THE ENERGY OF VAPORIZATION OF NON-IONIC NON-ASSOCIATED SUBSTANCES

54 Pages·01.792 MB·English

by  HICKMAN, JAMES B

The Pennsylvania State College
The Graduate School
Department of Chemistry
The Energy of Vaporization of Won-Ionic
Won-As so dated Substances
A thesis
t>y
James Blake Hickman
Submitted In partial fulfillment
of the requirements
for the degree of
Doctor of Philosophy
September 1950
Approved:
Acknowledgment
The author Is greatly indebted to
Professor J. H. Simons, who directed this
research, for unfailing guidance, encour­
agement and inspiration at every stage
of the work.
347004
Contents
Introduction
Energy of Vaporization of Substances Not Exhibiting
Significant Interpenetration
Energy of Vaporization of Materials Exhibiting
Significant Interpenetration
Alkane s
Cyclic compounds
Tempe rature Dependence of the Energy of Vaporization-
Polarizability Function
Energy of Vaporization of Materials Containing a
Dipole
Conclusions
Bibliography
1
Introduction
The Clapeyron equation, Trouton’s rule and Hildebrand’s
modification thereof are available for estimating energies
of vaporization of pure substances. Haoult’s law and
Hildebrand’s solubility equation can be employed simillarly
to calculate approximate energies of vaporization of compon­
ents of a binary mixture. None of these relationships, how­
ever, can give Information as to why a particular substance
has a given energy of vaporization, since the data upon
which they operate are themselves derived from measurements
involving vaporization.
The problem of this thesis will be to relate energies
of vaporization of pure substances to measurable physical
properties other than boiling points, vapor pressures or
simlliar quantities derived from experiments concerned with
the vaporization process.
Two recent important advances have Indicated that an
examination of energy of vaporization data may be fruitful,
and have been Invaluable In suggesting the method of ap­
proach to the study and the factors involved. The advances
22
are theses formulation by Simons and Dunlap of the con­
cept of Interpenetration, and the availability of physical
constants of a large number of fluorocarbons.
22
Simons and Dunlap found that pentane and pentforane,
although simlliar In those physical properties (such as en­
ergy of vaporization, polarlzabllity and molar volume) con-
-2-
sldered to be critical in determining solubility behavior,
formed mixtures deviating widely from Baoult*s law. The de­
viations from Kaoult*s law were explained by assuming that
pairs of hydrocarbon molecules intermesh or Interpenetrate,
while fluorocarbon molecules interpenetrate in a relatively
negligible amount either with one another or with hydro­
carbon molecules. A quantitative evaluation of the distance
of interpenetration, entirely consistent with the dimensions
of the molecules, was shown to account for the observed de­
viations from Eaoult's law.
as applied to the vaporization of pure substances, the
concept of interpenetration indicates that the total energy
of vaporization of an interpenetrated material such as a
hydrocarbon must involve both the energy required to trans­
port the molecule permanently into the vapor, and an initial
expenditure of energy to extract the molecule from its
interpenetrated condition. Since only the former quantity
is involved in the vaporization of non-interpenetrated
materials such as rare gases, fluorocarbons, and symmetrical
halides, they should present the simplest cases for applica­
tion of a theory of energies of vaporization.
The preparation and study of a large number of fluoro­
carbons has resulted in the availability of physical con­
stants of these substances, which duplicate most of the
structural variations of hydrocarbons in molecules of dif­
ferent weight and compactness. These new data are both a
challenge and a proving ground for a theory of energy of
vaporization. Such a theory must explain why the fluoro-
carhona have extremely low energies of vaporization relative
to their molecular weights, and why, in contrast to the
hydrocarbons, isomeric fluorocarbons have almost identical
energies of vaporization.
The approach to the problem has been entirely empirical
no attempt being made to derive an equation from a funda­
mental law of forces between molecules. The concept of
interpenetration guided the order in which materials were
considered, the first being those not expected to interpene­
trate or to have relatively low interpenetrations. Since
the literature contains many data concerned with energies of
vaporization at 298.2°K, it was possible to confine the
Initial work to this temperature. After an equation had
been developed representing energy of vaporization for both
non-interpenetrating and interpenetrating materials at this
one temperature, it was modified for use at temperatures
other than 298.2°K.
The equations developed do not contain mass as a term.
Theoretically, it seemed that by analogy to the behavior of
bodies in a gravitational field, mass must be involved. A
projectile must exceed a minimum velocity of escape in order
to leave the gravitational field of a planet. If a force
law simillar to gravity governed escape from liquid surfaces
a massive molecule would require more energy to bring It up
-4-
to the escape velocity, or, regarded from a different point
of view, the more massive of two molecules to which an equal
amount of energy had heen imparted would have lower velocity,
he longer within the field of force, and he more likely to
return to the surface.
Intuitively, high molecular weight, high hoiling point,
and consequent large energy of vaporization are associated.
This feeling probably arises from consideration of organic
homologous series; no equation involving mass could he found
to apply to the energies of vaporization of molecules made
up of atoms of different sorts, hence held together by
forces of different magnitude. For example, sulfur hexa-
fluoride2®, molecular weight 146, has an energy of vaporiza-
1 Q
tion considerably lower than that of butane-^, molecular
weight 58,
She equations developed allow some inferences as to the
structure of the molecules being vaporized, and their ar­
rangement in the liquid state, Such considerations cannot
be made on the basis of the type of relationships mentioned
In the first paragraph of this Introduction.
-5-
Energy of Vaporization of substances Not Exhibiting
Significant Interpenetration
Empirical examination of the literature in reference to
energy of vaporization indicates that substances whose
molecules do not Interpenetrate significantly exhibit a de­
pendence of energy of vaporization at 298. 2°K on polariz-
ability approximately represented by the linear equation*
e|98-2 : A ( « total . B ). (1)
298 2
In this equation, ev * is the energy of vaporization at
o
298.2 K, In ergs per molecule; O^total is ttL0 tot;al polariz-
abllity In cubic centimeters per molecule, calculated from
the Mosotti-Clausius equation*
^ D - 1 M 3
t0tfil= D ♦ 3 d 4TT N <2)
In which X) Is the dielectric constant measured at low fre­
quency, M Is the molecular weight in the gaseous state at
the designated temperature and pressure, d the density In
* By energy of vaporization is meant energy of vaporization
In ergs per molecule. It Is related toAEv, cal./mole, by
the equation* 7
AEV (cal./mole) x 4.184 x 10
ev =
6.02 x 1025
Within the accuracy of this work,Ajsv is considered to be
equal to AHy - RT.
-6
grams/cm3 at the temperature at which the dielectric constant
was measured, and U Is Avogadro*s number. A and ts are con­
stants having values respectively of 3.98 x 10^ and 2.55 x
1CT24.
in equation (1) C^total lias 136011 written to emphasize
the fact that the total polarizability, the sum of
^electronic and ^atomic ls meant- Sometimes a literature
value of OC Includes only the electronic polarizability, cal­
culated from the equation*
-r n2 - 1 M 3
electronic - — ---- — -----
n» + 2 d 4 Tf • N
in which n^ Is the Index of refraction at Infinite wave­
length, calculated by extrapolating a number of values de­
termined in the visible region. For rare gases, and
effectively for hydrocarbons, total andOCelectronic are
equal; for fluorocarbons, other halides and many organic
compounds other than hydrocarbons, atomic niakss a signifi­
cant contribution to the total polarizability and must be in­
cluded. This can be accomplished by using the form of the
Mosotti-Clausius equation involving the dielecetrie aonstant
or by measuring refractive Indices In the infra-red for in­
clusion in the determination of n^ . Physically,
^electronic represents displacements of electrons, while
CCatomic corresponds to distortion of the relative position
of the atomic nuclei In the molecule.
7-
Figure 1 and Table I show the applicability of equation
(1). The significance of the circles numbered 14 to 19 will
be explained in the section dealing with materials exhibit­
ing significant interpenetration.
Polarizability has the dimensions of volume. Its ab­
solute magnitude is much smaller than that of physical
volumes at 25°C propane has a volume per molecule of 140 x
10"24 crn^, a polarizability per molecule of 6.31 x 10“^
Unlike molar volume, the polarizability of a non-polar sub-
O
stance is practically independent of temperature . Its size
depends upon two factors: the inherent deformability of the
molecule, and how much material there is to deform. Thus,
it will increase regularly with increasing molar volume in a
series of related compounds, but a given molar volume -
polarizability ratio will not be duplicated in molecules
held together by forces of different magnitude.
The force against which a molecule leaving the surface
of a liquid acts is certainly not gravity, otherwise mass
would enter the equation for energy of vaporization. Once a
force whose effect depends upon the area over which it acts
is allowed, a physical picture of a possible relationship
between ev and polarizability can be imagined. The larger a
molecule is, and the more readily it is deformed in the
presence of a force field, the greater its effective area
will be, and the larger the amount of energy required to re­
move it some critical distance above the surface of the li­
quid, beyond which it will continue into the vapor rather