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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 .
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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
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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
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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 .
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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.