Table Of ContentThe Pennsylvania State College
The Graduate School
Department of Chemistry
The Departure of n-Butforane and n-Butane Solutions
from Ideality
A thesis
John Wilson Kausteller
Submitted in partial fulfillment
of the requirements
for the degree of
Doctor of Philosophy
January 1951
Approved:
ead, Department or Chemistry
Acknowledgement
I am indebted to Dr. J.H. Simone for his
suggestion of the problem and his continued interest
in it. To Dr. T.J. Brice go my thanks for his aid
and helpful advice.
I wish to thank the Minnesota Mining and
Manufacturing Company, sponsors of the project of
which this study was a part, for the opportunity
to do the work.
353399
TABLE OF CONTENTS
Introduction
Theory of Solubility of Non-Polar Substances
Interpenetration Postulates
Results and Conclusions
Liquid-Vapor Equilibrium
Mutual Solubilities
Heats and Free Energies of Solution
Solubility Parameters
Entropy of Mixing
Calculation of the Interpenetration Factor
Some Physical Properties of n-Butane and
n-Butforane
Experimental
Source and Purification of Materials
Vapor Pressures of n-Butforane
Liquid-Vapor Equilibrium Apparatus
Mutual Solubility Apparatus
Details of Operation of Equipment
Analysis of Mixtures
Densities of Mixtures
Volume Changes on Mixing
Summary
Bibliography 49
Appendix: Experimental Data
I Freezing Point of n-C^F^Q 50
II Vapor Pressure of n-C^F^Q 51
III Liquid-Vapor Equilibrium 52
IV Mutual Solubility 54
V Densities of Mixtures 55
1
INTRODUCTION
Investigations of the properties of solutions are aimed
at identifying their properties with a particular type of
force or forces "between the molecules. One approach to the
problem is the study of systems composed of non-polar mole
cules. The ultimate in this respect would be the rare gases.
They are spherically symmetrical, show no apparent associ
ation or chemical combination and are non-polar. Unfortu
nately their low boiling points and high price make them
undesirable tools for research. Fortunately, however, the
fluorocarbons offer a "high boiling rare gas" substitute in
that they have the attributes of the rare gases except for
the spherical symmetry. Vhile the latter property is lack
ing, they do have smoothed-out force fields. Lack of spher
ical symmetry may in reality be an advantage as moet real
molecules are not spherically symmetrical. Because of their
unique properties they have been the subject of interest in
some instances.
j
Hildebrand and coworkere ^*2,3 have shown that the
fluorocarbons they have investigated fit the Begular
Solution Theory even though the solubilities of solids and
liquids are exceedingly low compared to the analogous hydro
carbons. They have also predicted with a fair degree of
accuracy the critical temperatures of "binary liquid mix
tures having a flucrocarbon as one of the components.
In the study of the system n-pentforane - n-pentane
Simons and Dunlap ^ found large deviations from Raoult*s
law. The components of the system were nearly identical
with respect to "boiling points, melting points, molecular
dimensions, energies of vaporizations, and electron polar-
izabilities. Since the materials also show no association
the deviations were attributed to pentane having a degree
of liquid structure dependent on the interpenetration of
pentane molecules with each other in a gear-like manner.
The fluoroc^ rbon molecules were assumed not to interpene
trate appreciably with each other or with hydrocarbon
molecules.
Since the study indicated the possibility of the
adoption of fluorocarbons as a basis for solubility theory
investigations it would be highly desirable to pursue the
matter further. The system n-butforane - n-butane is at
tractive for several reasons. It would serve as a check
on the five-carbon-system, being next in the homologous
series. The physical properties of the components are
even closer than those of the other system, the properties
of hydrocarbons and fluorocarbons vs the number of carbon
atoms being closest at about four carbon atoms. As with
the previous study the materials are non-polar, show no
apparent chemical combinations, are of approximately the
3
same molecular size* and have a sufficiently large differ
ence of molecular weights to make analysis possible by gas
density measurements.
THEORY
To treat a system of non-polar molecules Hildebrand* 8
theory of Regular Solutions 5 has proven to be of general
application. In the development of the theory the liquid is
built up of molecules brought from an infinite distance to
the equilibrium distance r. In this fashion the potential
energy of a mole of a pure liquid may be expressed as
CD
where B° is the energy of vaporization at some temperature
T, N is Avogadro's number, V is the molal volume* r the
distance of closest approach of the centers of the mole
cules and k is the attractive force constant between two
molecules.
In adopting k to represent the force constant an ex
pression of the type postulated by Lennarlfi*Jones ® is used.
Here € is the total force constant between two molecules*
with j and k respectively the repulsive and attractive
constants. The distance between molecular centers is r
and n is a number, usually 12. Hildebrand neglects the
repulsive constant j and retains only the attractive term,
£
k/r. He further assumes a geometric mean between the
attractive constant k12 for two unlike molecules and k ^
and k22 for like molecules. Thus in a binary mixture the
basic equation for E° is
r
Where € is the force constant, W a probability function
expressing the arrangement of molecules around a central
molecule and the rest of the quantities are as described
previously. Taking W as nearly equal to one, and sub*
stituting for € we have equation (1).
For a solution of two components the total E for the
solution would be the sum of the individual E*s.
(4)
Where n is the number of moles of each component 1 or 2,
and the subscripts 11, 12, 22 refer to molecular combin
ations. This may now be differentiated with respect to
&X* giving the partial molal potential energy of species
1 in solution. Remembering that VsV^n^-f-Vfor no volume
change on mixing,, and subtracting E° for the pure com-
ponent we have the potential energy change for component 1
in placing a mole of pure component into an infinite
quantity of solution.
E - E ; = ZvN’f-.lrt-fv, fe f - f o d r
‘ ' L wiv< “*■ nzviJ L ' 2 J
(5) -
Here no cognizance has been taken of the volume changes
occuring on solution. If this is recognized the equation
becomes _ p r®9
‘ V' *1*
.09 pCO ~l
(6) _L f _ J£u-dr - -L I - J&dr I
H *•; w r * J
rru.i rn
Hildebrand uses equation (5) to predict the properties of
solutions from those of the pure components, in as much as
partial molal volumes are only obtained from measurements
on solutions, and the aim of the theory is to predict the
properties of solutions from the properties of the pure
components.
The energy of vaporization has been taken as indicative
of the forces acting in a pure liquid, and is set equal to
the potential energy change observed in condensing a mole of
infinitely separated molecules. For each of the terms in
the brackets in equation (5) we can write its equivalent
in terms of the energy wf vaporization and molal volume.
