THE THERMODYNAMICS OF ACID-BASE EQUILIBRIA.

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THE THERMODYNAMICS OF ACID-BASE
EQUILIBRIA.
BY
D. H.
EVERETT
AND
W.
F. K. WYNNE-JONES.
Received
28th
July,
1939.
1.
Introduction.
From the early days of the Ionic Theory the electrolytic dissociation
of acids has excited interest partly because acids form the greater portion
of the class of weak electrolytes which obey the Ostwald Dilution Law,
and partly because the extent of their dissociation clearly depends upon
their chemical structure. The problem of the relation between structure
and ionisation has retained its interest, but it has become obvious that
any exact study of this relationship must comprise also
a
consideration
of the effects of solvent and temperature upon ionisation.
The examination of the ionisation of acids from the standpoint of
the Law of Mass Action was first put on an exact modern basis by
Bjerrum and Bronsted,2 whose work, combined with the important
technical advances of MacInnes and Shedlovsky,* and of Harned and
Owen,* has made possible the precise determination of acid strength.
Mainly from the work of Harned and his collaborators we now have
accurate results for the dissociation constants of many acids at various
temperatures
:
it is our object in this paper to analyse critically these
and some other data for acid dissociation, and
t o
give a summary of the
values
of
the thermodynamical functions obtained from our analysis.
We believe that the results of our analysis are as accurate as the data
permit, but it must be remembered that experiments on equilibria
in
solution are necessarily restricted by the range of existence of the liquid
state: the most precise data for acid dissociation in water cover the
range
0°-600,
some less precise results extend to
IOO",
and a very few
go
up to
300".
To
a
certain extent the restriction of the temperature range
is compensated by the accuracy
of
at least some of the results, but it is
possible that the interpolation formulae which we have employed lose
their significance when used over
a
much wider range of temperature
than that actually investigated.
2.
Analysis
of
Experimental Data,
In carrying out the analysis of the data, we have taken the thermo-
dynamic equations
*
(1)
*
( 2 )
d l n K
AH
dT
- RT2
---
--
dt:)-ACD
,
.
1
Bjerrum,
2.
Electrochem.,
1918,
24,
321.
2
Bronsted,
J.
Chem.
SOC.,
1921,
I
19,
574.
3
MacInnes and Shedlovsky,
J.
Am.
Chem.
SOC.,
1932,
54,
1429.
4
Harned
and Owen,
ibid.,
1930,
52,
5079.
I
380
D. H.
EVERETT
AND W.
F.
K. WYNNE-JONES
1381
and made the simplifying assumption that
AC,
is independent of the
temperature, thereby arriving at the equation
l n K=A/T +%l n T +B
.
-
(3)
This equation has also been used
by
P i t ~ e r,~ who showed that with
a
value of
AC,
=
-
40
cal./deg.
a
better representation
of
the data
for
the fatty acids is obtained than with Harned and Embree’s empirical
uation
log
K
-
log
K,
=
p( t
-
e l 2
.
(4)
FIG.
I.
A( T log
W l,
2
~.
A(T log
Thy
2
NTh,
2
A(T)I,
2

2.
Formic.
9.
Benzoic.
3.
Acetic
I
I.
m-Nitro-benzoic.
4.
Propionic.
12.
o-Iodo-benzoic.
5. Butyric.
IS.
o-Toluic.
Since
AC,
is regarded as independent of temperature, we may write
the equations
AH
=
AH,
+
AC,T
.
*
( 5 )
As0
=
AS,,
+
AC,
In
T
.
(6)
AGOIT
=
AH,/T
-
AC,
In
T
+
(AC,
-
AS,,)
.
*
(7)
Dividing
( 5 )
by
T
and subtracting
(6),
we get
whence.
In
K
=
-
AH,/RT
+
4
In
T
+
(ASOo
-
AC,)/R
.
(8)
R
Pitzer,
J.
Am.
Chem.
SOG.,
1937,
59,
2365.
Harned
and Embree,
zbid., 1934,
56,
1050.
49
I
382
THERMODYNAMICS
OF
ACID-BASE EQUILIBRIA
and we see that the constants
A
and
B
of equation
(3)
have the signi-
ficance
A
=
AHo/R.
B
=
(AS,'
-
AC,)/R.
By rearrangement of equation
( 3 )
we obtain for two temperatures,
TI
and
T,,
r p l - T 7
=
A'
+
%Tl
log
Tl
+
B'T,,
T2
log
K,
=
A'
+
%T2
log
T,
+
B'T,,
whence on subtraction
+
B',
+
B'
.
(9)
TI
log
K1-
T2
log
K2
-
AC,
TI
log
TI
-
T2
log
T,
--
TI
-
T2 R. TI
-
T2
Al, 2(T) R
*
Al,2(T)
'
or
Al,
,(T
log
K)
=P
AC
Al,
,(T
log
T)
The slope of the straight line obtained by plotting
for
a
set
of
values of
Tl
and
T2
gives
ACJR
and hence
AC,.
The linearity
of
these curves, shown in Fig.
I,
is strong evidence
for
the validity
of
the assumption that
AC,,
is constant over t he range
of
temperature employed.
A
change of
2
cal./degree over the whole range
would Droduce
a
noticeable curvature.
From equation
( 3)
we see that if (log
K
- -
.
log
T)
is plotted
R
against
I/T,
straight lines should be obtained, and using our values
of
AC,,
we have the lines shown in Fig.
2.
The slope of each of these lines
is
A'
=
-
AHO/2.3o3
R.
From the values
of
AHo
and
AC,,
we can calculate the temperature
at
which
AH
=
o
for any particular acid. This temperature,
T,,
is
given by
-
AH0
T,
=
-
(10)
AC,,
Values of
T,
may also be obtained by graphical interpolation from the
plots
of
log
K
against temperature, since from equation
(I)
T,
is
the
temperature corresponding
to
the stationary value of log
K.
The agree-
ment between the results
of
the two methods
of
evaluating
T,
is
to
within one or two degrees, and shows both the consistency of the data
and the accuracy with which
our
equation represents them.
The results of the above analysis applied to the available data are
given in Table
I.
This also includes the values of
AGige.1
calculated
from log
K2 ~ 1;
of
AH29s.1
obtained from
and of
A S ~ Q&~
evaluated from
AHp
-
AH0
=
AC,T,
D. H.
EVERETT
AND
W. F. K. WYNNE-JONES
1383
The sixth and seventh columns give the values of
A
and
B
which, on
substitution in equation
( 3)
together with the appropriate value
of
AC,,
yield the equation which we consider to give the best representation of
the experimental data. Values of
AH,
have not been tabulated since
they may be calculated readily from
A.
This quantity is quite sensitive
FIG.
2.
log
K
+
log
T
v.
$
2.
Formic.
9.
Benzoic.
3.
Acetic.
I
I.
m-Nitro-benzoic.
4.
Propionic.
I
2.
o-Iodo-benzoic.
5. Butyric.
I
8.
0-Toluic.
to small changes in
AC,
so
that values of
AH,
calculated from it are
probably only reliable to about
&
ZOO
cal. In the range of experi-
mental measurements, however,
AH
is probably reliable to
&
50
cal.
The results
of
Harned and his collaborators have not always been
expressed in the same form, and their extrapolation methods have
undergone progressive change. We have therefore re-examined their
1384
THERMODYNAMICS OF ACID-BASE EQUILIBRIA
TABLE
I.*-VALUES
OF THE
THERMODYNAMIC FUNCTIONS
t
FOR
THE
DISSOCIATION
OF
ACIDS.'
13490
-
40
-
100
-
170
-
700
-1150
IOO
40
-3355
-
174
320
-3250
190
-2470
1000
170
800
-1400
70
300
600
-2990
--
6274.0
2684.1
2358.9
2265.9
2098.0
2286.4
2660.0
2362-6
809.0
2447'4
1302.8
3327.8
1980.0
3405-0
1683.5
2135.0
2444'9
24696
2578.0
2492'0
823.0
1233'0
I100
750
800
370
510
530
goo
390
250
60
2455
2332
2830
2950
2232
2235
2620
2595
2565
2525
38.8710
14.3118
30.1866
21.8654
7.7500
21.0224
22.1177
20'9395
21.0621
20.9843
671
1271
873
956
I940
970
1010
953
965
960
10600
11540
11800
10750
10870
10940
11580
10670
10880
10790
4175
3078
3826
3400
2800
3448
3587
3389
3433
3414
-
9.2
-
5'6
-
6.4
-
8.4
-
8.7
-
9.0
-
8.3
-
8.1
-
7-8
-
8.4
13328
I3455
I3449
13400
13370
13406
13249
13283
13911
I3302
-1790
820
3370
2691.8
3236.4
3967'3
0.0
+
7'5
f19-g
-0.54 12562 12400 2706.0
-
4'7 14484 13092 2374'0
-
9-5 14721
11880
1298.0
-15.3
+
2.8
f
8.1
13384
6265
3591
8828
7105
6007
-740'5
1553'0
1313-0
+-
C b M
025
7 z
v,.
-18.9
-17.3
-22.9
-24.4
-
16.9
-18.2
-
I
7-22
-18.9
-21.3
-14.7
-
24.0
-I
7.0
-21.5
-18.1
-
17.8
-22.4
-
19.2
-
18.9
-
18.1
-
19.1
-22'1
-
10'2
Tm
OK.
B.
70'4940
56.7186
47-6856
46.7696
45'2729
53.3068
54'7716
55'0749
48.7922
30.2255
50.9329
27.1195
50.3641
36.6278
67'5734
39'6774
68.7824
39'8765
43'4995
49'3
8
76
48.4156
38.2935
19122
5114
6483
6644
65 70
3898
5259
5222
5682
2980
4703
3903
5260
3926
405 5
5561
6110
5284
5785
5923
6009
2698
564'0
297.0
295.3
293'2
278.0
268.7
294.0
302.0
300.0
156.5
307.0
173.0
303.0
320.0
303.0
314.0
252*0
300.0
3 06.0
314.8
194.0
211'0
I
Water
.
2
Formic
.
3
Acetic
.
4
Propionic
.
5 Butyric
.
6
Chloracetic
.
7
Lactic
.
8
Glycollic
.
9
Benzoic.
.
10
o-NO ,-Benzoic
I I
m-NO ,-Benzoic
12
o-I-Benzoic
.
13
m-I-Benzoic
.
14
o-C1-Benzoic
.
15
Salicylic
.
16
m-OH-Benzoic
17
Anisic
.
18
o-Toluic
.
rg
m-Toluic
.
20
$-Toluic
.
21
Cinnamic
.
22
a-Br-Cinnamic
-51.0
-41'4
-36.6
-35.4
-34'6
-
39'0
-
40.2
-40.2
-
36.2
-23.7
-37'2
-21.9
-
37'0
-28.3
-47.7
-
29'9
-49.7
-
30.6
-32-6
-36.6
-29.0
-35.8
First Acid Dissociation of Amino-Acids.
23
Glycine
.
zq
Alanine (i)
.
24
Alanine (ii)
.
25
a-NH,-n-Butyric
.
26
a-NH,-n-Valeric
.
27
Norleucine
.
28
a-NH ,-iso-butyric
.
29
Valine
.
30
Leucine.
.
31
Isoleucine
.
Second
-33'8
-33'4
-41.0
-44'2
-32.6
-32.6
-
38-6
-38.6
-38.6
1
-
38.6
-
7'3
-
8-2
-
8.1
-
9'2
-
8.9
-
8-9
-
9'1
-
10.3
-
9'3
~-
9.8
3304
3190
3201
3116
3160
3183
3220
3116
3174
3160
47'9494
47'0521
58.1174
62.5409
42'7490
45'742I
54'4346
53-1
802
54'3797
544391
Acid Dissociation
of
-28.5
-
16.3
-
16.3
-
16.3
-16.3
-
16-3
-
16.3
-11.1
-
20'0
-
6.6
32
Glycine
.
33
Alanine (i)
.
33
Alanine (ii)
.
34
a-NH2-n-Butyric
.
35
a-NH,-n-Valeric
.
36
Norleucine
.
37
a-NH,-iso-butyric
.
38
Valine
.
39
Leucine.
.
40
Isoleucine
.
Inorganic Acids.
Phosphoric
(1st stage)
.
42
Phosphoric
(2nd
stage)
.
43
Metaboric
.
2895
9823
12591
65'7957
260.3
315.6
365'9
-47-4 -15.7
-47'0
-49'7
-
30.2
-
30'9
-
0.139
-I
1'9634'
-3 1-1634
-63.2534
0.614
1.772
44
Ammoniumion
.
45
Monomethyl-am-
monium ion
.
46
Dimethyl-ammon-
ium ion
.
47
Trimethyl-ammon-
ium
ion
.
48
Anilinium ion
.
49
o-C1-anilinium ion
.
+4I'O
0.0
0'0
[For
footnotes
see
opposite
page.
D.
H.
EVERETT
AND
W. F.
K. WYNNE-JONES
1385
data and in some cases, notably for butyric acid, revised the final values
of
K.
Assuming constancy of
AC,
over the whole temperature range,
we estimate the error in its evaluation for the fatty acids to be
0.5
cal. /degree.
The data of Schaller were obtained by a conductivity method, and
refer
t o
classical
"
Ostwald
"
constants. We have taken the mean
of
his results
at
several dilutions. The work is not as reliable as more
recent investigations, but i t covers a wider temperature range. Further-
more, although the absolute values may be in considerable error, it
seems likely that the deviations will be about the same at each tem-
perature,
so
that it is justifiable to use the data for analysis of the tem-
perature dependence. The uncertainty in
AC,
is about
-J=
2
cal. per
degree.
The values for the amino acids were obtained by Harned's method,
but are much less reliable than Harned's own mGasurements, and con-
sequently in most cases the values of
AC,
can only be determined to
&
5
cal./degree.
The values
of
AH
and
AC,
which we have tabulated are determined
by the first and second differential coefficients of the free energy changes,
i t is therefore important that in two instances we have confirmation of
these values from direct thermal measurements. For the ionisation of
water P i t ~ e r,~ from
a
review of measurements of specific heats
and'of
heats of neutralisation,*# has concluded that
AH,.,
=
13,358,
while
AC,
=
-
50,
compared with
13,490
and
-
51
given in Table
I.
For acetic acid Richards and Mair,lo using an incorrect method
of
extrapolation to zero concentration, found
AH,s.l
=
I
3,650
;
a
correct
*
Throughout, heat and energy changes are expressed
in
cal. /gram-molecule
;
heat capacity and entropy changes in cal. /gram molecule degree.
t
We have taken
R
=
1-986
cals./deg.,
T
=
t o
C.
+
273.1
for these
calculations.
7
(I)
Harned and Hamer,
J.
Am.
Chem.
Soc.,
1933, 55, *21g4
;
Harned and
Copson,
ibid., 1933, 55,. 4496
;
Harned and Mannweiller,
zbzd.,
1935,
57,
1873
;
Harned and Donelson,
zbzd., 1937, 59, 1280
;
Harned and Geary,
ibid., 1937, 59,
2032
;
Harned and
Cook,
ibid., 1937,
59,
2304.
(2)
Harned and Embree,
i bi d., 1934, 56, 1042.
(3)
Harned and Ehlers,
ibid., 1932, 54, 1350;
Harned and Ehlers,
ibid.,
(4)
Harned and Ehlers,
ibid.,
1933, 55, 2379.
(5) Harned and Sutherland,
ibid., 1934, 56, 2039.
(6)
Wright,
ibid., 1934, 56,. 314.
(7)
Martin and Tartar,
ibzd., 1937, 59, 2672
;
Nims and Smith,
J.
Bi d.
(8) Ni ms, J.
Am.
Chem. SOC., 1936, 58, 987.
(9)-(15), (17)-(22)
Schaller,
2.
physik. Chem., 1898,
25,
497.
(16)
Euler,
i bi d., 1898,
2 1,
257.
(23). (32)
Owen,
J.
Am.
Chem. SOC., 1934, 56, 24.
(24), (33)
(i)
Nims and Smith,
J.
Biol. Chem., 1933,
101,
401.
(24) (33)
(ii),
(z5)-(31), (34)-(40)
Smith, Taylor and
Smith,
ibid., 1937,
122,
(41)
Nims,
J.
Am. Chem.
SOC.,
1934,
56,
1110.
(42)
Nims,
i bi d., 1933. 55, 1946.
(43)
Owen,
i bi d., 1934,
56,
1695.
(44)
Everett and Wynne-Jones,
Proc.
Roy.
SOC.,
A,
1938, 169, 190.
(45)-(47)
Everett and Wynne- Jones
(unpublished).
(48)
Pedersen,
K. danske vidensk. Selsk. SKY., 1937,
14,
9.
(49)
Pedersen,
ibid.,
1937, 15, 3.
19333 55, 652.
Chem., 1936,
I
13,
145.
109.
Rossini,
BUY. Standards
J.
Research, 1931,
6,
847.
Rossini,
ibid., 1931,
7,
47.
lo
Richards and Mair,
J. Am. Chem.
SOC.,
1929,
51,
737.
I
386
THERMODYNAMICS
OF
ACID-BASE EQUILIBRIA
extrapolation yields the value
13,570.
From specific heat data, which
have been reviewed by Rossini,ll the heat capacity change for the
neutralisation
is
-
15,
and consequently
AHm.,
=
13,495
which, com-
bined with
AH298.1=
13,358
for the ionisation of water, gives
AH,,,.,
=
-
I37
for the ionisation
of
acetic acid, and
AC,
for the same reaction
is
-
35.
These values have
t o
be compared with the values
AH,.,
=
-
IOO
and
AC,
=
-
36.6
which are given in Table
I.
It is evident that the agreement is satisfactory.
3.
Other Methods
of
Representing the Experimental Data.
Harned and his collaborators represented their early results in the
form
a
l ogK
=
-
T
+
b
log
T
+
CT
+
d
.
-
(11)
which
is
derived
OR
the assumption that
AHp
is
given by
AHT
=
a'
+
b'T
+
c'T2,
and that
Equations of this type were shown to represknt the data well over the
temperature range examined, but as we have shown there is
no
need to
assume a temperature dependence
of
AC,
in this range. Examination
of Table
I1
indicates that equation
(3),
which involves the assumption
of
a constant
ACp,
gives at least as good a representation of the data as
Harned's four constant equation.
Later, Harned and Embree showed that the curves of log
K
against
T
for most acids have approximately the same shape, and that they can
be represented by
a
general parabolic equation of the form
AC,
=
b'
+
2c'T.
log
K
-
log
K,
=
p( t
-
e l 2
.
*
(4)
where
K,
is
the maximum value of
K,
0
"C. is the temperature
at
which
this maximum occurs, and
p
is
a
constant which Harned and Embree
took as
-
5 x
I O - ~
deg.-2 for all acids. Although this equation is
found to represent the data fairly well over
a
short range of temperature
near the maximum, i t was advanced as
a
purely empirical equation. It
is,
however, related to equation
(3),
as may be seen in the following
way
At the temperature,
Tm,
at which
K
is
a
maximum, we have
I n K,= - + ~ I n T,+ B.
A
T m
Combination
of
this with
(3)
gives
in which the right side may be expanded in a power series
T,- T
AC
T d - T
I
T - T 2
1nK- l nK,=A
(
-
TT,
)
--
R'{ T -;( - )
+'
*
*}.
For temperatures near the maximum we may neglect powers
of
(T,-T)/T
11
Rossini,
Bur.
Standards
J.
Research,
1930,
4,
313.
D. H.
EVERETT
AND
W.
F.
K.
WYNNE-JONES
1387
0.
5.
10.
-
5 +
5 +
-11
+17+1o-
-26-
5 +
3
+1g+20+
-
g +
-
a +
8 +
-
3 f 6 +
o f
3
+1 4 +
+IS
+15
-
7
greater than the second, and, since
A
=
-
AH,/R
=
AC,T,/R,
the last
equation becomes
15.
20.
25.
30. 35.
40.
45. 50.
55.
60.
El*(.
_____-----
-------
4 - 7 -
4 +
6- 13+ 3- 12- 8 + 4 +
2 -
4
77
z
o +
5
+r o
-
2
-20-16
o +
13
+
8114
- 5 + 3 + 3 - 4 - 6 - ~ + 1 2 + 1 + ~
o
0-
2 -
4 4 4
o+
3 + 7+22+10+ 8 +
4
0-
9 -
14111
5- 14- 15- 3 -
I -
6 -
z +
I +
5 +
13+ 7111
5+13+11+
5 +
g + ~ o +
9 -
8-14-
9 -
1 2 -
8122
I -
9-14-13+
2 -
4 + 7+23+49+ 80+124342
9 +
3 -
4
0 -
4 -
3- 17- 14- 4 f
4 f
20
89
- 5 + f + + + + I 3 f I + 4 f 4 - 7 - - - I 2 - 4 - 4 f
2 -
7
69
8
-20
-23
-14
-28
-15
+
6+56+108 f170465
o
-26
-26 -26 -34 -32
-12
- 5
+
13
+
25
238
(T
-
T,J2
.
I
log
K
-
log
K,
=
-
2
.
2.303 RT2
t.
25. 40. 50. 60.
70.
-----
Benzoic, Eqn.
(3)
.
-13
4-47 -9 -23
o-Nitro-Benzoic
Eqn.
(3)
'
.
-52
$37
-54
-22
+16
m-Toluic, Eqn.
(3)
.
-19 -34
4 1 7
-
3
-
4
whish is of the same form
as
the Harned-Embree equation with
80.
f 2 4
3-59
+33
On
substituting the value of
-
40
cal./degree for
AC,,
and
300"
K
for
T,
this gives
p
=
-
4-9
x
IO-~
deg.-2. Thus, equation
(4)
becomes
essentially identical with Pitzer's form of
( 3) when
go.
+
8
#.
99.
Zhl.
-1.5
I55
Formic
Eqn.
(3)
*
Eqn.
(11)
.
Acetic
Eqn.
(3)
-
Eqn.
(4)
-
Eqn.
(11)
.
Pitzer's form
Eqn'
(3s
Propionic
Eqn.
( 3)
-
Eqn.
(11)
.
Butyric
Eqn.
( 3)
-
Eqn.
(4)
*
Epn
*
(3
8
Pitzers
form
It
would,
of
course, be possible to remove the restriction that the maxi-
mum occurs near
25"
C.
by
adjusting the value
of
p.
Owen
7(43)
has
sug-
gested such
a
modification
of
the equation
of
Harned and Embree to
get better representation
of
the data.
In another respect the equation
of
Harned and Embree is unsatis-
factory. Equation
(12)
shows that if we regard
p
as
a
constant indepen-
dent
of
temperature, then
AC,
is proportional to
T2-a
relation which
predicts
a
very large temperature dependence
of
ACp
quite incompatible
1388
THERMODYNAMICS
OF
ACID-BASE EQUILIBRIA
with the data.
A
similar conclusion has been reached by Walde,12 who
showed that the values
of
p
required to represent the data accurately
must vary considerably with the temperature.
It
is of interest
t o
compare the various equations which have been
proposed to represent the temperature dependence of dissociation con-
stants. This is done in Table
I1
in which we give the differences between
the observed and calculated values
of
log
K
for several acids, using the
different equations mentioned above. The last column contains the
sum
of
the absolute values of the differences.
This acid
has been chosen since for it the relative accuracies
of
the various equa-
tions are most clearly shown; i t is seen that equation
(3)
of this paper
In Fig.
3
the data for butyric acid are shown graphically.
c
O.Of5
p
I
/
I
-
I
I
I
I
I
I
I
I
I
I
I
FIG. 3.
Butyric Acid.
0
Eqn.
3.
A
Eqn.
4 (Harned and Embree).
(log
Kcalc.
-
log
Kobs.)
v.
to
c.
Pitzer's form
of
(3).
gives the best representation of the data when the appropriate values
of
A,
B
and
AC,
are substituted. This equation is also best for the other
fatty acids, although the superiority is not
so
marked as in the case
of
butyric acid.
4.
The
Significance
of
AC,.
As
we have previously pointed out, Born's equation,lS based on
simple electrostatic principles, is incapable of accounting for the large
negative values of
AC,.
This we have therefore attributed to the
orientation of the solvent molecules round the ions
:
interaction with
the solvent
is
considered to result in the contributions to the specific
heat from the rotations of these molecules being lost, thus causing a
further decrease in the heat capacity
of
the system.
l2
Walde,
J.
physic.
Chem.
,
1935
,
39,
477.
l3
Born,
2. Physik,
1920,
I,
45.
D.
H.
EVERETT
AND
W.
F. K.
WYNNE-JONES
1389
The expression for the change in heat capacity derived from Born's
equation is
and to evaluate this we require to know how the dielectric constant
of
the solvent varies with temperature. It is of interest to see that both
the form of the right side of
(14)
and the values of
AC,
calculated from
it are very sensitive to the relation we assume between
D
and
T.
The equation most commonly employed is t hat suggested by Abegg
l4
l ogD=A- bbT
.
.
(15)
which on substitution in
(10)
yields
Taking
b
=
0-0020
deg.-l and
Y
=
I
A.,
this equation predicts
a
value
for
(ACJB.,.
of
-
26
cal./degree for a dissociation reaction in water
at
25'
C.
We see, however, that a large temperature dependence
is
indi-
cated.
An alternative form of equation which we find represents very closely
the data of Kockel
l5
and of Lattey, Gatty and Davis,ls but not
so
closely the recent data
of
Wyman and Ingalls,17
is
which gives
AC,
in the form
log
D
=
A
-
B
log
T
.
*
0 7 )
Putting
B
=
1.475
and r
=
I
A.,
the calculated value of
(AC,>B,c,
is
-
10
cal./degree in water at
25'
C.
Furthermore, since
DT
varies only
slowly with temperature, this equation predicts an almost temperature
independent
(AC,)
in agreement with the conclusions arrived
at
earlier
in this paper.
Of course,
if
Born's charging term is small, corresponding to an
ionic radius of
4
or
5
A,,
we cannot use the temperature independence of
AC,
as an argument in support of equation
(17)
as against
(IS).
Since simple electrostatic considerations based on Born's equation
cannot give us values large enough to account for the whole of the heat
capacity change we examine next orientation effects which seem capable
of accounting for the remaining portion of
AC,.
In general terms we see that
a
change in structure
of
a
solvent may
give rise to
a
large change in heat capacity-the heat capacity change
on freezing water is
-
g
cal./degree per mole.
It
is
possible to regard
the molecules oriented by an ion as resembling those in ice, differing
from ice molecules mainly in that they may still retain their trans-
lational degrees of freedom. Part of the
g
cal. difference between ice
and water is presumably due
t o
effective loss
of
translational degrees
of
freedom, and if we put this contribution
at
3/2R,
the decrease due to the
effective loss of rotational degrees of freedom is about 6 cal./degree per
mole. Taking this as equal to the loss in heat capacity due
t o
the
l4
Abegg, Wied. Ann., 1897,
60,
54.
l5
Kockel, Ann. Physik, 1925,
87,
417.
l6
Lattey,
Gatty and Davies,
Phil.
Mag.,
1931,
12,
1019.
l7
Wyman and Ingalls,
J.
Am. Chem.
SOL,
1938,
60,
1182.
19
*
1390
THERMODYNAMICS
OF
ACID-BASE EQUILIBRIA
orientation of water molecules round an ion, we see that if each ion
has a co-ordination number of four, the heat capacity change for the
ionisation of an uncharged acid will be about
-
48
cal./degree; this is
roughly equal to the observed changes.
For the purposes of our discussion we propose to retain the formal
division of
AC,
into two portions, the change calculated from Born's
equation, and that due to the orientation of the solvent molecules round
the ions. While we find this a convenient basis for discussion, we
realise that this separation of
AC,
into simple electrostatic and orienta-
tional contributions is arbitrary, since all dielectric phenomena are
concerned with the restriction of movement of the molecules of the
medium. The division consists essentially in considering the value of
AC,
calculated on the assumption that the solvent retains its macro-
scopic dielectric constant right up to the hydration shell of the ion, and
then regarding the difference between this and the observed change as
due to more or less complete orientation of the solvent molecules in the
neighbourhood of the ions
(ie.,
to saturation of the dielectric).
We obtain further support for the above interpretation of
AC,
from
a consideration of the effect
on
ACD
of change of solvent. In Table I11
TABLE III.-DISSOCIATION
OF
ACETIC ACID
IN
DIOXANE WATER
AND
METHYL
ALCOHOL
WATER MIXTURES.
THERMODYNAMIC
FUNCTIONS.
Solvent.
+ACp
(cd.
/deg.).
Water
.
20
%
Dioxane
.
45
yo
Dioxane
.
70
Yo
Dioxane
.
10
%MeOH
20
yo
MeOH
-36.6
-394
-43.0
-46-6
-45.4
-48.2
+ 4 9 8.1
(cal./deg.).
-22-1
-24.4
-
29-8
-39-9
-22-4
-22.6
are given the results of the analvsis of
4 9 8.1
(Cal.).
6483
7211
8598
11290
6685
6924
AH298*1
(-1.).
-
I00
-
70
-
300
-
600
I
60
0
- A.
2359
25 79
2724
2909
2956
3169
B.
47.6856
52'8474
56'2759
59'3522
60.4267
65.4282
the data of Harned and Embree.l8
anduof Harned and Kazajiani9 for the dissociation of acetic acid 'in
methyl alcohol water and dioxane water mixtures respectively. At
present these are the only data available on temperature coefficients in
solvents other than water.
The ionisation of acetic acid in dioxane water mixtures is essentially
the same process as that in pure water,
viz.
.-
CH3COOH
+
H20
=
H30+
+
CH,COO-,
and we may regard the hydration shell as remaining unchanged. The
variation of
AC,
with the solvent will then be caused by the change in
dielectric constant, and may be calculated from Born's equation. We
have expressed the results of Akerlof and Short
2o
for the dielectric
constant of dioxane-water mixtures in the form
of
equation
(17)
;
the
equations are given
in
the table below. From these relations we have
deduced values of the contributions to
AC,
of Born's charging process
setting
Y
=
5
A.
which is arbitrarily taken for the radius of the hydrated
la
Harned and Embree,
J.
Am. Chem.
SOL,
1935,
57,
1669.
l9
Harned and Kazajian,
ibid.,
1936,
58,
1912.
2o
Akerlof and
Short,
ibid.,
1241.
D.
H.
EVERETT
AND
W.
F. K. WYNNE-JONES
1391
Water
.
log
D
=
5.539
-
1.475 log
T
20
%
Dioxane
1
log
D
=
5.864
-
1-65
log
T
45
yo
Dioxane
.
log
D
=
5.872
-
1-74 log
T
70
yo
Dioxane
.
log
D
=
5-874
-
1-87
log
T
i on;
Column
4
of
Table
IV
contains observed values of
AC,
less the figures in column
3
;
TABLE IV.
these calculated values are given in column
3.
-
-
-
8
-20
Solvent.
Equation
for
D.
I
1-1
-
34'6
-36.0
-35.0
-
27.0
these should represent the contributions to
AC,
from the orientation
of
the water molecules.
The essential agreement of the first three figures in the last column
shows that it is reasonable to interpret the change of
AC,
on an electro-
static basis, and also indicates that the simple electrostatic term is not
large, particularly in water.
The data for methyl alcohol water mixtures do not extend over
a
sufficient range of dielectric constant to be usefully discussed at present
;
they do, however, appear to exhibit the same type
of
behaviour as the
dioxane-water mixtures, although we may expect complications, since
there is the possibility of both alcohol and water molecules being oriented.
5.
Value
of
ACD
Related
to
the
Structure
of
an
Acid.
Without
a
complete theory of the heat capacities
of
dissolved
substances it is impossible to give
a
quantitative explanation of the
variations in heat capacity changes corresponding to the various ionic
dissociations. It is indeed noteworthy that to
a
fair approximation
the value of
AC,
is
-
40
cal./degree for all the carboxylic acids con-
sidered
in
this paper. This undoubtedly arises from the fact that t he
ionisation process results in the disappearance
of
a
neutral molecule
and the formation in all cases
of
a hydrogen ion and
of
an anion closely
similar to the neutral molecule in all respects except that
i t
carries
a
charge.*
Nevertheless,
it
is interesting to consider the differences shown in
Table
I,
and
it
is possible to account for them in a qualitative way.
As
we have seen, the contribution to the heat capacity change from Born's
charging process is small,
so
that for acids
of
approximately the same
size, variations in the individual values of
AC,
must be due to the
differences between the orienting power
of
the respective anions, since
that of the hydroxonium ion is the same for all acids.
The orientation of solvent molecules by an anion will be controlled
by the electrostatic potential near the surface
of
the ion, which, in turn,
will be largely dependent on
t he
following two factors
:
*
Further evidence that the change in heat capacity is essentially due to the
formation of two ions with the disappearance of a neutral molecule is afforded
by
recent data for the reaction
AgX
+
Ag+
+
X-,
for which Owen and Brinkley
( J.
Am.
Chem. SOL,
1938,
60,
2233)
obtain values
of
ACo
of
between
-
35 and
-
40 cal./degree at
25'
for
the various halides.
'
solid.
I392
THERMODYNAMICS
OF
ACID-BASE
EQUILIBRIA
(a)
the distribution of charge in the ion-the more localised the
charge, the stronger the orienting power
;
(b)
a
steric factor which may arise
as
a result
of
groups in the ion
screening the solvent molecules from the effect of the localised negative
charge. If
a
group has such a screening effect the heat capacity change
for the ionisation will be diminished.
As
a
consequence of the variations in the electrostatic potential in
the anions of related acids, we may expect to find a correspondence
between the changes in
AC,
and in acid strength of which we regard
AH,
as
a
rough measure. An increase in the electrostatic potential will
cause more powerful orientation of solvent molecules, and hence
a
larger
negative value of
AC,,
but it will also make the removal of
a
proton
more difficult and therefore increase
AH,.
Equation
(10)
shows that
the ratio
of
AH,
to
AC,
determines the temperature
of
the maximum
value of
K,
so
we shall expect this temperature,
T,,
to be largely inde-
pendent of the strength of the acid. This is found to be true-of the
21
carboxylic acids we have examined,
16
have values of
T,
lying between
270°
K.
and
310"
K.
The exceptions are the o-substituted benzoic
acids in which we might expect to find disturbing steric effects.
The variation of
AC,
in certain series presents several interesting
features. For the fatty acids, as shown in Fig.
4,
AC,
varies from
-
41-4
cal./deg. for formic acid to an approximately constant value of
--
34
cal./deg.
for
the higher members of the series, and this seems to
be
a
consequence of the steric factor. The introduction of
a
methyl
group into the formate ion will result in a partial screening of the water
D. H.
EVERETT AND
W.
F. K.
WYNNE-JONES
1393
ACp.
AH0
AGggg.l
(cal./deg.).
(cal.).
(cal.).
molecules from the field
of
the charge, while further lengthening
of
the
hydrocarbon chain produces
a
smaller additional effect.
In the toluic acids the values
of
-
AC,
increase regularly from the
o-
to the p-acid
;
as the screening effect
of
the methyl group will decrease
in the same order we should expect just such a change in
AC,.
For the ionisation
of
lactic, glycollic and salicylic acids
AC,
is numeri-
cally much larger than for the corresponding unsubstituted acids. The
presence of the hydroxyl group thus appears to favour the orientation
of water molecules, probably on account of the capability of the hydroxyl
group forming a hydrogen bond with the oxygen of
a
water molecule.
With the benzoic acids the presence
of
substituents in the ring may
give rise to inductive and tautomeric effects which will tend to increase
or decrease the potential at the carboxyl group according to the nature
of
the substituent groups and their position in the ring. Superimposed
on this effect will be the steric factor which will in all cases tend to reduce
the value of
-
AC,,
being most effective in the ortho-position. Examin-
ation of Table
V
shows that, for the limited data available, the effects
are those which would be expected on the basis
of
modern electronic
theories.
TABLE
V.
ACp
AHo.
AGgg8,1
(cal./deg.).
(cal.).
(cal.).
c1
I
3
OCH,.
-28 5970 3926
-48 152.50
405.5
-22
3770 3903
-24 3710 2980
- -
-
0
-.
m
--.
-
- -
-37
I1220
5260
-37 11400 4703
-30
9076 5561
- -
-
P
-.
ACP
AHQ. AG&g.l
(cal./deg.).
(cal.).
(cal.).
Benzoic
;
ACD
=
-
36 cal./deg.,
AH,,
=
10800
cal.,
AG&,,
=
5682
cal.
If we assume that the toluic acids are influenced only
by
the steric
factor, then we can assign to the effect on
-
AC,
the approximate
values of
-
5,
-
3 and
o
cal./deg. for groups substituted in the
ortho-,
meta-
and para-positions respectively. The electrostatic effects would
then be about
-
5
and
+
4
cal./deg. for halogen or nitro substitution
in the
ortho-
and meta-positions respectively. For substitution
of
hydroxyl this factor causes an increase in
-
AC,
of 17 cal./deg. in the
ortho-position, and
a
decrease of 3 cal./deg. in the meta-position, while
para-substituted methoxyl has an electrostatic factor
of
14
cal./deg.
6.
Strengths of Organic Acids and their Structure.
It has been the common practice to regard the dissociation constant
of
an acid in water at
25'
C.
as a measure of its intrinsic strength and
on
this basis theories have been developed correlating acid strength and
chemical constitution. The simple electronic conceptions of the induc-
tive and mesomeric effects were found to be inadequate
;
the anomalies
require for their explanation the postulation
of
rather special effects for
whose existence there
is
often very little corroborative evidence. This
1394
THERMODYNAMICS
OF
ACID-BASE EQUILIBRIA
is somewhat unsatisfactory, and emphasises the need for a closer exam-
ination
of
the fundamental assumption which is involved.
Firstly,
the dissociation constant of one acid relative to another in the same
solvent and at the same temperature is found to depend upon the
solvent employed. This effect has been discussed by Wynne- Jones.21
He showed that for two acids,
HA,
and
HA,,
on plotting log
(Kal/KA,’i
against the reciprocal of the dielectric constant of the solvent,
a
straight
line is obtained. On extrapolation to
I/D
=
o
this gives a value of
log
(KAl/KAJ,
which it was suggested should be regarded as the true
value of the strength of one acid relative to another
at
the given
temperature.
Secondly, the relative strengths of two acids may not be independent
of
temperature. Attention was first drawn t o’ this possibility by
Hammett,22 who reviewed the data for a number of acids, and pointed
out that a theory based on heats of reaction at
25’
C.
would differ widely
from one based on standard free energy changes. The use
of
dissociation
constant data in discussing the structure of acids would only be possible
if
the effect of a substituent
on
the heat of ionisation were the same as
its effect on the free energy change. This has also been discussed by
Baker and Dippy;
23
Baker criticises the use
of
data
at
25’
C.,
and an
answer is made by Dippy.
As
an argument in support of his view Dippy says that in point of
fact there is
no
experimental evidence that relative strengths do depend
on the temperature of comparison. This statement is invalidated by a
closer examination of the data. To illustrate this we have plotted in
Fig.
5
the values of log
K
for
acetic and butyric acids against tempera-
t ure; the shapes of the curves below
0’
C.
have been calculated from
our empirical equations. The third curve
is
that of the relative strengths
of the two acids
;
there
is no
question that this curve must cut the axis
at about
-
10’
C.,
and that below this temperature butyric acid is
stronger than acetic.
It
is
now apparent that no justification exists, either on theoretical
or experimental grounds for the choice
of
an arbitrary temperature at
which to compare acid strengths.
Furthermore, the use of the maximum values
of
log
K,
as suggested
by Harned and Embree,5 has no theoretical basis.
The values of
AH,
obtained for the various acids as
a
result of our
analysis may now be discussed in relation to the strengths of acids.
If
it
were possible to assume that
AC,
remained constant for all tem-
peratures down to absolute zero, then
AH,
would be equal to
AGO,,
the
standard free energy of ionisation at absolute zero. We should then
have Hammett’s condition satisfied that the effect of
a
substituent on
heat and free energy changes must be the same in order to use the data
for discussion of intrinsic acid strengths. Unfortunately, this is an
unjustifiable assumption,
so
that in the first place we cannot expect to
be able to attach any theoretical importance to the absolute values of
AH,.
At
low
temperatures, however, we might expect the heat capacities
of
the anions to vary in
a
rather similar.manner in any given solvent.
This assumption may be criticised mainly on two accounts.
21
Wynne-JonesyProc. Roy.
SOC.,
1933,
40,
440.
22
Hammett,
J.
Chem. Physics,
1936,
4,
613.
23
Baker, Dippy and
Page,
J.
Chem.
SOC.,
1937, 1774
;
cf. ref.
25.
D. H. EVERETT
AND
W.
F.
K. WYNNE-JONES
1395
It seems probable, therefore, that the calculated values of
AH,
will fall
in
the same order as the true values of
AHo
or
AG,O.
The possibility
thus arises of employing the values
of
AH,
calculated above as measures
of the relative intrinsic strengths
of
acids.
The effect
of
a substituent on the heat and free-energy change of
ionisation will also be the same when
AGO
has a maximum value
( i.e.
ASo
=
0).
Since our analysis shows that in most cases the values of
AG;=.
and of
AH,
are in the same relative order, we shall confine our
discussion to the values of
AH,,.
/-
& -
0.04-
L
g -
3
f
"c.
-0.04.
-20
-10
0
10
20
.30
40
50 6,
I
I
FIG.
5.
Top
curve
:
log
&,tic
v.
to
c.
Middle
curve
log
Kbutsric
v.
t o
c.
Lower
curve
:
log
ITHac
-
log
KHBU
PI.
to
C.
In the following paragraphs we have examined the possibilities of this
basis of comparison. We must emphasise, however, that our suggestions
are tentative and provisional until further accurate data on the variation
of dissociation constants over a wide range of temperature become
available.
In
general
i t
can be said,
as
far as the available data allow
comparison, that the strengths of acids as measured by
AH,
exhibit
much more regularity than those deduced from measurements at
25'
C.
Many of the apparent anomalies which have necessitated modifications
of the theory based
on
values of log
K,,
disappear in the extrapolation.
I
396
THERMODYNAMICS
OF
ACID-BASE EQUILIBRIA
Fatty Acids.
At
2 5 O
C.
the order
of
the strengths
of
the fatty acids is
formic
>
acetic
>
butyric
>
propionic.
The apparently anomalous position
of
butyric acid has been discussed
by Bennett and and by Dippy.25 The explanations advanced
are, however, by no means convincing.
As
we have shown, the relative strengths of butyric and acetic acids
change with temperature. This is also true of the other fatty acids,
although the curves cut
at
much lower temperatures
(100'
K.
t o
200'
K.)
;
but uncertainties in the behaviour
of
AC,
will probably not yet be serious.
butyric
>
propionic
>
acetic
>
formic.
The order is now regular, and i t is worth noting that the only one
of
the thermodynamic functions showing any anomaly in this series is the
free energy change at room temperature; the values of
AC,,
AS&g.l
and
AH,.,
all form
a
regular series.
The values
of
AH,
indicate intrinsic strengths in the order
Chloracetic Acid.
The increase
of
the strength of
a
fatty acid
as
a
result of halogen
substitution is regarded as due to the influence of the halogen-carbon
dipole in decreasing the strength of binding of
a
proton to the carboxyl
group. The data in Table
I
indicate t hat the effect
is
largely on the
values
of
AC,
and
ASO,
and that although the
AH,
values do confirm
the enhanced strength of chloracetic acid, the magnitude of the effect
is
probably less than the values of
hGi98.1
would suggest.
We
have already mentioned that we do not place too much emphasis
on the values of
AH,;
especially for acetic and chloracetic acids it is
quite possible that
at
low temperatures the form of the
AC,
-
T
curves
will differ appreciably
;
such deviations will be less likely for the simple
fatty acids.
Toluic Acids.
The order
of
strengths
at
25'
C.
is
o-toluic
>
benzoic
>
m-toluic
>
p-toluic.
The position
of
o-toluic acid has been discussed from
a
same standpoint
as that
of
butyric acid.26
If
we take
AH,
as
our basis
of
comparison, we obtain the order
o-toluic
>
m-toluic
>
p-toluic
-
benzoic.
As
in the case of the fatty acids, the introduction of
a
methyl group
seems to cause an increase in acid strength. Furthermore, the effect
appears to fall off with distance and in the para-position the methyl
group has practically no effect.
Substituted Benzoic Acids.
The variations in
AGg98.1
between the ortho-substituted halogen and
nitro-benzoic acids are large, and the values
of
AC,
such that the order
24
Bennett
and
Mosses,
J.
Chew.
SOC,
1930, 2364.
25
Dippy,
ibid.,
1938,
1222.
26
Dippy, Evans, Gordon,
Lewis
and
Watson, ibid.,
1937, 1421.
D. H.
EVERETT
AND
W.
F.
K.
WYNNE-JONES
1397
of strengths remains unchanged on extrapolation to low temperatures.
For the meta-substituted acids, however, while the values of
AGi9e.1
indicate that the meta-nitro and meta-iodo acids are stronger than benzoic,
the
AH,
values show a small decrease in strength. Similarly, we see
that salicylic acid
is
weaker than benzoic, while m-hydroxybenzoic acid
is slightly stronger.
This would seem consistent with the general observation that
meta-
substitution has an effect opposite to
ortho-
and para-substitution.
In accordance with expectations, anisic acid is considerably weaker
than benzoic.
Further correlation of the strengths of these acids with their structure
is probably not justified with the rather meagre data at our disposal.
7. The Significance
of
ASo.
The fact that the heat and entropy changes
of
an ionic reaction are
not identical has been known for
a
long time, but it
is
only within recent
years that any attention has been paid to these differences. Thermo-
dynamically, the difference between the heat and the free energy is the
entropy term
TAP,
which is also related to the temperature coefficient
of the free energy by the equation
Latimer and his co-workers have obtained values of the entropy of
solution of many inorganic ions in water, and these values are all negative
and also depend upon the ionic radius and charge
in
a way which has
led Latimer
27
to suppose that the entropy can be interpreted purely in
terms of Born's charging process. Eley and Evans,28 on the other
hand, have considered the orientation of solvent molecules around the
ions, and have arrived
at
values for the entropy which are in fair agree-
ment with experiment.*
A
standpoint similar to Lat her's has been adopted by Gurney,29
who has discussed specifically the temperature dependence
of
the dis-
sociation constants
of
weak acids and has shown that,
if
the dissociation
energy
is
split into an electrostatic and a non-electrostatic term, i t
is
possible to give a qualitative explanation of the maximum in the dissocia-
tion constant- temperature curve
of
a weak electrolyte. His discussion
is based on the assumption that, while the non-electrostatic energy
required for dissociation is independent of temperature, the electrostatic
energy increases with temperature. The standard free energy of disso-
ciation is therefore given by the equation
AS'=
-
d(AGO)/dT
.
*
(19)
where
Gel,
is
the electrostatic free energy, and should ideally be repre-
sented by Born's equation.
In
consequence of the assumed temperature
independence
of
AG,O we have
d(AG*)/dT
=
dG,l,/dT
.
and Gurney regards this coefficient
as a
measure of the electrostatic
energy.
27
Latimer, Pitzer and Slansky,
J.
Chem. Physics,
1939,
7,
108.
28
Eley and Evans,
Trans.
Faraday
SOC.,
1938,
34,
1093.
*
We have examined the possibility
of
applying
t o
the calculation
of
ionic
heat capacities, the methods
of
Eley and Evans
for
the calculation
of
heats and
entropies
of
solution of gaseous ions.
2D
Gurney,
J. Chem. Physics,
1938,
6,
499.
I
398
THERMODYNAMICS
OF
ACID-BASE
EQUILIBRIA
The position of the maximum in
K
depends upon the relative im-
portance of the electrostatic and non-electrostatic contributions to the
free energy, and Gurney introduces
a
quantity,
x,
which is defined by
the equation
Of
this function Gurney states that, as
x
is
a
measure
of
the ratio of the
dissociation energy to the electrostatic energy,
i t
should be a
"
smooth
function
"
of the temperature at which
K
is
a
maximum. That this is so
x
=
-
IOg
KT/(d(AGO)/dT)T
.
*
( 2 2 )
0-3
'=25
0.2
FIG.
6.
- - x
v.
Tm.
Numbers correspond to Table
I.
is
shown
in
Fig.
6,
and Gurney regards this as proof of the correctness
of his treatment.
To
see the real significance of Gurney's assumptions, we must recall
that the temperature coefficient of the free energy change is the entropy
change of the process, and therefore the basic assumptions are that for
non-ionic and isoelectric
*
processes, the values
of AS0
and
ACp
are
zero. The function,
x,
can also be expressed in simpler form by using
thermodynamic relationships, which give us
*
Gurney describes
as
isoelectric those processes in which there is
no
change
in the number
of
ions.
D. H.
EVERETT
AND
W.
F.
K.
WYNNE-JONES
1399
It can now be seen that, if the value of
x
is determined
at
the temperature
corresponding to the maximum value of
K,
AH
is necessarily zero, and
hence
x
will be
-
1/2*303R.
If,
therefore, we examine
a
number of
acids with values of
T,
not far removed from room temperature, and
if
for all these acids
AC,
has the same sigrl,
it
is
inevitable that
x
will be
a

smooth function”
of
T,
;
such a relationship cannot, therefore, be
regarded as justifying the splitting
of
the dissociation energy into electro-
static and non-electrostatic terms
;
still less does
i t
prove the assumption
that
AS0
is purely electrostatic.
There are three main arguments against this assumption of the electro-
static origin
of
AS0:-
( I )
Non-ionic and isoelectric equilibria often have quite large values
of
ASO.
( 2 )
The dependence of
ASo
upon the dielectric constant
of
the solvent
suggests that only
a
part
of
the entropy
is
purely electrostatic.
(3)
For one ionic equilibrium we have found an extremely small
value of
ASo
and, moreover, this changes sign within the experi-
mental range.
-
40
-
30
FIG.
7.
-
AS250
v.
(1/D)250.
Acetic acid in dioxane water mixtures.
The evidence for the first statement is given
on
the one hand by
such gaseous equilibria as the dissociation of hydrogen iodide and
hydrogen selenide, and on the other hand by the values far isoelectric
equilibria, which may be calculated from the data in Table
I.
For the
dissociation of hydrogen iodide, Bodenstein’s
30
results give
ASo
=
13.6
cal./deg., while for hydrogen selenide
31A.9
=
4
cal./deg.
For isoelectric
equilibria we find that for the equilibrium,
ASo
=
-
14.2 cal./deg., and for the equilibrium,
ASo
=
-
7.1
cal./deg.
The dependence of
ASo
upon the dielectric constant can be deter-
mined from the results of Harned and Kazajian given in Table
111.
Their values of
ASo
are plotted against. the reciprocal of the dielectric
constant in Fig.
I,
and i t is seen that while there is
a
linear relationship,
n-Butyric acid
+
Salicylate
=
n-Butyrate
+
Salicylic Acid
n-Butyric acid
+
Formate
=
n-Butyrate
+
Formic acid
30
Bodenstein,
2.
physik.
Chem.,
1849,
29,
295.
31
Bodenstein,
ibid.,
429,
1400
THERMODYNAMICS
OF
ACID-BASE EQUILIBRIA
there is not proportionality between these quantities and
ASO
is still
large when
I/D
=
0.
The third argument is based upon the results of measurements which
we have just completed of the dissociation constants of mono-, di-,
and tri-methylamines. Details of this work, which has been carried
out in the same way as our work on the basic strength of ammonia,
will be published shortly; at present, we will simply mention that for
the ionisation of trimethylamine we obtain
AS0
=-
3-3
cal./deg.
at
25'
C.
and
AC,
=
-
92
cal./deg. It appears from our results that
ASo
actually changes sign at about
15"
C.
It seems clear that the sign of
ASo
is not characteristic of ionic
reactions, and that the attempted separation of an electrostatic energy
of ionisation fails. This conclusion is not unexpected, as there
is
no
method of deciding at what particular distance apart the separating
atoms are to be regarded as electrically charged. The quanta1 distinction
between exchange and coulomb forces is of no help to us, since this
distinction
is
a mathematical device which is useful in
a
particular
treatment, but has no physical basis.
In spite of the failure of Gurney's attempt to make a clear-cut
separation of electrostatic and non-electrostatic forces, there are obvious
differences between ionic and non-ionic equilibria, and from the data
collected in this paper we can assert that for ionisation processes
at
room
temperature the heat capacity is always negative and large and the
entropy change
is
also usually negative. These two thermodynamic
characteristics of ionisation processes are of considerable importance,
and we shall expect them to be exhibited not only in equilibria, but also
in reaction rates
;
in fact, there is already considerable evidence
32
that
in
the rates of such reactions as the formation of quaternary ammonium
salts the entropy changes are appreciable, and for other reactions heat
capacity changes have been recorded.
We conclude that in any reaction there will usually be finite values
of
ASo
and
AC,,
but in ionisation processes occurring in
a
polar solvent
the ionic charges produced will give rise to large negative values of these
functions, primarily because of the powerful orientation of solvent
molecules in the immediate neighbourhood of the ions. The resultant
values of
AS0
and
AC,
will therefore normally be negative and often
large. The exact calculation of these quantities can be performed only
by the methods of statistical mechanics, and at the moment presents
considerable difficulties.
(Added
in
proof.)
Harned and Owen
s3
have just published
a
review
of the thermo-dynamic properties
of
acid-base equilibria. Their values
of
the functions
AGO, AP,
and
AH
are mostly in goo,d agreement with
ours, but their values
of
AC,
are widely different. This discrepancy
is
the result of their calculating
AC,
not directly from the data but
through their empirical equation
(4).
In our discussion we have shown
that this equation
is
only an approximation and that i t must lead to
erroneous values
of
AC,.
Summary.
The experimental data for the electrolytic dissociation of weak acids
have been sybjected to
a
careful analysis from which
we
have obtained
values
of
AGO,
AH,
ASO,
and
AC,,
for the various equilibria.
s2
Wynne-
Jones
and Eyring,
J.
Chem. Physics,
1935,
3,
492.
s3
Harned and
Owen, Chem. Rev.,
1939,
25,
31.
D. H.
EVERETT
AND W.
F.
K.
WYNNE-JONES
1401
It
is noteworthy that
for
the ionisation
of
uncharged acids, such as
acetic acid, the values at room temperature
of
AS0 and
AC,
are usually
negative.
The sign and magnitude of the heat capacity change is to be explained
by
the orientation of solvent molecules around the ions.
We have also
considered in general terms the relationship between the molecular struc-
ture and the various thermodynamic quantities and have
shown
that,
for a proper comparison of the strengths
of
acids, it is necessary to take
into account not merely the dissociation constants
at
a
particula tem-
perature but the values of all the thermodynamic functions.
University
College,
Dundee.
University
of
St.
Andrews.