HERBERTS. HARNED AND F. H. MAXNESTLER
966
summary The heat capacities of the metatitanates of iron, calcium, and magnesium were measured in the temperature range 52 to 298'K. Ferrous metatitanate has a marked "hump" in its heatcapacity curve, the maximum being a t 57OK. There is approximately 0.95 unit of excess entropy in the "hump" above the "normal" curve. The following molal entropies a t 298.16'K.
[CONTRIBUTION FROM THE
VOl. 68
were computed: ferrous metatitanate, 25.3 * 0.3; calcium metatitanate, 22.4 f 0.1; and magnesium metatitanate, 17.8 * 0.1 E.U. Combination of the above entropies with related entropy data yields the following molal entropies of formation of the metatitanates from the respective oxides and rutile: ferrous metatitanate, - 0.4; calcium metatitanate, +0.5; and magnesium metatitanate, - 1.1 E.U. BERKELEY,
CALIFORNIA RECEIVED FEBRUARY 7, 1946
DEPARTMENT OF CHEMISTRY
OF Y A L E UNIVERSITY ]
The Ionization Constant of Acetic Acid in 50% Glycerol-Water Solution from 0 to 90° BY HERBERTS. HARNED AND F. H. MAXNESTLER' The experimental results obtained a t nineteen From electromotive force measurements of the cells, HZ HAC (ml),NaAc (mz),NaCl (mJ, temperatures have been expressed by the equation Glycerol (X),H2O (Y) I AgC1-Ag in which the E = E25 + a(t - 25) + b ( t - 25)' (1) solvent mixture was 50% by weight of glycerol, The constants, a , b and the electromotive force, the ionization constant of acetic acid has been , obtained from the first order five degree determined a t 5' intervals from 0 to 90'. This is E z ~were differences in electromotive forces by the graphical the widest temperature range over which measuremethod described by Harned and N i m ~ . These ~ ments of this kind have been made. are given in Table I as well as the average and maximum deviations between the observed elecExperimental Results tromotive forces and those calculated by the The measurements were carried on in cells and equation. The average deviations are quite by the technique of Harned and Morrison.2 small and the maximum always occurs in the Glycerol purified and analyzed by methods de- higher range of temperature. Although this scribed by us in an earlier communication3 was shows that less reproducibility is obtained from 70 used. The stock buffer solution was prepared by to 90°, the discrepancies are not large and we beneutralizing half the weight of acetic acid taken lieve that considerable confidence may be placed with sodium hydroxide. Water formed in the in the results over the entire temperature range. neutralization reaction was taken into consideraTABLE I tion,in computing its total weight in the cell soluFORCESOF THE CELLS, HI IHAc(ml), tion. The concentrations were: m l = 0.3947, ELECTROMOTIVE (X), WATER( Y )IAgClm2 = 0.3947 and m3 = 0.3997. The cell solutions NaAc(m,), NaCl(ma), GLYCEROL Ag ACCORDING TO EQUATION E = E,, + a(t - 25) + were prepared from this solution. b(t - 25)' Two series of cell measurements were made a t Valid from 0 t o 90"; ml = 0.99992, m2 = 0.98756 ms; given concentrations of cell electrolytes, one = m2 + mr = 2.0125 m2 = 1.9876 ma. A (av.) and A through a temperature range from 0 to 50' and an- p(max.) equal average and maximum deviations of calother from 50 to 90'. After the temperature culated from observed electromotive forces. X = Y = readings were recorded, the cell was brought to 50% by weight. A(av.) A(max.) Em a X 10' b X 10' Ir 25' for the low temperature series and to 50' for 0.61131 6 . 5 5 -4.00 0.05 0.21" 0.02234 the high temperature series. Excellent recovery .lo .44" ,59756 6.06 -2.25 ,03805 values were obtained a t 25'. Recovery values -2.00 .05 ,58231 5.50 .19" ,06878 a t the higher temperatures were not so good but ,56972 5.04 -2.00 .05 .13* .11281 were considerably better for these celk-containing .04 .13" ,56393 4.82 -2.50 ,14211 a buffered solution than for those containing only ,55727 4.59 .05 .15b .18439 -2.35 hydrochloric acid.3 Since the cells were run in a At 90". At 50". At 60". triplicate a t six concentrations, eighteen recovery checks at 50' were made. Of these four were Constant and Derived Thermowithin 0.1 mv. and sixteen within 0.3 mv. of the The Ionizationdynamic Quantities initial values a t this temperature. The ionization constant was determined by (1) This communication contains material from a dissertation preusing the equation of the cell in the form6 sented by F. H.Max Nestler t o the Graduate School of Yale Uni-
I
versity in partiaI fulfillment of the Degree of Doctor of Philosophy, June, 1943. (2) Harned and Morrison, A m J . Sci., 33, 161 (1937). (3) Harned and Nestler, THIS J O U R N A L , 68, 665 (1946).
(4) Harned and Nims, ibid., 64, 423 (1032). ( 5 ) Harned and Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Corporation, New York. N. Y.. 1943, P . 497.
June, 1946
IONIZATION CONSTANT OF ACETICACIDIN GLYCEROL-WATER SOLUTION
YHAOYCIlog YAC
- log K ;
(2)
E is the electromotive force of the cell, Eo its standard potential, K A the ionization constant and mHAc etc., Y H A ~etc. are the molalities and activity coefficients of the species denoted by the subscripts. Since the activity coefficient function is unity a t infinite dilution and very close to unity at all ionic strengths employed, the plots of the left side of the equation or (-log K 6 ) wrsus the ionic strength are nearly horizontal straight lines. The slopes of these plots are given in Table 11. We note that the activity coefficient function, log (YHA~YCI/YAJ changes sign with variations of temperature. As a result the extrapolation to zero ionic strength where (- log K& = o equals (-log Ka) can be carried out graphically with a high degree of accuracy. The values of Eaemployed are given by the equation3 Ea = 0 18392 - 7 45 X lo-' (t
- 25) - 3
X lo-' ( t
- 25)2 (3)
TABLEI1 IONIZAT~ON CONSTANT K O = 5 379 X lo-'; TO= 304 3 " ; AKA = (KA(ca1cd ) K A obs )) X loo a is slope defined by equation: -log = -log KA a# KA (obs.) AKA a x 10-0 x l@
+
0 5 10 15 20 25 30 33 40 45
0 070 06.5 060
060 035 050
045 040 035 030
4.778 1.960 5 097 5.222 5.316 5.352 5.378 9.373 5.330 5.270
+0.007
-
+ -
+ -
-
+ +
,001
,007 ,003 ,013 ,004 ,001 ,004 ,003 ,005
50 55 BO 65 70 75 80 85 90
0.020 013 ,010 ,005 ,000 - ,015 ,020 ,025 - .030
-
5.184 5.068 4.951 4.806 4.6.54
4.475 4.315 4.137 3.935
+0.004 ,011 ,003 ,005 ,002 ,010 - ,008 ,012 - ,004
+ + + + + -
The results of this computation are compiled in Table 11. The ionization constant as a function of temperature may be expressed by the equation A* log Kr = - - + D* - C*l' (-1 T
967
which was shown by Harned and R ~ t i n s o nto~ be -~ valid for many weak electrolytes over the temperature range from 0 to 60'. Analysis of our results indicates that this equation may be employed successfully from 0 to 90'. In other words, the results are not sufficiently accurate to show a deviation from a quadratic function for the variation of the free energy of ionization with the temperature. The standard free energy, heat content, specific heat and entropy of the ionization reaction as functions of temperature can be calculated by the equations A T = A' AH: = A'
+ D ' T + C'T2 - C'T2
AC;, = -2C'T ASP = D' -2C'T
(5) (6)
(7) (8)
where A', D' and C' equal 2.8026 R times A*, D* and C*. The maximum value of K A denoted K O and t h e , temperature TOa t which K A is a maximum may be calculated by the functions To = (d*/C*)'/z log KO = D* - 2(C*A*)'/r
(9) (10)
The constants of equation (4),obtained by the method of least squares, are A* = 1321.4256, D* = 3.4148 and C* = 0.014268. Table 11 contains the deviations of the observed from the values calculated by equation (4). The average deviation in A K A X lo6 is 0.006 which is less than 0.2% in KA. Summary 1. The ionization constant of acetic acid in 5OyOby weight glycerol-water solutions has been determined from 0 to 90' by means of cells without liquid junctions. 2. The results may be expressed within the accuracy of the method by an equation which is a quadratic in temperature for the free energy of ionization. NEWHAVEN,CONN
RECEIVED MARCH 6, 1946
(6) Harned and Robinson, Trans F a r o d i r S O L ,36, 673 (lY40 . see also Harned and Owen, ref 5 p 583
