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Partial Molal Volumes of Hydrocarbons in Water Solution

W. L. Masterton 

Citation: J. Chem. Phys. 22, 1830 (1954); doi: 10.1063/1.1739928 

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THF:

J O U R N A L

OF

C H E M I C A L P H Y S I C S V O L U M E 2 2 ,

N U M B E R 11

N O V E M B E R , 1 9 5 4

Partial Molal Volumes of ydrocarbons in Water Solution

W.

L.

MASTERTON*

Department of Chemistry and Chemical Engineering, University o f Illinois, Urbana, Illinois

(Received April 12 1954)

The partial molal volumes of benzene, methane, ethane and propane in water solution have been deter

mined

at

temperatures ranging from 1D-40°C. All

the

volumes measured were less

than

those of

the

same

hydrocarbons in nonpolar solvents. This decrease in volume is explained in terms of the abnormally high

internal pressure of water, which decreases the free volume available to the hydrocarbon molecules. The

temperature dependence of the partial molal volumes of the aliphatic hydrocarbons differs sharply from

. that of benzene. I t is suggested that this is caused by a difference in solution structure in the two cases.

INTRODUCTION

T

HE thermodynamics of aqueous solutions of

hydrocarbons have been investigated in this

laboratory during the past several years. Claussen and

Polglase

1

determined the solubilities, heats of solution,

and entropies of solution of methane, ethane, propane

and butane in water. Bohon and Claussen

2

carried out

a similar study for the aromatic hydrocarbons.

I t

has long been known that the lower aliphatic

hydrocarbons form solid hydrates. Structures of the

clathrate type have been proposed for these hydrates,3

and verified by x-ray diffraction studies/,r; (see urea

I C ~ ~ I I ~ 18

I

r--

6

----1"2. .

6 -

.

8

TT

oS

NJ

-

 

-

VI

LA

-

L.. \..

FIG. 1.

Copper block (vertical section).

*This paper is based on a thesis presented by the author in

partial fulfillment of the requirements for the Ph.D. degree at

the University of Illinois, June, 1952.

1

W. F. Claussen and M. F. Polglase, J. Am. Chern. Soc. 74

4817 (1952). '

2

R.

L.

Bohon and W. F.

Claussen,].

Am. Chern. Soc. 73 1571

(1951). '

3 W. F. Claussen,

J.

Chern. Phys.

19,259,662, 1425

(1951).

4

R. Cole, Ph.D. thesis, University of Illinois (1951).

clathrates).6 These ice-like structures contain voids

large enough to accommodate hydrocarbon molecules.

Such structures must exist in solution as well as in the

solid phase. One may then picture hydrocarbon mole

cules in solution as being surrounded by oriented cages

of water molecules. Claussen and Polglase

1

used this

concept to explain the negative enthalpies and entropies

of solution of the aliphatic hydrocarbons.

No hydrates of the aromatic hydrocarbons have ever

been reported, presumably because these molecules are

too large to fit into the voids in the hydrate structures.

I t has been found possible to explain the thermo

dynamics of aqueous solutions

of the aromatic hydro

carbons without assuming the presence of structures of

the type described above.

I t

is of interest to determine whether the partial

molal volumes of hydrocarbons in water solution agree

with this model of their solution structures. The partial

molal volume V in these extremely dilute solutions was

found to be identical with the apparent molal volume

1/- .

The latter can be determined from the specific gravities

and concentrations of the hydrocarbon solutions by the

following equation:

(1)

where M

2

=molecular weight of hydrocarbon,

y=con-

centration of hydrocarbon

in glcc,

and d do=densities

of solution and pure water, respectively, at the tem

perature at which is measured.

Since the solubilities of the hydrocarbons are ex

tremely small (benzene,

1.

70 X

10-

3

glcc; methane,

2.30X 10-

5

g/cc , an extremely sensitive method must

be chosen for the determination of the specific gravities.

Such a method should give results accurate to about

seven decimal places.

Several methods are available for the determination

of specific gravities of extremely dilute solutions.

Various modifications of the float method have been

described in the literature. They suffer from the common

problem of temperature control. A procedure in which

the solution and reference liquid were compared simul

taneously would obviously reduce this difficulty. Such

5

M. V. Stackelberg, Naturwiss. 36, 327, 359 (1949).

6 F. Cramer, Angew. Chern. 64, 437 (1952).

1830

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P A R

T I A L J\I 0

LA

L VOL U M E S 0 F H Y D ROC ARB 0 N S N \V ATE R

1831

a method is

that

of Frivold

7

which utilizes the principle

of communicating tubes.

In

this method, solution

and

reference liquid air

free conductiv ity water) are placed in two vertical tubes

connected

at

the

bottom and

near the top

by

valves.

Upon first allowing the upper valves to be opened for

equilibration

and

then opening the lower valves,.

flo.w

will occur if the solution differs from the reference hqmd

in specific gravity. Wirth, Thompson, and Utterback

8

measured indirectly the drop

of

the liquid level in one

of the tubes as a result of this flow. An alternative

procedure is to measure the volume

of

liquid which

must be withdrawn from one side of the apparatus to

prevent

flow.

This volume is simply related to the

specific gravity of the solution by the equation

Vjah l d jd

n

, (2)

where = volume of water withdrawn to achieve equi

librium, a= cross sectional area of the liquid surfaces in

the tubes,

h=distance

between the upper a.nd lower

valves, and

jd

o

=

specific gravity of the solutlOn.

EXPERIMENTAL

A. The Copper Block Specific Gravity Apparatus

t was found necessary to construct the apparatus

out of copper

so

as to allow for the rapid equilibration

FIG.2 . Glass capillary.

1 ~ 3 8 . 1

MM

1.. i

4MM.

U

T ~

.46 ii:r-

1

6

MM.

of

any

temperature difference between the two tubes.

An accuracy of one part in ten million in specific

gravity requires temperature control accurate to

±O.OOOloC

which is difficult to achieve in a glass

apparatus. The dimensions of the apparatus are indi

cated in Fig.

1.

The copper block was enclosed in a wooden insulating

chamber which formed

an

air ba

ho

Attached to the

inside of each of the walls of the chamber was a hollow

steel

tank

one inch thick.

By

circulating water from a

refrigeration bath through these tanks, experiments

could be made

at

temperatures as low as Soc. A re

sistance coil inserted inside the chamber permitted

operating temperatures up to

SO°C.

The temperature of

the air bath could be maintained to within ±O.O1 °c

while the high thermal conductivity

of

the copper block

itself insured

that

the temperatures of the two columns

of liquid would be equal within ±O.OOOOl°C. The

copper surfaces

of the block were lined with tin to

prevent corrosion.

In order to detect flow of liquid through the lower

valves, a glass capillary was inserted into the lower con-

7

O. E. Frivold, Physik. Z. 21, 529 1920).

8 Wirth, Thompson, and Utterback, J. Am. Chem. Soc. 57,

400 1935).

8 7 ~ - - ~ - - - - , - - - ~

4

BENZENE

54

... .

<

~ 5

::J

.J

5

>

41

3 9 r ~ ~ .

J

7

w

::J

..J

g

35

69

J

~ 67

...

:li

::J

..J

65

>

2 3

41

TEMP.oC

METHANE

41

FIG. 3. Change of partial molal volume with temperature.

necting tube and a dye was injected

at

one edge

of

the

capillary.

The

flow of dye through the capillary was

observed through an optical system with the eyepiece

outside the apparatus. The dimensions

of

the capillary

are quite critical; if it is too large, a significant amount

of

flow

will

occur before it can be detected, leading to

low

values of in Eq. 2). On the other hand, too fine

a capillary would greatly reduce the rate of

flow

of the

dye

and

seriously affect the sensitivity

of

the instru

ment. The capillary chosen was 1.6 mm in length and

0.4

mm

in diameter.

Its

design

is

shown in Fig.

2.

The glass tube was sealed into the lower horizontal

tube with sealing wax. t was found that the dye would

move across the capillary by diffusion and mixing in

about ten minutes while a difference

of

one

part

in ten

million in specific gravity would cause the dye to flow

across the capillary in three minutes.

The volume

of liquid withdrawn to achieve equi

librium was accurately measured in a capillary burette.

This consisted of a piece of calibrated capillary tubing

fastened to a meter stick.

Frequent blank runs were made in the course

of

the

experimental determinations. These consisted of filling

both sides of the apparatus with conductivity water

and measuring the difference in specific gravities of the

two columns

of

water. In no case was a difference de

tected greater than one part in ten million, the limit

of

accuracy

of

the experiments.

B. Preparation

and

Analysis of Solutions

Special precautions were taken to insure that the only

factor producing a difference

in

specific gravity between

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1832

W .

L. M S T E R S O N

TABLE I Apparent molal volumes of benzene in water solution.

T=IO.IOC

T

=2S.2°C

T=30.0·C

y

I d/do

'

y

I d/do

'

y

I d/do

'

10'

XlO

cc

XIO

X1O'

cc

XIO

XIO

cc

1.62 0.78 81.9 1.24 0.90 83.7

1.81

1.29 83.6

1.96 0.82 81.4 3.07 1.95 83.0 2.13 1.42

83.2

2.48

1.09 81.5 3.75

2.41

83.1

2.44 1.54

83.0

3.79 1.84 81.8

4.00

2.68 83.4 3.47 2.26 83.2

3.99 1.92 81.8 5.87 3.53 82.8 4.72 3.07 83.2

4.57 2.26 81.8

5.02 3.30 83.3

6.04 2.80 81.7 5.88 3.78 83.2

6.52 4.36 83.4

Av.=81.7 Av.=83.2 Av.=83.3

T

=34.9°C

T=39.9°C

y

I d/do

'

y

I dido

'

IO

XIO

co

XIO

XIO

cc

2.50 1.85 83.9

1.76

1.50 84.7

4.69

3.59

84.1 2.57 2.16 84.8

6.67 4.85 83.9 4.01 3.16 84.4

4.58 3.49 84.0

4.79

3.89 84.6

Av. = 84.0 Av. = 84.5

solution and standard was the presence of the solute

being investigated. A difference in concentration of dis

solved air or of isotopic composition would cause

spurious specific gravity differences.

To

avoid this a

sample of conductivity water was rendered air-free by

boiling under vacuum. t was then split into two por

tions, one of which served as the solvent for the hydro

carbon solution and the other as reference liquid.

1.

Benzene soltttions

The benzene used to prepare the solutions was

purified by the method of Mair

et al

The solutions

were prepared by placing one portion of the air-free

conductivity water in contact with benzene vapor

arising from a tube connected to the solution flask. The

solution process was hastened by stirring the water in

the solution flask with a magnetic stirrer. Solution was

carried out under vacuum.

The concentrations of the benzene solutions could be

adjusted by varying the time of exposure of the solution

flask to benzene vapor. Stirring was continued for

several minutes after the solution was shut off from

contact with the benzene vapor. This insured uniform

concentration of the solution. Solution and standard

were then successively admitted to the block. About

fifteen minutes were allowed for the liquids to come to

the temperature of the block. The specific gravity of

the solution was then determined. In each experiment

measurements were taken until three successive deter

minations agreed within one part in the seventh decimal

place.

Portions of the solution were then withdrawn from

the block

and

analyzed by means of an ultraviolet

• Mair, Termini, Willingham, a nd Rossini,

J.

Research Nat .

Bur. Standards 37 229 (1946).

spectrophotometer. t was found that the absorption

peak

at 2537

A obeyed Beer's law within

t

of 1 percent

at optical densities up to 1.0. Portions of the solution

withdrawn from various sections of the block showed

uniform concentrations within at least 1 percent.

Evaporation of benzene apparently occurred only from

the trays above the vertical tubes provided the solutions

were analyzed within two to three hours after admission

to the block.

From the concentrations of the solutions and their

specific gravities the apparent molal volumes could be

calculated

by

means of Eq. (1). The data on benzene

solutions is given in Table I

2

Aliphatic Hydrocarbon Solutions

The aliphatic hydrocarbons studied were methane,

ethane, and propane. The hydrocarbons used were all

of research grade (99 mole percent pure). They were

TABLE II. Apparent molal volumes of aliphatic hydrocarbons

in water solution.

=16.S·C

y

did .

XIO XIO

2.30 2.48

2.31

2.58

2.34 2.48

2.35 2.95

2.41

2.54

2.43 2.57

Av.=33.2

=16.9·C

cc

33.3

33.8

33.0

36.2"

33.0

33.0

Y

XIO

1.43

1.44

1.49

1.55

1.58

y

I-d/do o

XIO XIO cc

3.61 2.17 48.2

=16.9°C

y

I dido

o

X 10

XlO

cc

6.48 2.96 64.1

6.53

2.83

63.2

7.79 3.45 63.5

Av.=63.6

Methane

T=23.0°C

y

I d/do

'

10 XIO

cc

1.04

1.35 36.8

1.53 1.92 36.2

1.95 2.47 36.5

1.95 2.38 35.5

1.96 2.50 36.5

2.25

2.81

36.0

2.63 3.42 36.9

Av.=36.3

T=3S.IOC

I d/do

XIO

1.95

1.93

2.10

1.92

2.19

Av.=38.2

Ethane

T=23.0°C

y

I d/do

o

XIO

X 10

cc

3.68

2.52

50.7

4.70 3.20 50.5

5.14 3.44 50.2

5.61 3.82 50.5

Av.=50.5

Propane

T =23.0°C

Y

I d /d .

'

IO

XIO

cc

4.88 2.52 66.8

5.30

2.64 66.8

5.63 2.93 67.0

6.31 3.13

65.9

Av.=66.6

a Value omitted in obt in ing average

T =29.1 °C

y I dido

XIO XIO

1.63 2.23

1.75 2.44

1.83 2.48

Av.=38.0

cc

37.9

37.6

38.7

35.9"

38.3

y

XIO

3.35

4.59

T =29.1 °C

I dido

X 10

2.49

3.34

o

cc

38.0

38.4

37.8

o

cc

52.3

51.9

Av.=52.1

T =29.I ·C

y

I d /d .

o

X 10 X 10

cc

3.91 2.10 67.8

4.45

2.34 67.3

4.66 2.45

67.3

Av.=67.S

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PAR T I A L MOL A L VOL U M E S 0 F H Y D ROC

ARB

0 N S N W A T E R

1833

freed of traces of carbon dioxide by passing over

ascarite. The purified gases were brought into contact

with samples of air-free water stirred by means of a

magnetic stirrer in an apparatus similar to that used

for benzene.

Experiments were run to determine the time neces

sary for saturation.

It

was found

that

four hours were

sufficient to achieve saturation with the technique used.

Samples saturated for periods up to twelve hours gave

partial molal volumes identical with those obtained

after four hours contact.

Before admitting the hydrocarbon gas to the satura

tion apparatus all the air was removed from the system.

The initial pressure read on the manometer was then

the vapor pressure of water at the temperature of the

solution. Gas was admitted to the solution flask until

the desired pressure, as read on the manometer, was

reached. The final pressure of the gas after saturation

was reached was recorded.

The difference between final

and

initial pressures gave the partial pressure

of

the

hydrocarbon gas. From this pressure and the tempera

ture of the solution, it was possible to calculate the

concentration of the solution. Henry S law was used to

calculate the effect of pressure on the solubility;

data

in the literature indicates that it holds within one-half

of one percent for such extremely dilute solutions.

The

data of Claussen and Polglase

 

was used to calculate

the solubilities of the gases

at

one atmosphere pressure

at the temperature

of

the solution.

The specific gravities of the solutions were measured

in the same manner as those

of

the benzene solutions.

Once again it was found that the apparent molal

volumes were independent of concentration.

The data on solutions of methane, ethane, and pro

pane is given in Table

II It

will be noted

that

the

precision is considerably less than for the benzene

solutions, probably because the concentration data was

less accurate.

DISCUSSION OF RESULTS

It

is instructive to compare the partial molal volumes

of the hydrocarbons in water solution to their volumes

in nonaqueous solvents. The molal volume of pure

benzene at 25°C is 89.5 cc; the partial molal volume in

water is 83.1

cc.

This is a decrease in water solution

of

6.4

cc.

The simplest explanation of this decrease in volume

involves the large internal pressure of water as com

pared to that of benzene itself. Gjaldbaek and Hilde

brand

lO

found that the part ial molal volume of methane,

ethane, and nitrogen decreased sharply as the internal

pressure of the solvent increased. The fact that the

decrease in volume for benzene is relatively small is

10

J.

C. Gjaldbaek

and J. H

Hildebrand,

J.

Am. Chern.

Soc.

72,

1077 (1950).

TABLE

III

Partial molal volumes of methane and ethane at 25°C.

Solvent (int.)

Methane Ethane

Per-flu oro n-heptane 1430 atmos

68.4 cc 82.9 cc

n-hexane 2190

60.0

69.3

Carbon tetrachloride

3050

51.7 66.0

Water 12000

37.3

51.2

probably due to the rather small compressibility of

benzene at high pressure.

l

The coefficient of expansion

a

of benzene in water solution is independent of tem

perature and slightly smaller than

that of pure benzene,

as would be expected in a solvent of high internal

pressure.

The partial molal volumes of the aliphatic hydro

carbons in water solution are considerably less than the

corresponding values

in

nonaqueous solvents. Table III

gives the partial molal volumes of methane and ethane

at

25°C in various solvents. The values for carbon

tetrachloride are taken from Horiuti

;12

those for the

other organic liquids are from Gjaldbaek and Hilde

brand.

10

Values of the internal pre?sures are taken from

Hildebrand and ScottY

It

will be noted from the curves

that

the change of

partial molal volume with temperature for the aliphatic

hydrocarbons is of a quite different nature than

that

of benzene. The linear increase observed with benzene

does not occur with the aliphatics; instead the rate of

increase

of

the partial molal volume with temperature

(the coefficient of expansion a decreases with increasing

temperature. This leads one to believe that there are

two competing processes going on in the case of the

aliphatic hydrocarbons. The normal thermal expansion,

which increases iT would be expected to give a nearly

linear slope as it does with benzene. The other process

is apparently a breaking down

of

the cage-like structure

of water molecules around the aliphatic hydrocarbon

molecules. This produces a decrease in the part ial molal

volume analogous to that observed when ice melts. The

above curves thus represent the net result of these two

processes.

ACKNOWLEDGMENT

The author is greatly indebted to

W.

H. Rodebush,

who suggested this problem and under whose advice

and guidance the work was performed.

W.

F. Claussen

designed the apparatus and supervised its construction,

installation and testing.

The research was aided by funds supplied by the

Office

of

Naval Research and

by

a predoctoral fellow

ship provided by the U.

S.

Atomic Energy Commission.

P W. Bridgman, J. Chern. Phys. 9 794 (1941).

12

J Horiuti, Sci. Papers Inst. Phys. Chern. Research (Tokyo)

17, 125 (1931).

13 J. H Hildebrand and R. L Scott,

The Solubility oj Non-

  lectrolytes

(Reinhold Publishing Corporation, New York, 1950).