HERBERTS. HARNED
336
Vol. 60
[CONTRIBUTION FROM THE DBPARTMENT OF CHEMISTRY OF YALEUNLVEWTTY ]
The Thermodynamics of Hydrochloric Acid in Dioxane-Water Mixtures from Electromotive Force Measurements. 111. Extrapolations According to the Gronwall-La Mer Extawion o€ the Debye and XuckeI Theory BY H E ~ E RS.TIEARNED
In the introductory contributions to the study of the thermodynamics of hydrochloric acid in dioxane-water mixtures, Harned and MorrisonlJ have shown that the electromotive force measurements of the cells Hz 1 HC1 ( m ) , X% Dioxane, Y% H201 AgC1-Ag may be obtained with an accuracy comparable to that obtained in water, and described a technique by which this result could be accomplished. They obtained measurements of these cells in 20, 45, and 70% dioxane-water mixtures of which the dielectric constants were approximately 60, 40, and 20, respectively. The acid concentrations were from 0.003 to 0.1 M , and the measurements were made from 0 t o 50” a t 5’ intervals. A first approximation of the standard potentials oE the cells was made by means of the Debye and Huckel
of higher dielectric eonstant (D>sO), the results afford an excellent illustration of the effect afthe extended terms. Extrapolations at 25 “.-The extrapo€ations were carried out by empIoying the function E’, defined by E’ = E
+ 2k log, m - 1 +2 Ak v 4%
- 2k
E‘e
+ f(m>
log (1
+ 0.002 Gom) (1)
E is the observed electromotive force of the cell, k equals 2.3026 RTIF, u is the universal constant of the Debye and Huckel theory, A is the parameter
which involves the apparent ionic diameter, 0 , GOis the mean molecular weight of solvent (ref. I, Eq. e), and E; is the standard potential of the cell. E’ was first calculated using a preliminary value for the apparent ionic diameter, a. Then the: value of the Gronwall, La Mer, and Sandved correction, 0.16400 E’ (5.5K.) corresponding to this value of “a,” E’ (5.4w.) was computed from their functions E‘ ( 5 . 3 A . ) and their Table 5 . This quantity E’ - E E X (5,5A.) multiplied by 2 k shall be designated 0.18350 E’ - EEX (5.4A.) EEX,since it is the contribution to the Y E ’ - E E X (5.3K.) electromotive force corresponding to the extended terms of the theory. The functions E‘ and E‘ EEX were plotted, and if E’ E E X was not (5,OA.) constant a t the lower concentrations - E E X (5.0A.) (m>0.02 M ) , another value of “a” 0 0.01 0.02 0.03 0.04 0.05 was employed. This process was rem. peated until such constancy was obFig. l . - S t a n d a r d potential extrapolation a t 25” of the 20% and 45% di- tained. With a little experience this oxane-water mixtures: 0(20’%) = 60.79, 0 ( 4 5 % ) = 38.48. method of arithmetical approximation could be accomplished in two to three trials. limiting law without the refinement of the exBoth E’ and E‘ - EEXequal the standard potentended theory of Gronwall, La Mer and S a n d ~ e d . ~ tial of the cell, E:, when m equals 0. Values of c I n the present communication the results have employed to compute E’ were obtained from the been reexamined from the point of view of the data of Harned and C alm~n.~ extended term theory and a slight revision of the The method of extrapolation is clearly shown in standard potentials has been made. In the media Fig. 1. The group of six curves a t the top of the (1) Harned and Morrison, THISJOURNAL, 68, 1908 (1936). figure represent the values of E’ and E’ - E,, of (2) Harned and Morrison, A m . J . Sci., 33, 162 (1937). (3) Gronwall, L a Mer and Sandved, Physik. Z.,29, 358 (1928); the 4570 dioxane-water cells a t 25’. The three La Mer and Parks, THIS JOURNAL, 63, 2040 (1931); Cowperthwaite
I
-
Rnd La Mer, i b i d . , 6S, 4333 (1931).
( 4 ) Harned and Calmon, ibid., 60,334 (1938).
Feb., 1938
THERMODYNAMICS OF HYDROCHLORIC ACIDIN DIOXANE-WATER
337
top curves are plots of E‘ versus m, and the three lower curves are similar plots of E’ - E E x for values of “a” equal to 5.5, 5.4, and 5.3 respectively. \ve note that when “a” equals 5.4 E‘ - EEX becomes constant a t the lower concentrations.
theless, a single illustration of an extended theory extrapolation in 70% dioxane-water mixtures is shown in Fig. 2 . The four upper curves are plots of the function E‘, and the lower curves similar plots of E’ - E E X zlersus nz a t the designated values of “a.” Vi‘e note that the values of E’ - E E X a t 6.1 A.are constant a t concentrations from 0.01 to 0.003 11. The extended correction is about 3 mv. a t its maximum. Upon E’ (6.5 A.) examination of these curves, it becomes evident that results must be obtained at concentrations E’ - E E X (6.5&) below 0.003 AI before the extrapolation can be accomplished with certainty. For this reason, E‘ (6.2 we have discontinued these computations until E’ (6.1 4.) we have ascertained whether results of sufficient E‘ (6.0 A.) E’ - E E X(6.2i.) accuracy in very dilute solutions may be obE’ - EEX(6.1 {.) tained. E‘ - EEX *‘) The temperature effectof the extended theory is illustrated in a striking manner by Fig. 3 in 0.0 0.01 0 02 0.03 0.04 0.05 0.06 which the three top curves represent plots of the m. deviation of the Debye-Huckel function a t 0, Fig. 2.-Standard potentialextrapolation at 25’ of the 70% di25 and SOo, respectively. These plots of E‘ oxane-water mixtures: D = 17.69. EA against m show the maxima characteristic of The curves when “a” equals 5.5 and 5.3 A. have the extended term deviations and the increasing slopes of opposite sign. The result a t 5.4 A.was magnitude of the effect with increasing temperaemployed for extrapolation. This method was ture. The three lower curves, the plots of E‘ employed for all the results of the 20 and 45% E; versus WZ, show how the extended mixtures. The two lower curves in Fig. 1 o.oo15 illustrate the behavior of the 20% dioxane-water mixtures a t 25”. I n this case the dielectric constant of the mixture is 60.79 and conse- 0.0010 quently the extended term effect is considerably smaller than in the case (E’ - E;) (500) of the 4570 mixtures of dielectric 0.0005 constant 38.48. The results as illusE‘ - E ; (25’) trated in Fig. 1 are a good confirmation of the extended term theory. E’ - E‘ (0’) The results in media of dielectric O.OOOO E’ - E E X - EL (0’) constant greater than 30 are not comE‘ - E E X - EA (25’) plicated by effects of incomplete ionization. Conductance measurements 0 0.01 0.02 0.03 0.04 0.05 m. E‘ - E E X (50”) carried out in this Laboratorv indicate practically complete ionization Fig. 3.-Temperature effects on the extrapolation functions, E‘ - EL and
A., A.,
4.)
E‘
- E;
- E E x : X = 45; Do
( K > 1). On the other hand, the ionization constant of hydrochloric acid from conductance measurements in TOYc dioxane-water mixtures of dielectric constant 17.69 is found to be approximately 0.006, and consequently some doubt is present of the validity of the usual method of applying the extended term corrections. Never-
44.28;
0 2 6
= 38.48; Djo
33.43.
term theory takes care of these deviations. We note that in order to apply this method, values of “a” which decrease with increasing temperature are necessary. 5.7, 5.4 and 4.7 A. were employed a t 0, 25 and 50”, respectively. There is some doubt about such a trend in “a”
HERBERTS. HARNED
338
x
TABLE I VALUES OF EXTRAPOLATION FUNCTION, E'
x
= 20'
m
qso
00
0.000 ,003 ,005 ,007 .01 .02 .03 .05
(0.20303) .20298 ,20304 ,20303 ,20305 .20305 .20291 .20265 60.79
(0.18946)
D
Vol. GO
450 2.59
50'
(0.16358) .16357 ,16358 .16359 ,16361 .16360 .16345 .16325 38.48
....
.18957 ,18948 .18937 ,18932 .18932 .18934 44.28
- EEX
3
(0.13282)
.... ,13288 ,13283 ,13282 ,13286 ,13274 ,13244 33.43
x
= 705
m
250
0.00000 ,00316 ,00519 ,00645 ,00961 ,01927 ,03203 ,05633
(0.06472) ,06471 ,06473 ,06474 ,06477 ,06465 ,06415 ,06342 17.69
From results smoothed to round concentrations. * From original electromotive forces. (Values of dielectric constants and limiting slopes are given in Table 11, Harned and Morrison.')
since the extrapolation has been made without consideration of other parameters such as the one which corresponds to the change in dielectric constant of the medium caused by electrolyte addition. The accuracy of estimating E,' by this method is shown by the results in Table I. E' - E E X is given a t some concentrations for the cases illustrated in the figures. The values a t m equals 0 are the standard potentials as estimated. In most cases, the numerical uncertainty in this estimation is very small and of the order of a few hundredths millivolt. The worst result of all is the one a t 0" in column three where the results a t the lowest concentration show a trend which indicates an error. However, the uncertainty is not greater than *0.07 mv. The last row in the table contains values of the dielectric constant, D.
The Standard Potentials Table I1 contains the standard potentials derived b y this method of extrapolation. The second and fourth columns give the values "a" necessary to render the extrapolation function, E' - E E X , constant a t the lower concentrations (m
