EXPERIMENTAL STUDIES O F T H E IONIZATION OF ACETIC ACID' HERBERT 5. HARNED Department of Chemistry, Yale University, New Haven, Connecticut
Received October 1.8, 1938
From measurements of the electromotive forces of cells without liquid junction of the type
Hg 1 HAc(ml), NaAc(m), NaCl(m), X % solvent-Y% H20 I AgC1-Ag we have succeeded in obtaining accurate ionization constants of acetic acid in aqueous solution (3), in some methanol-water mixtures (5), and in 20,45, and 70 per cent dioxane-water mixtures (6). These determinations ' to 50°C., so that were extended to cover a temperature range of from 0 they constitute the most extensive, accurate determination of a n ionization constant of a weak electrolyte as a function of the temperature and of the dielectric constants of the solvent media. The values of the ionization constant in dioxane-water mixtures determined by Harned and Kazanjian (6) were preliminary, and depended on standard potentials of the cells derived by the Debye and Huckel theory without the use of extended terms. These have been reevaluated (1, 2) by the more refined method, and final values of the ionization constant have been computed. Because of the value of results of this kind as an experimental contribution to the statics and kinetics of ionization reactions, i t seems appropriate to give a resum6 of the final results and an estimation of their accuracy. I n addition the heat content, the heat capacity, and the entropy of the reaction have been computed. THE IONIZATION CONSTANT
Table 1 contains the revised values of the ionization constant K in dioxane-water mixtures containing 20 per cent, 45 per cent, and 70 per cent by weight of dioxane. No revision has been made of the values obtained by Harned and Ehlers (3) in water and by Harned and Embree ( 5 ) in methanol-water mixtures. Presented at the Symposium on Intermolecular Action, held at Brown University, Providence, Rhode Island, December 27-29, 1938, under the auspices of the Division of Physical and Inorganic Chemistry of the American Chemical Society. 275
276
HERBERT 8 . HARNED
The absolute accuracy of these results is difficult to estimate, since uncertainties arise not only in the extrapolation which yields the required standard potential of the cell, but also in the extrapolation from which the ionization constant is obtained. At 25°C. an error of 0.1 millivolt in the extrapolated electromotive force corresponds to an error of 0.002 and 0.003 in (- log K ) , or an uncertainty of 0.5 to 0.7 per cent in the value of K. In aqueous solutions where the extrapolations are more certain, TABLE 1 Ionization constant o j acetic acid i n diozane-water miztures X = per cent of dioxane by weight: D = dielectric constant 1lN
'c. K X 1W
D
69.2 67.4 65.7 64.0 62.4 60.8 59.9 57.7 56.3 54.8 53.4
0
5 10 k5 20
25 30 35 40 45 50
4.75 4.87 4.98 5.05 5.09 5.11 5.08 5.03 4.95 4.86 4.73
D
K X la
44.3 43.0 41.9 40.7 39.6 38.5 37.4 36.4 35.4 34.4 33.4
D
4.78 4.89 4.96 4.96 4.96 4.93 4.86 4.75 4.61 4.44 4.28
K X 10'
20.4 19.8 19.2 18.7 18.2 17.7 17.2 16.7 16.3 15.8 15.4
4.75 4.83 4.89 4.83 4.83 4.78 4.69 4.56 4.42 4.22 4.05
TABLE 2 Parameters and constants of eowrtion 1 MLVENT
PER CENT ET WEIQET OS" METHANOL OR DIOXANE
Water. , . . . . . . . . . . . . . . . Water-methanol . . . . . . . Water-methanol . . . . . . . Water-dioxane . . . . . . . . . Water-dioxane . . . . . . . . . Water-dioxane . . . . . . . . -
10 20 20 45
Km
5.2456 5.0959 6,9207 6.7073 7.6951
e
LOG
22.6 27.0 31.5 24.6 15.26 10.42
Km
- p@
5.1945 5.0585
6.8710 6.7073 7.6951 9.6868
2pB
0.00226 0.00270 0.00315 0.00246 0.001526 0.001042
the error in the determination of K is of the order of f 0.2 per cent. In the other solutions the error is estimated to be not less than f 0.3 per cent and not more than f 0.7 per cent. The uncertainty increases ~ t h decrease in the dielectric constant. The experimental results may be expressed accurately by the simple equation of Harned and Embree (4), namely, log K = [log K,,, - p821
+ 2pet - ptz
(11
277
IONIZATION OF ACETIC ACID
where K,,, is the value of K a t its maximum, 0 is the temperature a t which K is a maximum, p has the value of 5 X deg.-2, and tis the Centigrade temperature. Values of the paqameters and constants of this equation are given in table 2. The maximum deviation between the observed values and those calculated by this equation is 0.004 in log K and occurs in the cases of media containing 45 per cent and 70 per cent of dioxane. The average deviation is 0.002 or less. This is approximately the estimated accuracy of the experimhtal values. HEAT CONTENT, HEAT CAPACITY, AND ENTROPY CHANGES
The changes in heat content and heat capacity accompanying the reaction are given by the equations
AH
= -4.575
A C ~= -4.575
x x
1 0 - 4 ~ y t- e)
+
(2)
1 0 - 4 ~ ( ~2 (t
- e))
(3)
derived by the differentiation of equation 1. The changes in free energy and subsequently in the entropy may be obtained from the customary fundamental thermodynamic relations, AF = - 2.3026RT log K
(4)
Values of these quantities at 25°C. are given in table 3. TABLE 3 Free energy, heat content, heat capacities, and entropy changes at W C . 1 0OLYENl
PERCENT R',","," OFYETH-
j
'
I
I
I D
'/____I___ DIOXANE Water, . . . . . , . . . . . . . . . , Water-methanol . . . . . , . Water-methanol . . . . . . . . Water-dioxane . . . . . . . . , , Water-dioxane . . . . . . . . . . Water-dioxane . . . . . , . .
10 20 20 45 70
ACd
(-AS)
calories
calorisa
41.3 40.1 38.9 40.8 43.3 44.6
22.1 22.2 22.4 24.3 30.2 40.1
(-
.-
78.5 74.0 69.2 80.8 38.5 17.7
6930 7216 8600 11347
264 -16 -394 -594
The determination of AF is accurate and the error in its estimation is less than 0.1 per cent. Owing to the difficulties of determining a quantity by differentiation, the values of A H are subject to a large error, estimated to be of the order of 100 cal. It is possible that by using the same function (equations 1 and 2) the relative error is less than this. In any case, the
278
HERBERT 8. HARNED
increase in AH with increasing alcoholic content and the decrease with dioxane content of the solvent have a real significance. The error in A S is determined by the error in AH and amounts to approximately 0.3 cal. The absolute value of (-AC,) is probably known within f 3 cal., but the relative error is less than this, and the tendency of this quantity to decrease in the alcoholic solutions and to increase in the dioxane solutions is real. The temperature, e, at which the maximum of K occurs is known within 2°C. in all cases, and probably within a narrower limit than this in most cases. These estimates are approximations designed to show how much confidence may be placed in these results. This method of computation gives the best results in the middle temperature range and should be reliable from 10” to 40°C. VARIATION OF IONIZATION CONSTANTS WITH MACROSCOPIC DIELECTRIC
CONSTANT
This method measures the sum of the concentration of free protons, hydronium ions, and solvated protons which we represent by mH. The principal reaction is certainly HAC + HIO S HsO+
+ Ac-
since even in the 70 per cent dioxane mixtures the mole fraction of water is of the order of 0.7. Evidence for this conclusion may be derived from the studies of hydrochloric acid in these mixtures both by conductance and by electromotive forces. The latter may be computed by the extended Debye and Huckel theory by employing the same mean distance of approach of the ions, a, at all temperatures from 0” to 50°C. in 70 per cent dioxane solution as in water (2). Conductance measurements give, according to Bjerrum’s theory of ionic association, a value for “a” of 6b. in 82 per cent dioxane mixtures, whereas 5.6b.fitted the electromotive force measurements in the 70 per cent solutions. This is not direct evidence, but it shows that the results may be computed on the assumption that the same species of solvated ion is predominant in all the media. Transference number data may help to elucidate this question. I n figure 1, log K - log K Ohas been plotted against the reciprocal of the dielectric constant. K Oand K are the values of the ionization constant in pure water and in the water-solvent mixtures, respectively. The lower curve represents the variation of the ionization constant of acetic acid, ( m H r n A c / m ~ o ) rin - Odioxane-water mixtures (circles), Values of this quantity in methyl alcohol-water mixtures are indicated by crosses within squares. For purposes of comparison, log K O- log K (derived from ~ ~ Mivent, ol recent results2)of the ionization constant of water, r n ~ r n o ~ l a purr
* Measurements of suitable cella by Mr. Leslie Fallon in this laboratory.
IONIZATION OF ACETIC ACID
279
is shown in the middie curve. The top curve is a similar plot for where N H l 0 is the mole fraction of water. This quantity may be used as a rough estimate of m H m H . ~ H ~ ~ N H ~ O / U J & punO lolvant, ]
1/D
FIG.1. Plots of log K O- log K versus 1/D in dioxane-water mixtures in methanol-water mixtures
m=l 11, H
in dioxane-water mixtures pure solvent
1
WHNH~O
- aH,O
punsolvent
in dioxane-water mixtures
280
HERBERT S. HARNED
There are a few conclusions apparent from this plot: (1) The plots possess a distinct curvature. (2) The extent of the variation of the ionization constant of water is of the same order of magnitude as the variation of the ionization constant of the acid. On the other hand, since the scale of the figure is not large, the difference is considerable and may be measured accurately. The reaction for the water ionization may be assumed to be
HzO
+ HzO e H30f + OH-
so that the difference between the water and acetic acid curves corresponds
to the variation in the logarithm of the equilibrium constant of the hydrolysis reaction, Ac-
+ HzO $ HAC + OHSUMMARY
1. Revised values of the ionization constant of acetic acid in dioxanewater mixtures have been tabulated. The probable accuracy of the results has been estimated. 2. The results have been expressed as a function of the temperature by the approximate equation
log K - log K ,
=
p ( t - e)?
(1)
and the parameters K , and 0 have been tabulated. 3. Values of AH, ACp, and A S of the ionization reaction a t 2 5 T . have been tabulated. The probable errors of their determination have been estimated. 4. The variation of the logarithm of the ionization constant with the reciprocal of the dielectric constant has been discussed and contrasted with a similar variation of the ionization constant of water. REFERESCES (1) HARNED:J. Am. Chem. SOC. 60, 336 (1938). AND CALMON: J. Am. Chem. SOC. 60, 2130 (1938). (2) HARNED (3) HARNED AND EHLERS: J. Am. Chem. SOC.64, 1350 (1932); 66, 652 (1933). (4) HARNEDAND EYBREE:J. Am. Chem. SOP.66, 1050 (1934). (5) HARNED AND EMBREE: J. Am. Chem. SOC 67, 1669 (1935). (6) HARNED A N D KAZANJIAN: J. Am. Chem. SOC. 68, 1812 (1936).
