The vapor phase dissociation of ammonium salts: ammonium halides, ammonium rhodanide, ammonium nitrate, and ammonium bicarbonate


Kruif, C.G. de

Journal of Chemical Physics 77(12): 6247-6250

1982


Vapor pressures as a function of temperature of the ammonium salts are measured by means of a simultaneous torsion effusion and mass-loss effusion technique. From a theoretical analysis, which is given first, it is shown that the enthalpies of sublimation and the degree of dissociation b in the vapor phase are related to the measured quantities. The degree of dissociation appears to be a weak function of temperature and is evaluated by b(NH4F, 288.91 K) = 0.97; b(NH4Cl, 352.02 K) = 0.85; b(NH4Br, 380.06 K) = 0.51; b(NH4I, 385.03 K) = 0.39; b(NH4CNS, 313.78 K) = 0.61; b(NH4NO3, 351.89 K) = 0.66; b(NH4HCO3, 270.56) = 0.85. It is assumed that NH4HCO3 dissociates into NH3, H2O, and CO2. At the given temperatures, total vapor pressure is 0.40 Pa.[TVA].

NH
4
X(g)
Hsub
(
N
11
4X)
NH
3
1())+HX(g)
/Nub
2
NH
4
X
(solid
state)
FIG.
1.
Phase
reactions
of
ammonium
halides.
The
vapor
phase
dissociation
of
ammonium
salts:
Ammonium
halides,
ammonium
rhodanide,
ammonium
nitrate,
and
ammonium
bicarbonate
C.
G.
de
Kruif
Chemical
Thermodynamics
Group,
State
University
of
Utrecht,
Padualaan
8,
Transitorium
III,
Utrecht,
The
Netherlands
(Received
6
May
1982;
accepted
18
August
1982)
Vapor
pressures
as
a
function
of
temperature
of
the
ammonium
salts
are
measured
by
means
of
a
simultaneous
torsion
effusion
and
mass-loss
effusion
technique.
From
a
theoretical
analysis,
which
is
given
first,
it
is
shown
that
the
enthalpies
of
sublimation
and
the
degree
of
dissociation
b
in
the
vapor
phase
are
related
to
the
measured
quantities.
The
degree
of
dissociation
appears
to
be
a
weak
function
of
temperature
and
is
evaluated
by
b
(NH„F,
288.91
K)
=
0.97;
b
(NH,CI,
352.02
K)
=
0.85;
b
(NH,Br,
380.06
K)
=
0.51;
b
(NH
4
I,
385.03
K)
=
0.39;
b(NH
4
CNS,
313.78
K)
=
0.61;
b(NH
4
NO
3
,
351.89
K)
=
0.66;
b
(NHJIC0
3
,
270.56)
=
0.85.
It
is
assumed
that
NH
4
HCO
3
dissociates
into
NH
3
,
H2O,
and
CO,.
At
the
given
temperatures,
total
vapor
pressure
is
0.40
Pa.
I.
INTRODUCTION
Of
the
ammonium
halides,
ammonium
chloride
(salamoniac)
is
the
one
which
has
been
most
often
and
thoroughly
investigated.
It
is
particularly
the
solid
state
properties
which
have
been
studied.
Callanan
et
al.
have
measured
vapor
pressures
of
NH
4
C1
and
of
NH
4
Br.
They
made
assumptions
and
speculations
about
the
degree
of
dissociation
of
the
salts
in
the
vapor
phase
on
the
basis
of
vapor
density
measurements,
2,3
ab
initio
calculations
by
Clementi,
4
and
Knudsen
effusion
mass
spectrometry
by
Gold-
finger,
5
again
for
NH
4
C1
only.
As
Callanan
et
al.
pointed
out
very
precisely,
a
correct
interpretation
of
the
excess
enthalpies
of
mixing
of
the
solid
state
based
on
the
basis
of
their
total
vapor
pressure
measurements
of
mixtures
requires
a
knowledge
of
the
degree
of
dis-
sociation
of
the
vapor
phase
molecules.
For
NH
4
C1,
this
value
was
expected
to
be
near
unity.
2,3,5
Regarding
the
other
ammonium
salts
there
is
no
information
in
the
literature.
Since
we
have
at
our
disposal
combined
torsion
effusion
and
mass-loss
effusion
apparatus
we
are
in
a
position
to
solve
the
problem,
at
least
in
princi-
ple.
We
show
that
the
"apparent
enthalpy
of
sublimita-
tion"
as
derived
from
the
temperature
dependence
of
measured
vapor
pressure
is
not
unambiguously defined
but
is
a
function
of
the
degree
of
dissociation
and
the
method
used.
In
the
following
section,
we
shall
there-
fore,
give
a
derivation
of
the
equations
that
are
ap-
plicable
to
the
experimental
methods
used
and
explain
how
the
relevant
thermodynamic
properties
are
evaluated
from
the
experimental
results.
In
Sec.
III,
the
experi-
mental
setup
will
be
described
and
in
Sec.
IV
the
re-
sults
obtained
will
be
given.
p
i
=
C
/
,
(1)
where
I
is
the
electric
current
required
for
compensa-
tion
and
C
is
a
constant
depending
on
the
geometry
of
the
set-up
only.
The
mass
loss
effusion
experiment
is
based
on
the
Hertz—Knudsen
equation:
dm/dt
=
A
p(27TRT)-1/2
m
1/2
(2)
in
which
dm/dt
is
the
mass
loss
per
unit
time,
A
the
orifice
area,
p
is
vapor
pressure,
and
M
the
molecular
mass
of
the
effusing
species.
If
the
vapor
consists
of
i
different
species
with
molecular
mass
M
t
and
partial
pressure
p
i
,
Eq.
(2)
is
written
as
E
dm,/dt=A(27TRT)-1/2
E
p
i
Mi
l/2
(3)
under
the
condition
that
E
Pi
=
Pool
=
Ptorsion
Pt
(4)
In
general,
additional
conditions
are
set
by
the
stoichiometry
of
the
vaporization
process.
For
instance,
in
our
case
it
is
assumed
that
the
ammonium
salts
dis-
sociate
in
the
vapor
phase
into
ammonia
and
acid.
The
equilibria
involved
are
shown
schematically
in
Fig.
1.
The
gas-phase
reaction
b
NH
4
X
=NH
3
+
FIX
+
Ofl
ats
(5)
is
assumed
to
be
fast
and
to
represent
the
predominant
aHdiss
II.
THEORETICAL
In
the
torsion
effusion
experiment
the
recoil
force
exerted
on
the
cell
by
the
effusing
molecules
is
pro-
portional
to
their
momentum.
The
recoil
force
is
com-
pensated
electromagnetically
6
and
therefore
the
quantity
measured
corresponds
to
a
true
pressure.
Hence
p
ore
.
o
is
found
from
J.
Chem.
Phys.
77(12),
15
Dec.
1982
021-9606/82/246247-04$02.10
©
1982
American
Institute
of
Physics
6247
6248
C.
G.
de
Kruif:
Dissociation
of
ammonium
salts
species
involved.
Associated
with
Eq.
(5)
we
have
a
gas-phase
dissociation
constant
b(T)
and
an
equilibrium
constant
K
s
,:
'f
p
=
p(NH
3
)
p(HX)
p
-1
(NH
4
x)
=
1)
2
(1
b)
-1
(1
+
b)
-l
p
Furthermore,
we
have
AG°
14
,(T)=
—R
T
ln(I
C
o
)
,
midis
=
—Rdln(K
i
)/d1/T
,
and
from
Fig.
1
1
-
A
-
follows
that
Ali
i
,„
b
(NH
i
X)
+
4.H
dt
.
=
_
sub
(NH
__3„,
FIX)
Alisub2
The
dissociation
constant
b
is
determined
as
follows.
During
the
experiment
we
insert
into
Eq.
(2)
the
molecu-
lar
mass
M
for
.
of
NH
4
X
and
we
then
calculate
p
oi
ac-
cording
to
p„,=
rh
A
-1
(27TR
T)1/2(Mit„)-
1
/
2
(10)
in
which
p
m
is
the
"apparent"
vapor
pressure
and
the
time
derivative
of
the
total
mass
loss.
Taking
one
mole
NH
4
X
we
have
from
Eq.
(4)
p(NH
4
X)
=
(1
b)(1
+
b)"lp
t
;
p(NH
3
)
=
p(HX)
=
b(1
+
b)
-1
P
t
(11)
Substituting
in
Eq.
(3)
the
pressures
of
Eq.
(11)
and
equating
dm
i
/dt
tom
of
Eq.
(10)
leads
to
P.A
1
1,r
2
.=
P
t
(1
+
b)
-1
{(1
b)m1,41
2
4
x+
bmilH
2
3
+
(12)
Rearranging
and
dividing
by
ML
1
r
2
m
=
M
i
N
i
a
2
4
x
gives
b=
(1
9
.1
0
t
i
1)
{(m=
3
/
M
=4x
)
112
+
(Aix/m=4
x)112
P.
Pi'
—1
1
-1
(13)
If
the
ratio
p
m
/p
t
=
1,
then
b
=
0,
which
means
that
there
is
no
dissociation
in
the
vapor
phase.
For
the
sym-
metrical
case,
i.
e.
,
when
the
substance
under
investi-
gation
dissociates
into
two
fragments
of
equal
molecular
weight,
Eq.
(13)
reduces
to
b
=
(
1)(1,/
2
—p„,pi
l
1)
-1
(14)
and
for
b
=
1,
i.e.
,
complete
dissociation,
the
ratio
Pnipt=
1,12=
0.71.
The
degree
of
dissociation
can
thus
be
evaluated
from
the
ratio
p„,/p,
and
from
the
molecular
mass
of
the
va-
por
species.
If
the
composition
of
the
vapor
phase
is
unknown,
an
apparent
molecular
mass,
defined
as:
MAD
=
>
X
i
My
2
,
(15)
(where
X
i
is
the
gas-phase
mole
fraction)
can
be
cal-
culated
from
Map=
(P.Pi
l
1412
n)
2
(16)
So
far
we
have
assumed
a
constant
temperature
and
evaluated
b
from
p,,,
and
p
t
at
that
temperature.
Ad-
ditional
information
can
be
gained
from
the
temperature
dependence
of
p
n
,
and
p
t
.
The
equilibria
as
given
in
Fig.
1
obey
two
independent
relations:
R
dln[p(NH,x)]
/
1/T
=
—R
dln{(1
b)(1
+
b)
-1
p
i
l/d1/T
=
Afi
i
b
(NH
4
X)
(17)
and
—R
d
ln(K
p
)/
d
1/T
=
dis
(NH
4
X)
(18)
and
are
connected
through
Eq.
(9).
Subtracting
Eq.
(18)
from
Eq.
(17)
leads
after
some
rearranging
to:
R
d
b/d
T
=
—1(1
b)
b
I
die
_
e
o
s
(NH
X)1
(19)
This
equation
describes
the
temperature
dependence
of
the
degree
of
dissociation
in
the
saturated
vapor
phase.
From
literature
values
of
b
and
from
the
results
obtained
here
it
can
be
inferred
that
[AH511
AHsab
(NH
4
X)]>
0
.
Therefore,
with
0<
b<
1,
it
follows
that
d
b/d
1/T
is
negative.
In
other
words,
the
degree
of
dissociation
of
NH
4
X
will
increase
with
temperature.
So
although
with
increasing
temperature
the
total
pressure
rises,
which
tends
to
diminish
dissociation,
it
is
the
higher
value
of
Mi
dis
which
causes
increased
dissociation
at
higher
temperatures.
The
Clausius—Clapeyron
plots
(lnp
against
1/2)
of
both
p,,,
and
p
t
appear
to
be
straight
lines
and
thus
have
a
constant
slope
within
experimental
error.
Now
from
the
torsion
experiment
we
determined
the
slope
—Rdln(p
t
)/d1/T
EAR,
.
(20)
From
Eq.
(17)
it
follows
that
—R
d
ln(
p
i
)/d
1/T
=
Rdln{(1—b)(1+
b)
-1
1
d
1/T
+
AH.„„(NH
4
X)
,
(21)
or
with
Eq.
(19)
it
follows
that
g(b){
6
Lifcti.
AHsub(N114X)}
+
lifisub
(N1-14X)
(22)
with
g(b)
E
b(1
+
b)
-1
.
Differentiating
the
logarithm
of
Eq.
(12)
with
re-
spect
to
reciprocal
temperature
results
in:
AR„,
=
f
(s,
b)
(23)
1
,0
kHdis
AH
sub
(N11
4
X)1+
t
with
s
=im1/
NH3
'"
2
An1.
l12C
/
2
A
n/
2
714
1-1/
2
NH4X
and
f
(s,b)=
(s
-1)(1—
b)b
{2(1+b)(l+
sb)}"
1
Writing
Ali
dt
,,
and
4.11,,„
b
(NH
4
X)
in
Eqs.
(22)
and
(23)
ex-
plicitly
leads
to
midis=
aH
t
+
[1
g(b)]
f
-1
(s
,
b)
(All
t
)
,
(24)
AH„,,
b
=
Wi
t
—g(b)
f"(s,
b)
(1111„,
Ali
t
)
.
(25)
So,
in
principle,
the
values
of
AH
dis
and
Ali.„
b
can
be
cal-
culated
from
b
obtained
from
Eq.
(13)
and
414
These
values
are
obtained
as
follows.
The
experimental
"apparent"
vapor
pressures
p,
and
p„,
are
calculated
from
Eqs.
(1)
and
(10).
Then
these
values,
for
each
technique
separately,
are
fitted
to
the
following
equation:
R
ln(p/p
0
)
=
AG(9)/9
+
AH(0)(1/0
1/T)
,
(26)
where
p
o
is
a
reference
pressure
(1
Pa),
B
is
a
ref-
erence
temperature
usually
chosen
midrange
and
in
such
a
way
that
p,(e)
=
0.400
Pa.
AG(6)
and
AH(8)
are
the
coefficients
to
be
evaluated
and
if
p„,/
p
i
=
1
they
are
the
Gibbs
energy
and
enthalpy
of
sublimation,
respec-
tively.
We
always
made
several
independent
measure-
ments
of
p
m
and
p
t
as
a
function
of
temperature,
and
J.
Chem.
Phys.,
Vol.
77,
No.
12,
15
December
1982
C.
G.
de
Kruif:
Dissociation
of
ammonium
salts
6249
TABLE
I.
Experimental
results
expressed
in
terms
of
the
coefficients
of
Eq.
(26).
AG
and
All
must
be
considered
as
apparent
values,
(see
the
text).
Mt
arm
T
1
gr
mor
t
K
T
2
K
0
K
Torsion
effusion
AGt(o)
Alit(o)
J
mor
i
kJ
mor
l
P
((in
Pa
Mass-loss
effusion
AG
„,(0)
AH„,(0)
J
mor
l
kJ
mol
t
P„,(0)
Pa
Pt(0)
NH
4
F
37.04
275
298
288.91
2201
72.3
0.40
3020
71.1
0.28
0.71
NH
4
C1
53.49
337
364
352.02
2682
86.9
0.40
3645
86.3
0.27
0.72
NI1
4
Br
97.95
367
394
380.06
2895
91.9
0.40
3717
92.5
0.31
0.77
NH
4
I
144.94
373
401
385.03
2933
92.6
0.40
3649
92.8
0.32
0.80
NH
4
CNS
76.12
302
326
313.78
2391
80.2
0.40
3121
79.1
0.30
0.76
NH
4
NO
3
80.04
336
364
351.89
2681
89.9
0.40
3559
89.1
0.30
0.74
NH
4
HCO
3
79.06
262
280
270.56
2061
68.8
0.40
3263
67.4
0.23
0.59
reported
values
of
the
coefficients
of
Eq.
(26)
are
mean
values
of
these
so-called
runs.
III.
EXPERIMENTAL
The
principal
dimensions
of
the
experimental
set-up
have
been
described
previously.
6
An
extensive
de-
scription
of
the
fully
automated
measuring
procedure
is
given
in
Ref.
7.
The
effusion
cell
used
(resembling
a
garden
sprinkler)
has
two
effusion
orifices
of
1
mm
diameter
made
in
6µm
platinum
foil
and
placed
20
mm
apart.
No
Clausing
corrections
are
necessary.
The
cell
is
loaded
with
approximately
300
mg
of
sample
and
up
to
ten
runs
are
made
each
consisting
of
120
data
points
over
a
temperature
range
as
indicated
in
Table
I.
Usually
after
a
few
runs
AG
and
All
of
Eq.
(26)
(apparent
values
in
this
case)
become
constant.
Mean
values
are
reported
in
Table
I.
The
samples
were
used
as
delivered.
For
the
am-
monium
halides
we
found
an
initial
mass
loss
already
at
low
temperatures;
this
was
obviously
a
result
of
adsorbed
water.
As
measurements
were
not
constant
and
reproducible,
probably
as
a
result
of
nonvolatile
impurities
accumulating
on
the
sample
surface,
we
puri-
fied
these
samples
by
vacuum
sublimation
under
a
con-
tinuous
evacuation
(10
-2
Pa)
and
at
temperatures
as
given
in
Table
I.
The
results
obtained
with
these
sam-
ples
were
reproducible
and
are
reported.
IV.
RESULTS
AND
DISCUSSION
In
Table
I
we
give
the
experimental
results
expressed
in
terms
of
the
coefficients
(AG
and
Ali)
of
Eq.
(26).
These
coefficients
must
be
regarded
as
apparent
values
or
as
intercepts
and
slopes
of
the
so-called
Clausius-
Clapeyron
plots.
In
addition,
we
give
Mf orm
as
used
in
Eq.
(10),
and
the
experimental
temperature
range.
The
imprecision
8
in
the
pressure
measurements
does
not
exceed
5%,
and
for
All
it
is
±1
kJ
mol".
Inac-
curacy
8
is
estimated
to
be
not
more
than
twice
these
values.
When
measuring
pure
substances
in
our
set-
up
we
always
found
0.95
<p
m
/p
t
<
1.05.
From
this
we
infer
that
the
inaccuracy
in
the
degree
of
dissociation
is
±
0.1,
see
Table
II.
One
might
be
doubtful
whether
the
results
of
Table
I
represent
equilibrium
data,
as
the
methods
used
are
essentially
dynamic
in
nature.
Moreover,
Chaiken
et
al.
9
report
an
accommodation
(evaporation)
coef-
ficient
of
-
le.
If
total
vapor
pressure
data
(p
t
)
are
compared,
one
finds
that
the
results
of
Callanan
et
al.
1
at
higher
temperatures
but
obtained
with
a
static
method
combine
most
satisfactorily
both
for
NH
4
C1
and
for
NH
4
Br.
Extrapolating
their
vapor
pressure
equation
over
a
range
of
150
K
we
calculate
at
the
reference
temperature
9
of
Table
I:
p
t
(NH
4
C1,
352
K)
=
0.45
Pa
and
p
t
(NH
4
B
4
,
380
K)
=
0.35
Pa.
In
view
of
the
extrap-
olation
range
this
result
makes
us
confident
that
our
results
can
be
regarded
as
equilibrium
data
also.
An
extremely
small
evaporation
coefficient
would
have
led
to
nonreproducible
results
dependent
on
sample
size.
Preliminary
experiments
in
the
same
setup
with
a
Langmuir
effusion
cell
indicated
that
the
evaporiza-
tion
coefficient
would
probably
be
smaller
than
unity
but
not
below
0.1.
A
further
and
extensive
compari-
son
with
other
literature
data
will
not
be
made
as
this
would
require
an
elaborate
discussion
of
results
ob-
tained
at
(much)
higher
temperatures
and
the
recalcula-
tion
and
reinterpretation
of
these
results
in
view
of
the
varying
degree
of
dissociation
and
methods
used.
Al-
though
this
would
be
interesting
we
feel
that
it
is
out-
side
the
scope
of
this
investigation.
Taking
into
account
the
indicated
error
ranges
we
can
conclude
that
only
NF
4
F
is
completely
dissociated
in
the
vapor
phase
and
that
the
other
salts
are
not.
In
the
literature
2
r
3
'
9
experimental
determinations
of
b
are
found
only
for
NH
4
C1.
These
investigators,
working
at
(considerably)
higher
temperature,
report
values
for
b
which
are
practically
unity.
From
this
we
conclude
that
in
the
case
of
NH
4
C1
the
degree
of
dissociation
is
a
weak
function
of
temperature,
as
is
described
by
Eq.
TABLE
II.
Numerical
values
of
the
degree
of
dissociation
b,
of
g(b)
[see
Eq.
(22)]
of
s
and
fis
,
b)
[see
Eq.
(23)],
and
of
the
equilibrium
constant
If
t
(8).
b(0)
g(b)
s
100*
f
(s
,
b)
NH
4
F
0.97
0.49
0.41
-0.33
6.05
NH
4
C1
0.05
0.46
0.39
-1.57
1.04
NH
4
Br
0.51
0.34
0.33
-4.75
0.144
NH
4
I
0.39
0.28
0.28
-5.56
0.070
NH
4
CNS
0.61
0.38
0.35
-3.97
0.235
NH
4
NO
3
0.66
0.40
0.35
-3.57
0.309
NH
4
HCO
3
0.85
0.46
0.69
-1.45
0.093
J.
Chem.
Phys.,
Vol.
77,
No.
12,15
December
1982
6250
C.
G.
de
Kruif:
Dissociation
of
ammonium
salts
(19),
and
that
db/dT
is
positive.
It
is
also
interesting
to
note
that
dissociation
diminishes
in
the
series
from
fluoride
to
iodide.
For
the
calculations
on
ammonium
bicarbonate
we
assumed
that
it
dissociates
into
three
molecules
(NH
3
,
H
2
O,
CO
2
)
and
the
relevant
equations
were
adjusted
accordingly.
Ammonium
nitrate
shows
a
solid
phase
transition
at
357.4
K
and
connected
with
this
there
is
a
small
enthalpy
change
of
1.34
kJ
mor
1
.
This
transition
was
not
visible
in
the
vapor
pressure
measurements.
In
Table
II
we
give
the
degree
of
dissociation
b
as
calculated
with
Eq.
(13)
and
the
numerical
values
of
g(b),
s,
f
(s,
b),
and
K
i
,(8)
as
defined
in
Eqs.
(22),
(23),
and
(6),
respectively.
As
can
be
seen
from
Table
I
the
values
for
Ali
t
and
AH„,
are
equal
within
ex-
perimental
error.
The
maximum
difference,
including
errors,
is
about
13.51
kJ
mor
l
.
Unfortunately,
this
means
that
because
of
the
addition
of
errors
the
cal-
culation
of
AH
dte
and
AH
su
b
(NH
4
C1)
with
Eqs.
(24)
and
(25)
is
not
useful
in
this
case.
A
possible
alternative
might
be
to
use
a
literature
value
for
AH
dia
or
&Haub
(NH4C1).
As
indicated
above,
because
the
dis-
sociation
is
more
or
less
complete
no
experimental
values
for
Al/„„
b
(NH
4
C1)
can
be
found
in
the
literature.
For
Ali
d
i,
Clementi
and
Gayles
4
calculated,
using
ab
initio
methods,
that
Ali
dia
(NH
4
C1)
=
67
kJmor
l
,
while
Goldfinger
and
Verhaagen
5
found
from
their
Knudsen
mass-spectrometrical
experiments
that
AH
d1
,,(NH
4
C1)
=
(42
±13)
kJ
mor
l
.
Taking
an
average
value
of
(NH
4
C1,
g)
=
(55
±15)
kJ
mor
1
for
AHdi
e
leads
with
Eqs.
(24)
and
(25)
to
(DIi
n
,
—Ali
t
)
+
0.95
±
0.45)
kJ
mor
1
and
AI-1,,
ub
(NH
4
C1)
=
(114
±15)
kJ
mor
l
.
Then
from
Eq.
(9),
W
i
eub2
=
(169
±
15)
kJ
mor
t
.
Now
this
result
contradicts
the
observation
that
NH
4
C1
is
completely
dissociated
in
the
gas
phase
at
higher
temperatures.
Therefore,
we
conclude
that
AR
die
die
AH
ub
(NH
4
C1),
which
implies
that
[see
Eq.
(19)]
b
is
only
a
weak
function
of
temperature.
The
same
phenomenon
is
observed
for
the
lower
car-
boxylic
acids
also."
It
is
therefore
difficult
to
predict
in
a
general
way
the
temperature
dependence
of
b.
The
assumption
that
b
increases
with
temperatures,
as
is
observed,
implies
that
Afi
di
,,>
(gy
m,
Ali
au
b)
changes
Atioub(NHIC
1
).
When
sign,
b
will
start
to
decrease
and
a
maximum
value
will
be
found,
as
with
the
carbox-
ylic
acid.
11
In
conclusion,
it
can
be
said
that
the
degree
of
dis-
sociation
will
be
a
weak
function
of
temperature
and
it
therefore
can
best
be
determined
by
direct
methods.
1
S.
J.
F.
Callanan
and
N.
0.
Smith,
J.
Chem.
Thermodyn.
3,
531
(1971).
2
H.
Braun
and
S.
Kuoke,
Z.
Phys.
Chem.
135,
49
(1928).
3
W.
H.
Rodebush
and
J.
C.
Michalek,
J.
Am.
Chem.
Soc.
51,
748
(1929).
4
E.
Clementi
and
J.
N.
Gayles,
J.
Chem.
Phys.
47,
3837
(1967).
5
P.
Goldfinger
and
G.
Verhaegen,
J.
Chem.
Phys.
50,
1467
(1967).
6
C.
G.
de
Kruif
and
C.
H.
D.
van
Ginkel,
J.
Chem.
Thermo-
dyn.
9,
725
(1977).
7
1slato
A.S.I.
Series
(Reidel,
Dordrecht,
1982,
to
be
published).
8
A
Report
of
IUPAC
Commission
1.2
on
Thermodynamics,
J.
Chem.
Thermodn.
13,
603
(1981).
9
R.
F.
Chaiken,
D.
J.
Sibbett,
J.
E.
Sutherland,
D.
K.
Van
de
Mark,
and
A.
Wheeler,
J.
Chem.
Phys.
37,
2311
(1962).
"Landolt—Bornstein,
Zahlenwerke
and
Functionen.
II
Band,
4
Teil.
(Springer,
Berlin,
1961).
11
C.
H.
D.
Calis-van
Ginkel,
G.
H.
M.
Calis,
C.
W.
M.
Timmermans,
C.
G.
de
Kruif,
and
H.
A.
J.
Oonk,
J.
Chem.
Thermodyn.
10,
1083
(1978).
J.
Chem.
Phys.,
Vol.
77,
No.
12,
15
December
1982