i r from the solvent t r a n s f e r f l a s k through I I

stopcock "e" into f l a s k "B". I t i s then frozen with a mixture of dry

ice i n acetone and the glass ware completely evacuated. A f t e r evacuating,

a l l stopcocks but "a" and "d" are closed, the Dewar f l a s k containing the

dry i c e mixture removed from around "B", and a small percentage of the

benzene allowed to d i s t i l l i n t o the cold t r a p . Stopcock "a" i s then

closed, the f r e e z i n g mixture placed around f l a s k "A", and stopcock "c"

opened. A f l a s k of warm water i s placed around "B" and the benzene d i s t i ­

l l e d under vacuum into f l a s k "A". When a l l but about 5$ of the benzene

has been d i s t i l l e d , stopcock "c" i s closed, stopcock "a" opened, and the

rest of the benzene d i s t i l l e d i n to the cold t r a p . Since the p a r t i a l pre­

ssure of a i r over the d i s t i l l i n g solvent w i l l be very much less than one

atmosphere, the amount of a i r occluded i n the frozen benzene w i l l be quite

small. The benzene i s d i s t i l l e d back and f o r t h between f l a s k s "A" and "B"

i n t h i s manner, reevacuating (the apparatus between each d i s t i l l a t i o n , u n t i l

a l l the dissolved a i r i s removed. Since, i n each case, the p a r t i a l press­

ure of a i r over the benzene i s due almost e n t i r e l y to that occluded during

the previous d i s t i l l a t i o n and f r e e z i n g , i t w i l l r a p i d l y drop to a n e g l i ­

g i b l e value. A f t e r a l l the a i r has been removed, the solvent i s d i s t i l l e d

i n t o f l a s k "E" i n preparation f o r the t r a n s f e r to the e q u i l i b r i u m c e l l .

A s i m i l a r procedure i s used with the normal propyl alcohol with the excep­

t i o n that the i n i t i a l t r a n s f e r from the storage f l a s k must be made by

vacuum d i s t i l l a t i o n f o r the reasons discussed e a r l i e r .

I I Unless otherwise noted, a l l references to stopcocks and f l a s k s r e f e r to f i g u r e 3 and a l l references to valves r e f e r to f i g u r e 4.

-75-

When both solvents are i n f l a s k E i n the desired proportions, the

bath surrounding the equ i l i b r i u m c e l l i s cooled as much as possible by

running cold water through the copper cooling c o i l . The mercury l e v e l

i n the c e l l i s then lowered u n t i l the c e l l w i l l hold the solvent mixture,

and the mixture i s tra n s f e r r e d from f l a s k E to the c e l l by vacuum d i s ­

t i l l a t i o n through stopcock j and valve D.

Since, during the t r a n s f e r , the constant temperature bath i s kept

as cold as pos s i b l e , the next step i s to heat i t to the temperature at

which the equ i l i b r i u m measurements w i l l be made. In order to heat the

bath q u i c k l y , both 2500-watt heaters are i n i t i a l l y turned up to the point

where they are working at the maximum permissible watt density. When the

desired temperature i s reached, the heaters are turned down u n t i l the

temperature s t a r t s to drop slowly. The 500-watt heater i s then turned on

and adjusted u n t i l the temperature s t a r t s to r i s e again. Once t h i s adjust­

ment has been made, the thermoregulator relay combination i s turned on to

control the bath temperature.

The bath, and thus the eq u i l i b r i u m c e l l temperature, i s measured,

using both the platinum resistance thermometer and the iron-constantan

thermocouple. I t i s determined f i r s t with the resistance thermometer and

then at the same l e v e l i n the bath with the thermocouple. The thermocouple

i s next lowered two inches and the temperature again measured. This pro­

cedure i s repeated u n t i l a temperature p r o f i l e i s obtained f o r the e n t i r e

bath. I f there i s a s i g n i f i c a n t change i n temperature through the bath,

the p o s i t i o n of the s t i r r e r i s adjusted and the measurements repeated.

While taking readings with the thermocouple, care i s taken to obtain a

reading at the l e v e l of the platinum thermohm because the manufacturers do

not supply a temperature-resistance c a l i b r a t i o n with t h i s thermometer.

-76-

The pressure applied to the e q u i l i b r i u m c e l l at any p a r t i c u l a r temp­

erature i s varied by changing the volume occupied by the solvent mixture.

To decrease the volume and thus increase the pressure, mercury i s tr a n s ­

fe r r e d to the eq u i l i b r i u m c e l l from the storage c e l l below. • This t r a n s f e r

i s accomplished by d i s p l a c i n g the mercury with nitrogen from the nitrogen

c y l i n d e r . To increase the volume and thus decrease the pressure, some of

the nitrogen i n the storage c e l l can be vented to the atmosphere through

valve M. The pressure on the e q u i l i b r i u m c e l l i s measured with the dead

weight t e s t e r described e a r l i e r . Valve "F" i s closed, i s o l a t i n g the equi­

l i b r i u m c e l l , and valve "E" opened. The p o s i t i o n of the i n t e r f a c e between

the mercury from the bomb and the o i l from the dead weight t e s t e r i s ad­

justed so that i t i s v i s i b l e i n the glass l e v e l i n d i c a t o r . The pressure

i s then measured by pla c i n g weights of known value on the dead weight

t e s t e r piston u n t i l they j u s t balance the upward pressure of the o i l . The

pis t o n i s spun continuously during the balancing to reduce the f r i c t i o n

between i t and the containing sides. Since the minimum weight a v a i l a b l e

f o r the t e s t e r represents one pound per square inch at pressures up to 400

pounds per square inch, and 5 pounds per square inch at pressures up to

4000 pounds per square inch, i t i s u n l i k e l y that an exact balance can be

made using the weights alone. Values w i t h i n these i n t e r v a l s can be obtained,

however, by r a i s i n g or lowering the p o s i t i o n of the mercury o i l i n t e r f a c e

and thus varying the s t a t i c head between the c e l l and the t e s t e r . Chang­

ing the p o s i t i o n of the i n t e r f a c e w i l l change the pressure at the c e l l as

w e l l as that at the t e s t e r , of course, because the e f f e c t i v e volume of the

c e l l w i i l change. Since t h i s change occurs, i t i s necessary to allow time

f o r the solvent to come to a new e q u i l i b r i u m before making the f i n a l pres­

sure measurement. I f a f u r t h e r change i n the p o s i t i o n of the i n t e r f a c e

-77-

i s necessary, the above procedure must be repeated. The dead weight

t e s t e r i s designed so that small amounts of o i l leak out around the p i s ­

ton when measuring the pressure. For t h i s reason the valve connecting

the t e s t e r to the bomb should be kept closed except when a c t u a l l y making

measurements.

The pressure measured by the dead weight t e s t e r i s not, of course,

the pressure i n the equi l i b r i u m c e l l . A c o r r e c t i o n must be applied to

the value obtained i n order to take into account the s t a t i c head of o i l

and mercury i n the l i n e connecting the c e l l and the t e s t e r . In order to

ca l c u l a t e t h i s c o r r e c t i o n , the differ e n c e i n height between the mercury

surface i n the bomb and the oil-mercury i n t e r f a c e i n the l e v e l i n d i c a t o r

must be known, as must the difference between the i n t e r f a c e and the dead

weight t e s t e r . The second difference can be measured d i r e c t l y with a

cathetometer, but the f i r s t can not, as the mercury i n the bomb can not

be seen. However, during the c a l i b r a t i o n of the measuring head, the

height of mercury i n the l e v e l i n d i c a t o r required to balance a known

height of mercury i n the eq u i l i b r i u m c e l l was determined. Therefore, by

measuring the change i n l e v e l of the mercury surface i n the bomb from that

at the time the c a l i b r a t i o n was madejand also i n l e v e l of mercury i n the

i n d i c a t o r from the l e v e l at the time of c a l i b r a t i o n , the head due to mer­

cury can be ca l c u l a t e d . A c o r r e c t i o n f o r the depression of the mercury

surface i n the l e v e l i n d i c a t o r caused by c a p i l l a r y action w i l l not be nec­

essary, as a s i m i l a r depression w i l l have occurred when i n i t i a l l y deter­

mining the balance between the two l e v e l s . The sum of the pressures due

to the head of o i l and to the head of mercury w i l l give the t o t a l correc­

t i o n to apply to the dead weight t e s t e r reading.

Before any fu r t h e r measurements can be made on the solvent mixture,

the gas and l i q u i d phases must be i n equil i b r i u m . In order to reduce the

time required to reach t h i s e q u i l i b r i u m , the mixture i s s t i r r e d with both

the magnetic s t i r r e r and the measuring head. As soon as the sample i s

transferred into the bomb, the magnetic s t i r r e r i s turned on and i t i s

l e f t running u n t i l a l l the needed measurements have been made. Unless the

l i q u i d l e v e l i n the bomb i s quite high, t h i s s t i r r e r w i l l operate only i n

the gas phase, and therefore, to s t i r the l i q u i d phase, the measuring head

i s rotated back and f o r t h o c c a s i o n a l l y as w e l l .

When the two phases are i n eq u i l i b r i u m , the volume of each i s deter­

mined with the measuring head. The p o s i t i o n of the head i s adjusted so

that the mercury contact j u s t touches the mercury surface and the volume

of c e l l occupied by the solvent then found from the c a l i b r a t i o n determined

e a r l i e r . With the head l e f t i n t h i s p o s i t i o n , the resistance of the gas-

l i q u i d i n t e r f a c e wire i s balanced with the Wheatstone bridge described

e a r l i e r . Once the balance has been obtained, the head i s slowly raised

u n t i l the point where the resistance of the wire suddenly changed i s found.

This change i n resistance of the wire indicates that i t has passed from

the l i q u i d to the gas phase. The volume of gas above the wire i s again

found from the c a l i b r a t i o n curve. When the measuring head i s raised or

lowered, care must be taken that valve "F" on the l i n e j o i n i n g the two

bombs i s open. I f i t i s not, moving the head w i l l change the volume of

the c e l l occupied by the solvent and thus the eq u i l i b r i u m between the two

phases.

Before an attempt to obtain samples of the two phases can be made,

the sampling chamber must be completely f i l l e d with mercury. F i r s t the

a u x i l i a r y mercury storage c e l l i s f i l l e d by the same method as was used

-79-

i n f i l l i n g the main mercury storage bomb. The mercury t r a n s f e r f l a s k i s

f i l l e d with mercury at the vacuum s t i l l and then connected to the equi­

l i b r i u m apparatus. A f t e r the f l a s k i s placed i n p o s i t i o n , valve "Kn i s

opened and the three-way stopcock positioned so that the a u x i l l i a r y s t o r ­

age c e l l and tubing connecting i t to the t r a n s f e r f l a s k are evacuated.

The mercury i s then allowed to run into the c e l l and valve "K" closed.

When the c e l l has been f i l l e d , nitrogen pressure i s applied to the mercury

surface through valve "H" u n t i l the pressure i s approximately the same as

i n the e q u i l i b r i u m c e l l . Before mercury can be t r a n s f e r r e d from the s t o r ­

age c e l l into the sampling tube, the tube i s evacuated through the l i n e

connecting the vacuum pump to the sample c o l l e c t i o n vessel ( f i g u r e 2) by

opening valve "L". When a l l the a i r has been removed, valve "L" i s

closed, valve " J " opened, and mercury forced by the nitrogen pressure

from the storage c e l l into the sampling chamber. Once i t has been f i l l e d ,

valves "A" and "B" are opened very s l i g h t l y and a l i t t l e mercury forced

through the valves into the e q u i l i b r i u m c e l l . The tubes connecting the

e q u i l i b r i u m c e l l to the sampling chamber are flushed with mercury i n t h i s

manner i n order to remove any solvent that might have c o l l e c t e d i n them.

I f any solvent accumulated i n these tubes, as would be almost sure to

happen i f they were not completely f i l l e d with mercury, then, when samples

were taken of each phase, t h i s material would be c o l l e c t e d as w e l l . The

error introduced i n t h i s manner could be very serious, p a r t i c u l a r l y when

sampling the vapor phase at r e l a t i v e l y low pressures. The volume of vapor

c o l l e c t e d when sampling v a r i e s with the height of mercury i n the bomb, but

i t i s l e s s than 20 m i l l i l d t r e s . I f a small amount of l i q u i d had condensed

or been splashed into the vapor l i n e and was c o l l e c t e d with the vapor

sample, i t , when vaporized, could have a larger volume than that of the

- 8 0 -

sample. The composition of the l i q u i d would be that of the l i q u i d phase

and not that of the vapor, and therefore the error introduced would be very

large. When enough mercury has been forced through the l i n e s to c l e a r

them, valves "A" and "B" are shut very slowly so as to leave the tubes

f i l l e d with mercury. I f they are not l e f t f i l l e d , then as soon as the

valves are closed solvent w i l l accumulate i n them again.

Since, i n order to c l e a r the tubes, mercury i s forced into the bombs,

the volume of c e l l occupied by the solvent w i l l be reduced s l i g h t l y and

thus the pressure and e q u i l i b r i u m between the two phases changed. For t h i s

reason, enough time f o r the phase to return to e q u i l i b r i u m mustbe allowed

before sampling. The gas phase can then be sampled by f i r s t opening valve

"A" and then valve "C". The mercury i n the sample chamber runs out through

valve "C! i n t o the c e l l and i n doing so, forces an equal volume of gas

through valve "A" into the sample chamber. Since t h i s displacement involves

no change i n volume and thus none i n pressure, the e q u i l i b r i u m between the

phases i s not affected and a representative sample i s obtained. Once the

sample has been transferred to the sampling chamber i t i s i s o l a t e d there

by c l o s i n g the two valves. The sample i s removed from the chamber by

vacuum d i s t i l l i n g i n to sample c o l l e c t i o n f l a s k "F" ( f i g u r e 2). In order

that t h i s d i s t i l l a t i o n can be made, both f l a s k s "F" and "G" ( f i g u r e 2) are

evacuated, the valve connecting the two closed, and the three-way stopcock

positioned so as to connect the f l a s k s to the sampling chamber. A cold

trap i s then placed around f l a s k "F" and valve "L" opened s l i g h t l y . The

sample i n the sampling tube and, depending upon the bath temperature,

p o s s i b l y the mercury as w e l l , w i l l d i s t i l l i n t o f l a s k "F". Care must be

taken that valve "L" i s opened very slowly since the sample i n the tube

i s under the same pressure as i n the e q u i l i b r i u m c e l l , and a sudden release

-81-

of t h i s pressure could shatter the glass r e c e i v i n g f l a s k . Once the sample

i s i n f l a s k "F", valve "L" i s closed, the cold trap i s tr a n s f e r r e d to

f l a s k "G", and the solvent vacuum d i s t i l l e d i n to "G". Since the tempera­

ture required to t r a n s f e r the sample from "F" to "G" i s only s l i g h t l y

above room temperature, any mercury present w i l l remain i n "F". The stop­

cock between the two f l a s k s i s then closed, f l a s k "G" removed, and the

sample analyzed.

The procedure f o r obtaining a sample of the l i q u i d phase i s p r a c t i c a l l y

i d e n t i c a l . Once the vapor sample has been removed, the sampling chamber

i s evacuated and r e f i l l e d with mercury. Samples of the l i q u i d phase are

then obtained by opening valves "B" and "C", thus allowing the mercury to

run into the c e l l through "C" and the sample out into the sample chamber

through "B". One difference that does a r i s e i n the sampling i s that the

po s i t i o n s of the mercury-liquid i n t e r f a c e and v a p o r - l i q u i d i n t e r f a c e i n

the bomb must be known. In order to obtain a sample of the l i q u i d phase,

the mercury l e v e l must be below that of the point where the tubing from

valve "B" enters the bomb and the l e v e l of the va p o r - l i q u i d i n t e r f a c e

must be above t h i s point. I f the phase boundaries are not i n the correct

p o s i t i o n , then e i t h e r the amount of solvent i n the c e l l or else the press­

ure applied to the solvent must be changed. Once the samples have been

obtained, they must of course be analyzed. The composition of the l i q u i d

phase i s determined from the r e f r a c t i v e index of the l i q u i d sample. The

r e l a t i o n s h i p between r e f r a c t i v e index and composition i s determined by

using the P u l f r i c h refTactometer described e a r l i e r f o r mixtures of known

composition and the indek f o r the l i q u i d sample i s compared to t h i s c a l i ­

b r a t i o n . The sample from the vapor phase i s analyzed using a gas f r a c t o -

meter. This sample can not be analyzed by using the refTactometer because

-82-

the volume of l i q u i d obtained by condensing the gas i s i n s u f f i c i e n t f o r

a measurement.

The sampling procedure described above can be used to obtain as many

samples from each solvent mixture as desired, the only r e s t r i c t i o n being

that s u f f i c i e n t solvent remains i n the c e l l that the two i n t e r f a c e s are

i n the correct p o s i t i o n . In general, i t i s suggested that two samples of

each phase be taken at each temperature and pressure before changing these

v a r i a b l e s .

-83-

BIBLIOGRAPHY

1. Addison, C.C., J . Chem. S o c , 1945, 98.

2. Akers, W.W., Attwell} L.L., and Robinson, J.A., Ind. Eng. Chem., 46: 2539, 1954.

3. Akers, W.W., Burns, J.F., and F a i r c l i i l d , W.R., Ind. Eng. Chein., 46: 2531, 1954.

4. Al-Mahde, A.A.K. and Ubbelodhe, A.R., Proc. Roy. Soc. (London), A220: 143, 1953.

5. Amer, H.H., Paxton, R.R., and Van Winkle, M., Ind. Eng. °hem., 48: 142, 1956.

6. American Instrument Company, Superpressure and C a t a l y t i c Hydrogena-t i o n Apparatus, Catalog 406. American 1 Instrument Company, 1947.

7. American Petroleum I n s t i t u t e Samples and Data O f f i c e , Research Pro­j e c t 44. P i t t s b u r g , Carnegie I n s t i t u t e of Technology.

8. Anchor Packing Company Ltd., Anchor Packings and Products No. 2.

Montreal, The Anchor Packing Co. Ltd.

9. Aroyan, H.J. and Katz, D.L., Ind. Eng. Chem., 43: 185, 1951.

10. Ashley, J.II. and Brown, G.M., Chem. Eng. Progr. Symposium, No. 10: 129, 1954.

11. Bahlke, W.H. and Kay, W.B., Ind. Eng. Chem., 24: 291, 1932.

12. Banks, R.E. and Musgrave, W.K.R., J . Chem. Soc., 1956, 4682.

13. Barbaudy, J . , J . Chim. Phys., 23: 283, 1926. 14. Barr, W.E. and Anhorn, V.J., S c i e n t i f i c and I n d u s t r i a l Glass Blowing

Laboratory Techniques. P i t t s b u r g , Instruments Pu b l i s h i n g Com­pany, 1949.

15. Benedict, M., Johnson, C.A., Solomon, E., and Rubin, L.C., Trans. A.I.Ch.E., 41: 371, 1945.

16. Benedict, M., Solomon, E., and Rubin, L.C., Ind. Eng. Chem., 37: 55, 1945.

17. Berner, E., Z. physik. Chem., 141A: 91, 1929.

18. Bloomer, O.T. and Parent, J . , Chem. &ig. Progr. Symposium, No. 6: 11, 1953.

19. Broughton, D.B. and Brea r l y , C.S., Ind. Eng. Chem., 47: 838, 1955.

-84-

20. Brown, H.C. and Jungk, H., J . Am. Ohem. Soc., 77: 5584, 1955.

21. Brown, I . and Smith, F., A u s t r a l i a n J . Chem., 7: 264, 1954.

22. Brunei, H.F., J . Am. Chem. S o c , 45: 1334, 1923.

23. Brunei, R.F., Crenshaw, J.L., and Tobin, E., J . Am. Chem. S o c ,

43: 561, 1921.

24. Campbell, A.N. and M i l l e r , S.N., Can. J . Research, 25: 282, 1947.

25. Canjar, L.N., Horni, E.C.,md Rothfus, R.A., Ind. Eng. Chem., 48:

427, 1956.

26. Carley, J.F. and Bertelsen, L.W., Ind. Eng. Chem., 41: 2806, 1949.

27. Carlson, H.C. and Colburn, A.P., Ind. Eng. Chem., 34: 581, 1942.

28. Carney, T.P., Laboratory F r a c t i o n a l D i s t i l l a t i o n , New York, The

MacMillan Company, 1949.

29. C a r r o l , M.M., B.A.Sc. Thesis i n Chemical Engineering, U.B.C..,. 1952.

30. Chang, Y. and Moulton, R.W., Ind. Eng. Chem., 45: 2350, 1953.

31. Cines, M.R., Roach, J.T., Hogan, R.J., and Roland, C.R., Chem. Eng.

Progr. Symposium, No. 6: 1, 1953.

32. Clark, A.M., Trans. Faraday S o c , 41: 718, 1945.

33. Clark, A.M., Din, F., and Robb, J . , Proc. Roy. S o c (London), A221:

517, 1954.

34. Clegg, H.P. and Rowlinson, J.S., Trans. Faraday S o c , 51: 133, 1955.

35. Cohen, E. and B u i j , J.S., Z. physik. Chem., B35: 271, 1937.

36. Comings, E.W., Ind. Eng. Chem., 39: 948, 1947.

37. Comings, E.W., High Pressure Technology, New York, McGraw-Hill Book

Company Inc., 1956.

38. Cook, D., Proc. Hoy. Soc. (London), A219: 245, 1953.

39. Copeland, C.S., Silverman, J . , and Bensen, S.W., J . Chem. Phys. 21: 12, 1953.

40. Coulson, E.A., Hales, J.L., and Herington, E.F.G., Trans. Braday Soc., 44: 636, 1948.

41. Davies, R.M., P h i l . Mag., v i i 2 1 : 1, 1936. 42. Davison, J.A., J . Am. Chem. S o c , 67: 228, 1945.

-85-

43. Dean, M.R. and Took, J.W., Ind. Eng. Chem., 38: 389, 1946.

44. Deffet, L., B u l l , soc. chim. Belg., 44: 41 and 97, 1935.

45. Denbeigh, K., The P r i n c i p l e s of Chemical Eq u i l i b r i u m , Cambridge,

Cambridge U n i v e r s i t y Press, 1955.

46. Dixon, J.A. and Schiesster, R.W., J . Am. Chem. Soc., 76: 2197, 1954.

47. Dodge, B.F., Chemical Engineering Thermodynamics, New York, McGraw-

H i l l Book Company Inc., 1944.

48. Donnelly, H.G. and Katz, D.L., Ind. Eng. Chem., 46: 511, 1954.

49. Dorochewsky, A.G., J . Russ Phys. Chem. S o c , 41: 972, 1909.

50. Dorochewsky, A.G., J . Russ. Phys. Chem. S o c , 43: 66, 1911.

51. Drago, R.S. and S i s l e r , H.R., J . Phys. Chem., 60: 245, 1956.

52. Dyrmose, L., B.A.Sc. Thesis i n Chemical Engineering, U.B.C., 1957.

53. Eakin, B.E., El i n g t o n , R.T., and Garni, D.C., I n s t . Gas Techno1. Research B u l l . , 26: 40, 1953.

54. Emerson, H.L. and C u n d i l l , T.G., B.A.Sc. Thesis i n Chemical Engineer­ing, U.B.C., 1951.

55. Eshaya, A.M., Chem. Eng. Progr., 43: 555, 1947.

56. Evans, R.B. and H a r r i s , D., Ind. Eng. Chem., Chem. Eng. Data Series,

1: 45, 1956.

57. Few, A.V. and Smith, J.W., J . Chem. S o c (London), 1949, 753.

58. Fenske, M.R., Braun, W.G., Wiegand, R.V., Quiggle, D., McCormick,

R.H., and Rank, D.H., Ind. Eng. Chem. (Anal. Ed.), 19: 700, 1947.

59. F o r z i a t i , A.F., J . Research Nat. Bur. Standards, 44: 373, 1950.

60. F o r z i a t i , A.F., Glasgow J r . , A.R., Willingham, C.B., and R o s s i n i , F.D., J . Research Nat. Bur. Standards, 36: 129, 1946.

61. F o r z i a t i , A.F., N o r r i s , W.R., and R o s s i n i , F.D., J . Research Nat. Bur. Standards, 43: 555, 1949.

62. F o r z i a t i , A.F. and R o s s i n i , F.D., J . Research Nat. Bur. Standards, 43: 473, 1949.

63. Garlock Packing Company, The Design and A p p l i c a t i o n of Methanical Leather Packings, American Leather B e l t i n g A s s o c i a t i o n , 1947.

64. Gibbons, L.C. et a l . , J . Am. Chem. S o c , 68: 1130, 1946.

-se­

es. G i l l e s p i e , D.T.C., Ind. Eng. Chem. (Anal. Ed.), 18: 575, 1946.

66. Gilmann, H.H. and Gross, P., J . Am. Chem. S o c , 60: 1525, 1938.

67. Gilmont, R., Weinman, E., Kramer, F., M i l l e r , E., Hashmall, F., and Othmer, D., Ind. Eng. Chem., 42: 120, 1950.

68. Glasgow J r . , A.R., Murphy, E.T., Willingham, J.C., and R o s s i n i , F.D., J . Research Nat. Bur. Standards., 37: 14, 1946.

69. Gornowski, E.J., Anick, E.H., and Hixson, A.N., Ind. Eng. Chem., 39: 1348, 1947.

70. Grimm, F.W. and P a t r i c k , W.A., J . Am. Chem. S o c , 45: 2794, 1923.

71. Griswold, J . , Andres, D., and K l e i n , V.A., Trans. A.I.Ch.E., 39: 223, 1943.

72. Grosse, A.V. and Wackher, R.C., Ind. Eng. Chem. (Anal. Ed.), 11:

614, 1939.

73. Grunberg, L., Trans. Faraday S o c , 50: 1293, 1954.

74. Guggenheim, E.A., Modern Thermodynamics by the Methods of W i l l a r d

Gibbs. London, Methuem and Company, L t d . , 1933.

75. Hamburg, A., B.A.Sc. Thesis i n Chemical Engineering, U.B.C., 1952.

76. Harrison, J.M. and Berg, L., Ind. Eng. Chem., 38: 117, 1946.

77. H i r a t a , M., Chem. Eng. (japan), 13: 138, 1949.

78. H i r s c h f e l d e r , J.O., C u r t i s s , C.F., and B i r d , R.B., Molecular Theory of Gases and L i q u i d s . New York, John Wiley and Sons Inc., 1954.

79. Hodgman, CD., Handbook of Chemistry and Physics. Cleveland, Chemi­ca l Rubber Publishing Company, 1949.

80 Hougen, O.A. and Watson, K.M., Chemical Process P r i n c i p a l s , New York, John Wiley and Sons Inc., 1950, Part 2.

81. Howey, G.R., M.A.Sc. Thesis i n Chemical Engineering, U.B.C., 1951.

82. Johnson, A.I. and Furter, W.F., Can, J . Technology, 34: 429, 1957.

83. J u Chin Chu, Getty, R.J., Brennecke, L.F., and Paul, R., D i s t i l l a t i o n

E q u i l i b r i u m Data. New York, Reinhold Pu b l i s h i n g Co., 1950.

84. Kay, W.B., Ind. Eng. Chem., 28: 1015, 1936.

85. Kay, W.B. and A l b e r t , R.E., Ind. Eng. Chem., 48: 422, 1956. 86. Kay, W.B. and B r i c e , D.B., Ind. Eng. Chem., 45: 615, 1953.

-87-

87. Kay, W.B. and Donfaam, W.E., Chem. Eng. S c i . , 1: 1, 1955.

88. Kay, W.B. and Rambosek, G.M., Ind. Eng. Chem., 54: 221, 1953.

89. Katz, D.L. and Kurata, F., Ind. Eng. Chem., 32: 817, 1940.

90. Katz, K . and Newman, M., Ind. Eng. Chem., 48: 137, 1956.

91. Keyes, F.G. and Winninghoff, W.J., J . Am. Chem. S o c , 38: 1178, 1916.

92. Kobayashi, R. and Katz, D.L., Ind. Eng. Chem., 45: 440, 1953.

93. Kretschmer, C.B., J . Phys. and C o l l o i d Chem., 55: 1351, 1955.

94. Kretschmer, C.B., Nowakowska, J . , and Wiebe, R., J . Am. Chem. S o c .

70: 1785, 1948.

95. Kretschmer, C.B. and Weibe, R.J., J . Am. Chem. S o c , 71: 1793, 1949.

96. Kumarkrishna Rao, V.N., Swami, D.R., and Narasinga Rao, M., J . S c i .

Ind. Research ( I n d i a ) , 16B: 233, 1957.

97. Laar, J . J . van., Z. physik. Chem., 72: 723, 1910.

98. La Rochelle, J.H. and Vernon, A.A., J . Am. Chem. S o c , 72: 3293, 1950.

99. Lee, S.C., J . Phys. Chem., 35: 3558, 1931. 100. Lewis, G.N. and Randall, M., Thermodynamics and the Free Energy of

Chemical Substances. New York, McGraw-Hill Book Company Inc., 1923.

101. L i c h t e n f e l s , D.H., Fleck, S.A., and Burow, F.H., Anal Chem., 27: 1510, 1955.

102. Linton, E.P., J . Am. Chem. S o c , 62: 1945, 1940.

103. Lowry, T.M. and Allsopp, C.B., Proc. Roy. Soc. (London), A113: 26, 1931.

104. Mair, B.J., Glasgow, A.R., and R o s s i n i , F.D., J . Research Nat. Bur. Standards, 26: 591, 1941.

105. Marek, J . and Standart, G., C o l l . Gzechos Chem. Comm., 19: 1074, 1954.

106. Margules, M., "Stizungsberichte der math-maturw" Class der Ka i s e r -

l i c h e n Akademie der Wissenschaften (Vienna), 104: 1243, 1895.

107. Marschner, R.F. and Cropper, W.P., Ind. Eng. Chem., 38: 262, 1946.

108. Maryott, A.A., Hobbs, M.E., and Gross, P.M., J . Am. Chem. S o c , 62: 2320, 1940.

-88-

109. Mason, M.S., Thesis i n Chemical Engineering, M.I.T., 1942.

110. McCracken, P.G. and Smith, J.M., A.I.Ch.E. J o u r n a l , 2:, 498, 1956.

111. McKenna, F.E., Tartar, H.V., and L i n g a f e l t e r , E.C., J . Am. Chem.

S o c , 75: 604, 1953.

112. Mertes, T.S. and Colburn, A.P., Ind. Eng. Chem., 39: 287, 1947.

113. Mumford, S.A. and P h i l l i p , J.W., J . Chem. S o c , 1950, 75.

114. Mundel, C.F., Z. physik. Chem., 85: 435, 1913.

115. Neff, J.A. and Hickman, J.B., J . Phys. Chem., 59: 42, 1955.

116. Newitt, D.M., High Pressure Plants and F l u i d s at High Pressure.

New York, Oxford U n i v e r s i t y Press, 1940.

117. N o r r i s h , R.S. and Twig, G.H., Ind. Eng. Chem., 46: 201, 1954.

118. O l i v e r , G.D., Eaton, M., and Hauffman, H.M., J . Am. Chem. S o c , 70: 1502, 1948.

119. Othmer, D.F., S i l v i s , S.J., and S p i e l , A., Ind. Eng. Chem., 44: 1864, 1952.

120. Otsuki, II. and Williams, F.C., Chem. Eng. Progr. Symposium, No. 6: 55, 1953.

121. Ottenweller, J.H., Holloway, C , and Weinrich, W., Ind. Eng. Chem., 35: 207, 1943.

122. P r a h l , W.H., Ind. Eng. Chem., 43: 1767, 1951.

123. Prigogine, I . , The Molecular Theory of Gases, Amsterdam, The North-

Holland Publishing Company, 1957.

124. P u r n e l l , J.H. and Bowden, S.T., J . Chem. S o c , 1954, 539.

125. Puschin, N.A. and Matavulj, P.G., Z. physik. Chem., A162: 415, 1932.

126. Ramsay, W. and Young, S., J . Chem. S o c , 47: 640, 1885.

127. Reamer, H.H., Sage, B.H., and Lacey, W.N., Ind. Eng. Chem., 45: 1805, 1953.

128. Reamer, H.H., Sage, B.H., and Lacey, W.N., Ind. Eng. Chem,, 42: 140, 1950.

129. Reamer, H.H., Se l l e c k , F.T., Sage, B.H., and Lacey, W.N., Ind. Eng. Chem., 45: 1810, 1953.

-89-

130. Redlich, 0., and K i s t e r , A.T., Ind. Eng. Chem.. 40: 341, 1948.

131. Re d l i c h , 0. and K i s t e r , A.T., Ind. Eng. Chem., 40: 345, 1948.

132. Riddick, J.A. and Toops, E.E., Organic Solvents, 2nd Ed., New York, Interscience Publisher Inc., 1955.

133. Robinson, C.S. and G i l l i l a n d , E.R., Elements of F r a c t i o n a l D i s t i l l ­

a t i o n , 4th Ed., New York, McGraw-Hill Book Co. Inc., 1950.

134. Sage, B.H. and Lacey, W.N., Trans. A.I.M.E., 174: 102, 1948.

135. Sage, B.H. and Lacey, W.N., Trans. A.T.M.E., 136: 136, 1940.

136. Sanderson, R.T., Vacuum Manipulation of Volatine Comppunds. New

York, John Wiley and Sons Inc., 1948.

137. Sandquist, C.L. and Lyons, P.A., J . Am. Chem. S o c , 76: 4641, 1954.

138. Scatchard, G. and Hamer, W.J., J,. Am. Chem. S o c , 57: 1805, 1935.

139. Scatehard, G., Wood, S.E., and Mochel, J.M., J . Phys. Chem., 43:

140. Scheeline, H.W. and G i l l i l a n d , E.R., Ind. Eng. Chem., 31: 1050, 1939.

141. Shemilt, L.W. and Singh, R., Unpublished C a l c u l a t i o n s .

142. Simonsen, D.R. and Washburn, E.R., J . Am. Chem. S o c , 68: 235, 1946.

143. Smith, E.R., J . Research Nat. Bur. Standards., 26: 129, 1941.

144. Smith, E.R. and Matheson, H., J . Research Nat. Bur. Standards, 20:

641, 1938.

145. Smith, J.M., Ind. Eng. Chem., 45: 963, 1953.

146. Steinhauser, H.H. and White, R.R., Ind. Eng. Chem.r,i 41: 2912, 1949.

147. S t r i e f f , A.J. and R o s s i n i , F.D., J . Research Nat. Bur. Standards, 39: 321, 1947.

148. Swietoslawski, W., Ebu l l i o m e t r i c Measurements. New York, Reinhold Publishing Company, 1945.

149. Timmermans, J . , Physico-Chemical Constants of Pure Organic Compounds.

New York, E l s e v i e r Publishing Company Inc., 1950.

150. Timmermans, J . and Delcourt, Y., J . chim. Phys., 31: 85, 1934.

151. Timmermans, J . and Martin, F., J . chim. PhyB., 23: 747, 1926. 152. Tompa, H., J . Chem. Phys., 16: 292, 1948.

-90-

153. Trew, V.C.G., Trans. Faraday S o c , 49: 604, 1953.

154. Trew, V.C.G. and Watkins, G.M.C., Trans. Faraday S o c , 29: 1310, 1933.

155. Tucker, M.S. Thesis i n Chemical Engineering, M.I.T., 1942.

156. Vogel, A.T., J . Chem. S o c , 1948, 1814.

157. Waldichuek, M., M.A. Thesis i n Arts and Science, U.B.C., 1950.

158. Week, H.I. and Hunt, H., Ind. Eng. Chem., 46: 2521, 1954.

159. Wehe, A.H. and Coates, J . , A.I.Ch.E. Jo u r n a l , 1: 241, 1955.

160. Wetzel, F.H., M i l l e r , J.C., and Day, A.ft., J . Am. Chem. S o c , 75:

1150, 1953.

161. White, N.E. and K i l p a t r i c k , M., J . Phys. Chem., 59: 1044, 1955.

162. Wild, A., B.A.Sc. Thesis i n Chemical Engineering, U.B.C., 1956.

163. Williams, R.B. and Katz, D.L., Ind. Eng. Chem., 46: 2512, 1954.

164. Wohl, L., Trans. A.I.Ch.E., 42: 215, 1946.

165. Wojciechowski, M., J . Research Nat. Bur. Standards, 19: 347, 1937.

166. Wojciechowski, M., J . Research Nat. Bur. Standards, 17: 721, 1936.

167. Woodson, C , Tucker, J . , and Hawkins, E.J., Ind. Eng. Chem., 46: 2387, 1954.

168. Young, S. and Fortey, E.C., J . Chem. Soc. (London), 83: 45, 1903.

169. Yu, K.T. and C o u l l , J . , Chem. Eng. Progr., 46: 89, 1950.

170. Zepalova, -., Mikkailova, L.A., Trans. I n s t . Pure Chem. Reagents (Moscow), No. 15: 1, 1937.

171. Zmaczynski, M.A., J . chim. Phys., 23: 282, 1926.