MARIOGOFFREDIAND THEODORE SHEDLOVSKY
4436
which satisfies eq 9 will be proved by showing that the function f(Uy)
= (1
-
auyy
[exp(nFrl/RT) 10
+
UY)'
throughout this interval. Differentiation of eq A7 yields
647)
where a 2 0, 7 1 0, b 1 1, and y 2 1, has precisely one root in -1 I UY I 0. There is at least one root of eq A7 in this interval, sincef(-1) = (1 > 0, andf(0) = 1 - exp(nPq/ RT) 2 0. To show that there is at most one root in -1 2 uy 2 0, we show that df/duy is negative
+
y[exp(nFrllRT) 1(1
+
UY)"'
(AB)
+
Now (1 - C Y U ~ ) ~ is - ' positive and (1 uY)#-' 2 0 in -1 I UY 5 0 which, together with the conditions a 2 0, b 1 1, y 1 1, and 7 2 0, yields df/duy < 0 in -1 I UY I 0. Hence eq 9 has precisely one solution, designated UY,,, in -1 5 UY I 0.
Studies of Electrolytic Conductance in Alcohol-Water Mixtures.1 V. The Ionization Constant of Acetic Acid in 1-Propanol-Water Mixtures at 15, 25, and 35"
by Mario Goffredi and Theodore Shedlovsky The RockejeEler UnCersity, New York, New York 10081 (Received M a y 8.4, 1967)
Measurements are reported on the conductance of dilute solutions of acetic acid and of sodium acetate a t 15, 25, and 35' in 1-propanol-water mixtures over the entire range of solvent composition. From these data and those on hydrochloric acid and sodium chloride solutions in the same solvent system previously reported by us, values for A. and the ionization constants, K, for acetic acid have been computed for these temperatures over the entire solvent composition range. The results are discussed briefly from theoretical considerations.
Introduction I n this paper, we present data on the electrolytic conductance of dilute solutions of acetic acid and also of sodium acetate at 15, 25, and 35" in 1-propanol-water mixtures over the entire range of solvent composition. The acetic acid ionization constants in the mixed solvents that contained 0,20,40,60,80,90, or 100 wt % 1propanol were obtained from these data supplemented by those from our work on sodium chloride2 and on The Journal of Physical Chemistry
hydrochloric acida solutions in a manner previously de~cribed.~
Experimental Section The preparation of the 1-propanol-water mixtures and their physical properties have been detailed in a (1) This research was supported by the National Science Foundation through Grant No. GB-3062. (2) M. Goffredi and T. Shedlovsky, J. Phys. Chem., 71, 2176 (1967).
ELECTROLYTIC CONDUCTANCE IN ALCOHOL-WATER MIXTURES
4437
Table I : Conductances of NaAc in Water-1-Propanol Mixtures -10'C
15O A
259
AA
104c
A
AA
350 A
AA
12.802 27.195 34.668 42.280 51.923 62.647
108.317 106.789 106.182 105.675 105.045 104.445
0.001 -0.007 -0.010 0.023 -0.002 -0.006
104c
0.00% n-CaH7OH 3.0086 8.8428 13.932 18.269 25.559 32.394
68.269 67.590 67.112 66.825 66.370 66.010
-0.031 0.032 -0.004 0.018 -0.001 -0.014
21.293 28.071 34.932 45.791 58.976
34.974 34.772 34.609 34.358 34.111
-0.003 -0.003 0.010 -0.001 -0.002
8.0927 15.123 20.961 25.487 31.330 37.199
20.00% n-CaH7OH 50.007 -0.005 49.539 0.001 49.238 0.005 49.031 0.002 48.795 -0.001 48.583 -0.003
3.9023 5.8900 9.9532 13.606 17.602 23,925
67.164 66.872 66.400 66.056 65.722 65.277
-0.007 0.000 0.005 0.007 -0.001 -0.004
9.1706 17.281 25.079 40.368 48.028
25.199 24.852 24.592 24.169 24.005
-0.005 0.003 0.007 -0.006 0.002
2.8227 7.8359 15.824 23.108 30.630 40.225
40.01 % n-CaH7OH 36.148 0.006 35.617 -0.007 35.085 0.005 34.694 -0.007 34.372 -0.001 34.018 0.004
2.4273 5.6386 9.9364 16.729 23.078 29.303
48.838 48.307 47.800 47.182 46.719 46.334
-0.002 0.001 0.003 -0.002 -0.003 0.003
5.0205 12.107 18.764 27.663 34.769 42.892
19.050 18.520 18.175 17.801 17.546 17.295
0.004
4.0282 8.6320 12,208 15.634 20.360 25.180
60.01% n-CaHTOH 26.879 0.000 26.301 0.000 25.954 -0.001 25.673 0.003 25.328 -0.003 25.031 0.001
6.1102 11.696 18.475 22.547 28.937 34.630
35.620 34.819 34.084 33.707 33.208 32.8M
0.000 0.001 0.002 -0.005 0.006 -0.002
3.7084 10.655 14.638 19.113 24.987 34.236
80.01% n-CaH.rOH 22.395 -0.002 20.943 0.008 20.329 -0.008 19.772 0.001 19.150 -0.002 18.365 0.000
6.8741 13.295 18.479 24.347 31.477 41.440
28.503 26.931 25.986 25.108 24.243 23.240
0.004 -0.007 -0.001 -0.003 0.010 -0.007
3.3142 5.2561 10.133 16.647 20.844 23.792
27.025 25.803 23.641 21.734 20.794 20.254
0,002 -0.003 -0.003 0.011 -0.015 0.004
4.3187 9.4356 14.376 19.207 24.635
14.532 11.466 9.953 8.976 8.200
0.003 -0.008 0.018 -0.005 0.006
-0.008 0.002 0.005 0.001 -0.002
6.2099 12.958 22.434 31.782 46.174
16.063 15.210 14.384 13.776 13.064
0.002 -0.004
6.185 13.634 24.440 33.438 42.802 49.770
14.983 13.579 12.322 11.584 10.993 10.623
0.006 -0.012 0.002 0,011 0.005 -0.004
7.7767 14.831 21.783 28.231 36.463 47.906
90.00% n-CaHvOH 19.281 -0.002 17.563 0.004 16.406 0.003 15.585 -0.010 14.780 0.002 13.917 0.000
5.5842 9.7302 14.485 17.670 22.903
9.976 8.641 7.699 7.238 6.656
0.002 -0.004 0.006 0.002 0.001
4.0892 7.9055 11.318 13.909 15.998 17.654
100.00% n-CIH70H 12.779 O.OO0 10.710 -0.002 9.609 0.000 8.996 -0.002 8.592 -0.001 8.313 -0.003
O.OO0 0.002 -0.002
Volume 71. Number 19 December 1967
4438
MARIOGOFFREDI AND THEODORE SHEDLOVSKY
Table 11: Conductance Parameters and Constants for NaAc
wt % l-CzH7OH
bo
d
KA
S
E
L
=A
62.86 32.65 29.93 34.49 47.55 47.24 66.90
8.67 9.86 17.09 33.39 77.61 76.11 137.2
117 73 48 100 107 102 112
0.03 0.006 0.006 0.006 0.004 0.01 0.005
81.57 47.96 43.93 49.84 67.25 80.85 89.27
12.11 14.56 25.47 49.74 116.6 177.5 202
173 109 71 187 154 173 185
0.04 0.004 0.007 0.003 0.007 0.007 0.003
101.7 66.03 61.67 69.39 92.15 108.8 115.5
15.52 19.81 36.69 72.34 172.8 260 278
177 112 93 197 201 216 271
0.01 0.006 0.003 0.005 0.009 0.01 0.02
15"
0.00 20.00 40.01 60.01 80.01 90.00 100.00
69.38 f 0 . 0 2 36.440 f 0.009 26.150f0.006 19.92f0.01 17.754f0.009 17.48f0.03 15.48f0.05
3.4 f 0 . 0 3 3.28 f 0.09 2.29 f 0.06 3.35 f 0.5 3.17 f 0.08 3.1 f 0.2 3.2 f 0 . 3
0.00 20.00 40.01 60.01 80.01 90.00 100.00
90.97 f 0.02" 51.361f0.004 36.907 f 0.005 28.031f0.006 24.20f0.01 23.75 f 0.02 20.06 f 0.02
3.9 f 0.2 3.44 f 0.05 2.38 f 0.04 2.8 f 0.1 3.24 f 0.03 3.53 f 0.07 3.6 f 0.1
0.00 20.00 40.01 60.01 80.01 90.00 100.00
111.86f0.01 68.485 f 0.005 49.836f0.002 37.59 f 0.01 32.11f0.03 30.97f0.03 25.3 f 0.1
3.31 f 0.06 2.76 f 0.07 2.36 f 0.02 3.5 f 0.3 3.51 f 0.03 3.25 f 0.01 4.0 f 0.4
9f2 55 f 1 194 f 5 1413 f 22 25O
13 f 1 60 f 2 223 f 3 2081 f 10 35O
9 f l 70 f 2 278 f 6 2994 f 48
a D. A. MZLC Innes and T. Shedlovsky, J . Am. Chem. SOC.,54, 1429 (1932); recomputed with new values of viscosity and dielectric constant for water at 25'.
previous paper.z The acetic acid was similar to the material formerly used in this laboratory,* and its molecular weight was taken as 60.053. The sodium acetate solutions were prepared from the Merck Certified anhydrous salt that had been dried at 200" for 2 days. The molecular weight was taken to be 82.04. To suppress hydrolysis, about 1%excess of acetic acid over the acetate concentration was added to the stock solutions of the salt. The apparatus and experimental procedure for preparing the solutions and carrying out the measurements on their conductance was the same as we had used in the studies on sodium chloridez and on hydrochloric acida solutions in the same solvents a t 15, 25, and 35". The electrolyte concentrations covered a range from a fraction to several millimoles per liter or a bit higher for acetic acid in some cases. Five or six concentrations were measured in each experiment and a t least two check experiments were always carried out. I n the work with acetic acid, the stock solutions were freshly prepared to avoid any difficulties that could arise from esterification on storage, and none were found. The Journal of Physical Chemistry
Results and Discussion Sodium Acetate. I n Table I are listed values of the measured equivalent conductances, A, at the concentrations C, in equivalents per liter, for the entire range of solvent composition at 15, 25, and 35". No data are listed for water at 25" since we already had the corresponding value for A. from earlier work.6 Although sodium chloride was not sufficiently soluble in pure 1-propanol for good measurements,z no such difficulty was encountered with sodium acetate. As in our former w ~ r k , the ~ J experimental values listed in the table are representative, being in agreement with other experimental series within 0.02 or 0.03%. These data were analyzed with the aid of a computer, programmed for the linearized Fuoss-Onsager conductance equation6 that we had used for the sodium chloride data and had (3) M. Goffrdi and T. Shedlovsky, J . Phys. Chem., 71,2182(1967). (4) H.0. Spivey and T. Shedlovsky, ibid., 71, 2171 (1967). (5) T.Shedlovsky and R. L. Kay, ibid., 60, 151 (1956). (6) R. M. Fuoss, L. Onsager, and J. T. Skinner, ibid., 69, 2581 (1965).
ELECTROLYTIC CONDUCTANCE IN ALCOHOL-WATER MIXTURES
already discussed.2 The results are thus summarized in the form of the conductance parameters and constants that appear in Table I1 which corresponds to Table I11 of our earlier paper.2 As before, A0 is the limiting equivalent conductance, K Ais the ion association constant, d is the mean ionic diameter in angstroms, S, E', and L are the constants in the Fuoss-Onsager equation, and ob is the standard deviation for the corresponding experimental series of measurements. Judged by the values of UA in Table I1 and AA in Table I, the Fuoss-Onsager equation represents the sodium acetate data with very good precision which was also the case for sodium chloride. However, ion pairing which is relatively insignificant below 60% 1-propanol for both salts is somewhat greater for the acetate than for the chloride with alcohol enrichment of the solvent. I n Figure 1, we show the variation in A. for sodium acetate with solvent composition at the three temperatures. There is a small dip in the curves between 90 and 100% 1-propanol, which however, is too small to be visible on the scale of a subsequent figure, Figure 2. Acetic Acid. The conductance data on acetic acid are given in Table I11 in which Lo is the measured specific conductance times lo3and K is the acetic acid dissociation constant corresponding to each experimental series. The table is otherwise self-explanatory. No data appear for water at 25' since they are known from earlier work (ref a, Table 11). The calculations of the ionization constants, K , were based on the mass action, Onsager conductance, and Debye-Huckel activity coeffi-
4439
I
0
I
1
I
1
20
40
60
80
Wt. per cent
I IO0
I-propanol
Figure 2. h~us. per cent 1-propanol at 25'.
120
90 80
I
0
Figure 3.
I
10
I
t
20
30
I
1
I
t
50 60 70 Wt. per cent 1-propanol
40
I
I
I
80
90
100
Acetic acid in water-1-propanol mixtures.
20-
IO1
1' 0
$0
3b
io
510
Wt. per cent
Figure 1.
6b i o
I-propanol
NaAc in water-1-propanol mixtures.
io
9'0
Id0
cient equations and were carried out by the method described in earlier papers.4J' Since acetic acid is too weak an electrolyte for obtaining reliable values of A0 by extrapolation of acetic acid conductance data alone, Volume 71, Number 13 December 1067
MARIOGOFFREDI AND THEODORE SHEDLOVSRY
4440
Table 111: Conductances of HACin Water-1-Propanol Mixtures 350
25'
15'
10'C
A
104~
10'C
A
A
0.00% n-CaH70H 3.4!106 9.4826 21.039 31.076 41.233 58,965
66.122 42.163 29.058 24.145 21.099 17.785
K = 1.743 x 10-5, L~ = 0.99
x
10-4
(K = 1.753 X lo+)
6.7700 13.103 18.778 25.264 34.540 41.818 48.029 K = 1.687 X
65.646 48.378 40.878 35.503 30.593 27.861 26.076 LO = 2.62 X lo-'
20.00% n-CaH70H 16.027 11.228 6.346 4.853 4.062 3.389
7.7327 18.442 60.259 104.63 150.37 217.57
K = 7.313
x
10-8,
L~ = 1.02
x
10-4
2.7833 5.2390 8.3394 14.331 20.542 35.540 49.944 K = 7.009 x 10-6,
34.149 25.551 20.589 15.954 13.441 10.325 8.772 = 1.91 x 10-4
9.0750 16.492 26.145 39.789 51.940
23.596 17.807 14.304 11.697 10.294
K = 6.659 X lo*, LO = 2.66 X lo-'
40.01% ~ - C I H ~ O H 5.2638 11.885 18.688 27.519 37.329
K = 2.535
x
7.547 5.173 4.165 3.500 2.978
10-6,
L~ = 1.00
x
10-4
1OA
10'C
6.6333 15.204 25.296 32.366 43.071 61.179 76.164 90.330 K = 2.456 x
10-8,
8.802 5.931 4.644 4.125 3.592 3.029 2.723 2.506 L~ = 1.63 x 10-4
10'C
8.3081 18.903 28.728 47.822 61.995 89.803
K = 2.174 X 104c
1OA
9.473 6.383 5.235 4.091 3.595 2.966
LO = 1.36 X lo-' 10a
60.01% n-CaH7OH 8.059 6.506 4.947 4.066 3.642
45.744 70.711 123.93 184.93 230.83
K = 6.375 X 10-7, Lo
=
0.36 X lo-'
6.4421 16.240 26.629 53.525 77.757 91.267 115.09 K = 6.189 X lo+, Lo =
27.377 17.529 13.800 9.818 8.184 7.562 6.754 0.60 X
26.289 53.598 78.555 116.26 149.26 178.89
K
=
5.385 X
16.228 11.471 9.509 7.848 6.929 6.498
Lo = 0.61 X lo-'
80.01% n-CaH7OH 4.101 2.688 2.159 1.621 1.361
5.8942 14,085 21.896 39.574 56.507
K = 7.648 X lo-*, Lo
=
0.20 X lo-'
The Journal of Phyaical Chemistry
6.4285 12.249 21.129 34.600 44.996 60.171 82.675 K = 6.897 X lo-*, Lo =
4.866 3.542 2.725 2.148 1.886 1.641 1.403 0.29 X lo-'
8.0095 26.238 61.577 105.67 192.50
K
=
5.626 3.171 2.090 1.624 1.187
6.630 X lo+, Lo = 0.61 X lo-'
ELECTROLYTIC CONDUCTANCE IN ALCOHOL-WATER MIXTURES
Table I11
444 1
(Continued) 25'
15'-
_ I
104c
10zA
18.743 73.542 108.92 191.17 232.89 K = 1.389 X
6.769 3.486 2.842 2.151 1.951 Lo = 0.088 X lo-'
104c
1O'A
3.1767 16.270 47.041 68.514 92.577
21.972 8.789 5.102 4.176 3.639
K = 3.524 X lo-", Lo = 0.014 X lo-'
104c
-350
1OzA
90.00% n-CsH.rOH 18.630 7.832 39.863 5.522 53.403 4.750 68.634 4.194 90.437 3.707 K = 1.225 X lo", LO = 0.13 X lop4 104c
LO = 0.061 X
102A
12.399 34.186 52.859 109.56 137.90 K = 9.081 x
1O*A
99.99% wC~H.IOH 23.458 2.461 41.910 1.883 62.455 1.514 80.630 1.351 107.04 1.219
K = 1.974 X
11.903 7.197 5.790 4.054 3.594 lo-@,La = 0.12 x 1 0 - 4
104c
103~
78.845 161.32 236.41 328.16 447.78 530.27 K = 1.440 X 10-11,
15.803 11.158 9.175 8.017 6.803 6.180 = 0.067 x 10-4
%
Ao(HC1)
Ao(NaC1)
Ao(NaAo)
Ao(HAC)
0 20.00 40.01 60.01 80.01 90.00 100
362.52 196.40 122.84 73.42 39.69 27.52 22.0
l5O 101.06 50.49 35.43 25.89 21.14 20.19 19.0
69.38 36.44 26.15 19.92 17.75 17.48 15.5
330. 84 182.35 113.56 67.45 36.30 24.81 18.5
0 20.00 40.01 60.01 80.01 90.00 100
426.59 252.43 162.11 96.82 52.02 36.77 2!2.8
25' 126.52 70.12 49.43 35.79 28.73 27.09 22.8
90.97 51.36 36.91 28.03 24.20 23.75 20.1
390.94 233.67 149.59 89.06 47.04 33.43 27.1
48!). 85 310.99 204.86 124.86 68.69 48.08 3!). 8
35O 153.94 92.34 65.33 47.38 37.96 35.34 27.7
0 20.00 40.01 60.01 80.01 90.00 100
8
111.86 68.49 49.84 37.59 32.11 30.97 25.3
447.77 287.14 189.37 115.07 62.84 43.71 37.4
these were found "synthetically" from the corresponding A, values for HCI NaAc and NaCl which are all listed in Table IV for 15, 25, and 35" and are shown graphically in Figure 2 for 25". I n Figure 3 we see the varia-
+
Lq
/
Table IV: Limiting Conductances, A, in H20-1-CsH70Hhiixtures
wt
>
104c
I
ii -3.34
'C
8, = 2.4 x
6 6 03
05
07
09
I./
1.3
15
1.7
Figure 4. Acetic acid in water-1-propanol mixtures.
tion of A, for acetic acid with solvent composition at the three temperatures, and the corresponding values for K and pK are listed in Table V. In the case of a mixed dipolar solvent such as water and an alcohol there is a competition for the proton of a weak acid such as acetic by water dipoles and alcohol dipoles as well as by the anion. There are thus two kinds of "hydrogen ions" that should really be considered rather than just "hydrogen ion" as in the usual mass action expression K = [(H+)(Ac-)]/(HAC) that we had used in our calculations. The process of weak acid ionization may be viewed as taking place in three steps, namely, (1) a force linkage between the acid and a solvent molecule, (2) a Volume 71, Number 13 December 1967
MARIOGOFFREDIAND THEODORE SHEDLOVSKY
4442
Table V : Ionization Constant and pK for Acetic Acid in H20-1-CaOTOH Mixtures a t 15, 25, and 35’ Wt % LCIH~OH
Kis
1.743 x 7.313 X 2.535 x 6.375 X 7.648 x 1.389 x 3.524 X
0 20.00 40.01 60.01 80.01 90.01 99.99
pKii
10-6
KU
(1.753 x 7.009 x 2.456 x 6.189 X 6.897 x 1.225 x 1.974 x
4.759 5.136 5.596 6.196 7.116 7.851 10.453
lo-’ 10-8 lo-* 10-11
I IIO
10-6) 10-6
lo-* 10-8 10-11
In K
-
0 O
I-propanol
x Ethanol
M8thanal
8-
7-
6-
I
I
I
90
80
I
70
Ks
PKU
4.756 5.154 5.610 6.208 7.161 7.912 10.705
(1.728 X 6.659 x 2.174 x 10-6 5.385 x 10-7 6.630 x 9.081 X lo-*
4.763 5.177 5.663 6.269 7.178 8.042
- In
+ (t2/kaDT) = In BE
[HzO]
in which [HzO]refers to water concentration in a mixed solvent, and B X refers to water-solvated ions. Thus a graph of pK log [HzO]should be linear with 1/DT below alcohol-rich solvents. Figure 4 shows such a graph for our values at the three temperatures and is reasonably linear except above 90% and below 40% 1propanol, similar to the finding for ethanoL4 It is interesting to compare the results for pK in methanolwater, ethanol-water, and l-propanol-water solvents and this is shown in Figure 5 , in which the pK values at 25” are plotted against the weight per cent water composition of the solvent. It is evident that the curves are very similar and are in fact much more so than if they had been plotted against the solvent dielectric constant. It would appear that solvent structural considerations play no negligible role in the “ionization” process of acids, but it is not our purpose to delve into this question at present.
+
9-
100
PKU
I
I
I
60 50 40 Weight per cent water
I
I
30
20
I
10
1
0
Figure 5. Plots of pK values us. weight per cent water composition of the solvents.
proton shift from the acid carboxyl group to the bound solvent molecule, and finally (3) the dissociation of this ion pair into its ionic component^.^^^ If these steps involve mass action considerations and mainly coulombic forces, application of the Bjerrum relationship, K = B . exp(e2/lcaDT) (where e is the electronic charge, IC is the Boltzmann constant, D is the dielectric constant, a is the mean ionic diameter, and B is the Bjerrum coefficient), leads with several simplifying assumptions to a linear expression. This expression is
The Journal of Physieal Chemistry
Acknowledgment. We are grateful to hlrs. Catherine Wolowodiuk for her skilled technical assistance throughout the progress of this work and to Mrs. Marion Angel1 for her help in the analysis of our sodium acetate data with the 7090 IBRI computer. (7) T. Shedlovsky in “Electrolytes,” B. Pesce, Ed., Pergamon Press Inc., New York, N. Y., 1962, p 146.
