Table Of ContentThe Pennsylvania State College
The Graduate School
Department of Chemistry
Zero-Point Entropy of Methylammonium Chloride
A Dissertation
fey
Kuo Hao Hu
Submitted in partial fulfillment
of the requirements for the degree of
Doctor of Hiilosophy
August 19£2
Approved:
July 21, 19$2
ofessor of Chemis
JUL 22 1952
Head of^tne Department
Acknowledgement
The author wishes to express her sincere appreciation to professor
J. G. Aston for his suggestion and direction for the investigation and
for the use of the facilities of the Cryogenic Laboratory.
The author is indebted to a group of facility and staff for their
helpful suggestions and assistance. The following are the members to
whom, acknowledgement is due:
Ur. C. W. Brouse and the staff of the shop for assistance in the
construction of the apparatus.
Dr. G. H. Fleming for his suggestion for the analysis of amine.
Dr. J. J. Fritz for his helpful discussions and suggestionsf or
the evaluation of E° and the Yfritting of this thesis.
O
Dr. A. W. Hutchison for his discusions.
Mr. F. J. riolloy for his assistance in the glassblowing.
Mr. L. F. Shultz and the members of the Cryogenic Laboratory for
various assistance.
Dr. T. Wartik for his suggestions concerning ivith the experimental
technique.
Contents
I. Introduction 1
II. The Determination of the Free Energy and Entropy
from Cell and Vapor Pressure Measurements S>
III. Experimental 7
A. Preliminary Survey of Experimental Conditions 7
B. Preparation of Materials 9
1* Preparation and Purification of Methylamine
and Methylammonium Chloride • 9
2. Purification of Ethyl Alcohol 9
3. Preparation of Standard Solutions 10
C. Electromotive Force Measurements 11
1. Apparatus 11
a. The Cell 11
b. hydrogen Electrodes 13
c. Silver-Silver Chloride Electrodes 13
d. Thermostat lU
a. Electrical Instruments-. lU
2. Operation l£
a. Testing of Electrodes l£
b. Electromotive Force Measurements 1$
D. Vapor Pressure Measurements 16
1. Apparatus 16
2. Analysis for Methylamine and Ethyl Alcohol 19
IV. Method of Calculation 21
1. Calculation of E° 21
Contents (cont1d)
2. Calculation of Partial Vapor Pressures 26
3. Calculation of Free Energy and Entropy 26
U. Calculation of Zero-Point Entropy 26
An Actual Example of Calculation 27
V. Results 30
VI. Discussion of Results 3U
VII. Summary 37
Bibliography 39
Appendix 1*2
Table V 1*2
Table VI 1*3
Table VII 1*1*
Table VIII 1*5
Table IX 1*6
Table X 1*7
ZERO-POINT ENTROPY OF METHYLAMMONIUM CHLORIDE
Introduction
The third law of thermodynamics states that the entropy of any
perfect crystalline substance be comes zero at the absolute zero tem
perature. If the entropy of a perfect crystalline substance at absolute
zero temperature is zero, then the entropy calculated from spectro
scopic data should agree within the limit of experimental error with
that determined calorimetrically. Otherwise,, the spectroscopic entropy
is larger than the calorimetric entropy, there is a positive entropy
at absolute zero, which is called zero-point entropy or residual en
tropy. There are a number of substances which show such residual en
tropy. Some examples are given in the table below.
Table I
Molar Entropy of Gases at 289.16°K and one atm.
Substance Calorimetric Spectroscopic Difference References
entropy entropy
cal./mole,deg. cal./mole,deg.
h2 29.7 31.23 1.52 (1, 2)
d2 33.9 3U.62 0.72 (3, U, $)
CO 14-6.2 U7.32 1.1 (6, 7)
NO* 143.0 143.7S 0.7S (8)
n2o Sl.Uli 52.S8 l.lU (9)
Hr>0 I4I4.23 U5.1 0.87 (10, 11)
d20 US.89 I4.6.66 0.77 (10, 12)
■*In the case of NO the data refer to 121,36°K.
Ia view of the previous work, it has been recognized that zero-
point entropy may result from one of several possibilities. They are:
1. Existence of nuclear spin, as in hydrogen and deuterium.
2. Existence of isotopes, ■which does not usually show in the change
of entropy of any process, but contributes to the absolute entropy
of an individual substance.
3. Existence of solid solution or mixture.
U. Existence of glasses (or super-cooled liquids).
5>. Existence of random orientation in the structure of the crystal.
Examples of orientation of ions or hydrogen nuclei are hydrogen and
deuterium oxide. Examples of orientation of molecules •will be dis
cussed in the following paragraph.
Carbon monoxide, CO, nitric oxide, NO, and nitrous oxide, MO, are
good examples of the random arrangements of molecules in the crystal.
Each of these molecules is linear and has unlike atoms at two ends5 but
the unlike atoms in each of these molecules are similar in size and
electronic configuration. Because the two ends of the molecule are so
similar, random arrangements of the molecules do not affect the crystal
lattice. Giauque and his collabarators (6, 7, 8, 9) have found the
zero-point entropy of each of the above compounds to be significantly
greater than zero. In these cases, each molecule has two positions,
so that for completely random arrangemnet, the entropy arising from
such randomness is equal to lc In 2 for one molecule; for one mole of
molecules is N k In 2 or R In 2 (1.38 e.u.). Giauque found the residual
entropies of NO, GO, and NNO are 0.75> 1.10, and l.ll; e.u./mole, deg.
respectively. These data show that there is a different degree of
randomness, -which is approaching the maximum value of I.38 e.u./mole,
deg., in these crystals.
Since different crystalline forms of methyl ammonium chloride (lU)
and amylammonium chloride (52) have equal corresponding entropies at
absolute zero and they are ionic crystals, if any randomness viould ap
pear, it must be due to the orientation of ions in the crystal. In the
amine halide molecule, the halide ion is spherical, so it is impossible
for the halide ion to have randomness. Thus, any randomness in the crys
tal is a question of the orientation of the RNH3 group.
The previous -work has verified that the similarity in size and elec
tronic configuration of nitrogen and oxygen leads to residual entropy
in nitric oxide. In the methylammonium ion, H^CNH^,. the relative size
and electronic configuration between the carbon and the nitrogen atom
is similar to that of between the nitrogen and the oxygen atom in nitric
oxide; in addition each of them has the same number of hydrogen atoms,
which must be arranged in the same vray in space. Therefore the two ends
of the ion will be distinguished only by the positive charge, if this
is localized. Since the nitrogen atom is slightly more negative than
the carbon atom, polarization is expected. Because the differences in
size and electronic configuration between the two ends of the ion are
so small, a small polarization could make the two ends of the ion so
similar that both the carbon atom and the nitrogen atom have the same
affinity for the positive charge; thus the positive charge will be sit
uated between the carbon and nitrogen atom. Since the methylammonium
ion is linear, an ellipsoidal charge distribution would result. (For
an ethylammonium ion, CII3CH2NH3, the angular C-C bonding would exert
h
a different effect on the pattern of the distribution of the charge,)
As a result of the even distribution of charge in the ion, the carbon
and nitrogen ends are not distinguishable, so that a random orientation
of the ion is possible. For completely random arrangement, each ion
has two positions available, thus the entropy associated with the ran
domness is R In 2 (1.38) e.u. per mole. This should be the difference
between the actual entropy at 23>°C and that determined calorimetrically
based on the third law of thermodynamics.
The calorimetric entropy of methylammonium chloride had been deter
mined by Aston and Ziemer(llp). They found that it exists in three crys
talline forms, two of which can be cooled to below 20° K. From the same
entropy value for the stable form at room temperature calculated by two
paths, they concluded that "there is no randomness in either crystalline
form or that both forms have the same degree of randomness". Since me
thylammonium chloride is a solid, and cannot be examined in the gas state,
its entropy cannot be calculated from spectroscopic data. However, the
entropy can be obtained by evaluation of AS0 for a reaction where the
absolute entropies of the other substances concerned are known.
In the present investigation the zero-point entropy of methylammon-
ium chloride was determined by comparison of the calorimetric value for
the entropy at 2£°C with the entropy evaluated from a study of the eq
uilibrium in the reaction: CHjNHg^g) + HCl^ = CH^NH^Cl^. Since
the equilibrium constant of the reaction at 2£°C is of the order of
1017, neither the vapor pressure of hydrogen chloride nor the vapor pres
sure of methylamine is high enough to give accurate direct measurement;
however, it is convenient to study this equilibrium by means of cell
measurements as described below.
5
The Determination of the Free Energy and Entropy
From Cell and Vapor Pressure Measurements
The standard free energy of the reaction, CHjNH2 (ideal gas at 1 atm.)
+ HC1 (ideal gas at 1 atm.) = CH^NH-jClt solid), can be expressed as:
*F° = -RT In K; and
K “ V (fHd x fCH3NH2 ^
where /IF° is the standard free energy of the above reaction ivhen each of
the substances is in its standard state; K is the equilibrium constant
of the reaction; fHG1 is the fugacity of HC1, and fcH^NH^ 'fche fugacrfcy
of CH^NH2* If fjjQi and are known, can be determined.
If a cell is made up of methylamine solution saturated with methyl-
ammoniuni chloride and equipped with hydrogen and silver-silver chloride
electrodes, the net cell reaction is
i«2(g) + ^ ( s ) ‘ H01(g) * ^ ( b)
and the potential of the cell is
E = E° - (RT/nF) In fHC1
where f^Q-j. is the fugacity of hydrogen chloride (when P^ = 1 atm., which
«
is taken as standard state of an ideal gas). Hence the fugacity of HC1
in the soliition can be calculated from the observed e.m.f.
At ordinary pressures the fugacity of any gas can be calculated ap-
£
proximately from the equation, p = 1 (Lewis and Randall, Thermody-
£
namics, p 1?8). For constant temperature it may be written as - = 1 - JBV*
The constant, p, can be evaluated from the Berthelot equation. The par
tial vapor pressure of methylamine in the solution can be determined by a
dynamic method; then the fugacity of methylamine can be calculated from
the above equation.
The 6S° of the formation of methylammonium chloride can be determined
by either one of the follovring methods.
1. From the free energy equation: /H?° = AH0 - TAS°.
Since the standard heat of formation, /ill0, at 2f?°C has been
determined by Aston and Ziemer (111), this value may be used in con
junction -with £1° (determined as described above) at 2%°C for the
calculation of AS° from the above equation.
2. From the Gibbs-Helmholtz equation: (^(4F°)/^T) = -AS°.
k*
In order to apply the Gibbs-Helmholtz equation it is necessary
to obtain values of ^F° at several temperatures by determinations
of fugacities of hydrogen chloride and methylamine. This alterna
tive method provides a check on the calorimetric value of ^H°*
When AS? is determined, the zero-point entropy of methylammonium
chloride can be calculated from the value of AS° together v/ith the ab
solute entropies of the other substances concerned .by the equation below
SCH3NH3C1 = AS° + Shci + sch3nh2*
