2032 After that time, all but 5 ml. of the solution was removed, and replaced by the 2% ml. of the original solution, the mixture shaken for twentyfour hours, the supernatant liquid removed and the process repeated once more. Knowing the volmes used and the bromide concentrations in the supernatant liquids, the amounts of bmmide ipI the precipitate could be calculated. The results are given in Table I V .
The vahfes obtained aftev three weeks of shaking are higher as tho Systein terids to approach equilibrium.
Summary The rapid formation of mixed crystals q m n shaking of a solution containing chloride and b r m i d e with well aged silver chloride cantlot be attributed to a: nortnal recrystallization of the solid by way of the solution. Expairhentally, TABLE IV it has been shown that the rate of distribution REPEATED ADDITIONOF BROMIDE TO A YEAROLD AgCl increases with increasing ratio of bromide in soluMiltinides Bf Period of Br- X lo' in precipitae K' to silver in the precipitate. When this ratio tion Step shsklng A B A B A B is very small the rate of distribution of bromide 1 24. h n . 2.72 4 . 9 7 0.439 0 . 3 9 1€0 107 2 24 hrs. 3 58 6 . 4 6 ,858 .74 175 164 is determined by the speed of recrystallization 3 24 hrs. 8 . 9 8 1 . 2 4 1 . 0 4 187 113 5.15 of the silver chloride by way of the solution. The 4 24hw 6.42 10 92 1.60 1.29 205 k85 5 24 hrs. 7 . 5 8 12.85 2.07 1 . 7 5 249 233 great initial speed of distribution folund when the 6 3 weeks 6 . 3 3 10.95 2 . 1 3 1 . 8 4 316 292 ratio of bromide to silver is larger is attributed to 7 24 hrs. 21% LQ.37 2.39 8 24 hrs. 11.03 2 64 247 a direct attack upon the structure of t h original particles. It is assumed that the bromide rapidly The values of K' obtained after each su~cessive taken up in the surface layer by exchange causes step of shaking f6r bwemty-four hows increase of the silver chloride lattice, exposing a disrupture g r a d d l y , showing that the kinetks of the t a c fresh surfaw to attack. tion after each new additbn wf hrom3dde afc of the same order. MINNEAPOLIS, MI". RECEIVED J U N ~14, 1937
[CONTRlBUTIONFROM T X E
DEP~~ME OFN CH TEMISTRY
OF YALE UNIVERSITY]
The Ionic Activity Coeficient Product and Imization of Water in Bariuiti Chfdride Solutions from 0 t o 50" B Y HERBERT 5. H A R N E D
Electromotive forces of the cells H2 1 BFL(OH)~ (0.005), BaClz (mz) I AgC1-Ag H P 1 HCI' (0.01), BaCb (%I) IdgGI1-Ag
(A)
03) h w e been obtained over the range 0 to XI6, and 0.03 to 3,u. Following the methods empl'oyed in this Laboratory,2-6 we have computed: (1) the standard potentid of the silver-silver chlorfde electrode from 0 to 50'; (2) the ionization constant of water from 0 to 50' ;(3) the activity coefficient of hydyochloric acfd in barium chloride solutions; (4) the ionic activity coefficient of water in barium chloride solutions; (5) the ioni(1) This contribution contains material from a disserialion presested b y Charles G Geary to the C2ratiuat.e School 08 Yale University in partial fulfilment of the requirements for the Degree of Doctor of Philbsophy, June, 1937 (2) Harned and €%tamer,THE ~ O U R N A L ,65, 3194 (1933). ibad, 66, 4496 (1933). (3) Harned and Copson, t b t d , SS, 4496 (1933) @$ Harned and Mamweiler, rbid , 67, 1873 (1933) (5) Harned and Donelson, * b i d , 69, 1280 (1937). (6) Harned and Mason, tbtd , 54, 3112 (1932).
AND
CHARLESG. GEARY~
zation of water in barium chloride solutions: (6) the relative partial molal heat content of hydrochloric acid in barium chloride solutions; (?) the heat of ionization of water in aqueous solution and barium chloride solutions,
Experimental Results The cells,were fun in triplicate and in two series a t 5" intervals, from 0 to Xi', and from 2B to 50°, so that a t 25', there were six check6 of the eketrodes used, and two on the cbmpositiom of each solution. Reproducibility was in general Mter than *0.06 mv., while the maxitnwm cEevi&ion was about *0.1 mv. The measurements were corrected to one ahmosphere of hydrogen by means of a specklb bab3e prepared for this purpose. The vapor preswes of the s o l d o n s wexe debermined (assuming the effects of 0.01 M hydzochloric acid and O.O&M
Oct., 1937
IONIZATION OF WATER M
barium hydroxide to be negligible) from the electromotive force measurements on barium chloride solutions, by the method of Harried,' using the data of Newton and Tippetts.8 The calculated values were in good agreement with those measured directly by Newton and Tippettsg and with the activities over the entire range as calculated directly from the data of Tamrnann'O The ratio p / p , was approximately constant throughout the temperature range, so that the vapor pressures of the solutions could be interpolated directly from a table of vapor pressures of water, by using the approximate relation l/To = 1/T k, or, less accurately, t = to k' where t is the temperature of the solution, to that temperature at which water will have the same vapor pressure, and k and k' are constant for each composition over the whole range from 0 to 50'. The electromotive forces were corrected to round temperatures by plotting on a large scale against T. They were also corrected to suitable round concentrations by the usual methods.
+
+
TABLE I ELECTROMOTIVE FORCES AT 25' OF CELLS(A) CONSTANTS OF EQUATION (1) P
0.03 .05 .07 .I .% .R
.7 1
2 c)
a' X 10,
E'S
1.04983 1.02783 1.01597 1.00444 0.98339 .9562(t ,94599 ,93482 ,91156 . 896033
0.52 .5l
12 - ti4 -154 - 186 -216 -284
.40 , :12
0.11
.(J
.It
.(IT'
,(I3
,ox
.02
.48
.(I
.o
. lli
- ,4
.t'x
25' 01; Cli1,IS EQUATION (2)
ELIICTROMOTIVE F O R C E S AT
CONSTANTS O F P
E.25
0.01 .02 .03 .05 .07 ,1 .2 .5 .7 1
0.46411 .45273 ,44529 ,43539 ,42864 ,42135 .40686 .38659 .37854 .36936 .34844 ,33280
2 3
a" X 10' b" X 106
178 142 117 85 65 42 0 - 52 7 74 - 97 -142 -174
0.04 .04 .03
.07 ,07 .10 , 09 , 00
-3.20 -3.15 -3.12 -3.12 -3.01 -2.96 -2.70 -2.33 -2.30 -2.20
,(I4 , 0.1 , l)4
,
-2.00
-1.63
(7) Harned, THIS JOURNAL, 44, 252 (1922). ( 8 ) Newton and Tippetts, ibid., 56, 1678 (1934). (9) Newton and Tippetts, ibid., 68, 280 (1936). (10) Tammann, Ann. Physik, 24, 549 (1886).
0.10 .05 .05 .06 .05 .07 .04 .08
.07 .07 .05 .07
E A = E,b f a'(t
- 25) f
EB = E;, f a"(t
- 25)
b'(t
- 25)*
+ b"(t - 25)'
(1) (2)
the constants of which are given in Table I. In the last two columns of the table are given the maximum and average absolute values, Amax. and A of the deviations between the observed and calculated results. The ranges of validity of the equations axe from 0 to 50'. The Standard Patential of the Silver-Silver Chloride Electrode from Cells of Type B The extrapolation of the measurements of the acid cells was made by a modification of the usual method. The equation for the electromotive forces of these cells, EB, may be expressed EB = Eo
- k'T log 0.01 (2ml + 0.01) - 2kT log 3 726
- 2k'T log
(3)
72s
where k' equals 2.3026RIF or 0.00019841, and y is the activity coefficient of hydrochloric acid in the barium chloride solution. Using an empirical equation suggested by the theory of Debye and Hiickel, log 7 2 6 may be expressed by log
716
=
-
in which the isothermal constants u, A , and B may be evaluated approximately as 0.5, 1.4 and 0.0533, respectively. Combining equations ( 3 ) and (3) and rearranging, we obtain EB
+ 0.01) -_ + k'7' log 0.01(2ntl (O,O1)p
+
2k,l
04
,m (u)
Arnut.,~tlv.A a v . , r t ~ v , '
2033
Since the original results were so numerous, they have been expressed by the equations
b' X 106 Amax.,mv. bav.,mv.
170 92 6(1
--;I;HJ
BARIUMCHLORIDE SOLUTION
0.02 .02 .02 .01
.02
.02 .01 .02 .02
.03 .02 .02
Plotting the left side of this equation against p , the intercept becomes EO 4 k'T. This method worked most favorably a t 25 O where the plot for low concentrations was almost horizontal. At the lower temperatures, there was a slight curvature upward but the extrapolation could still be made with confidence. At the higher temperatures, the plot showed considerable curvature downward and the extrapolation was more uncertain. But here also the points showed a tendency to scatter so no attempt was made to refine the procedure. The values of Eo obtained by this procedure differed from those obtained by Harned and Ehlersl' from the cell containing
+
(11) Harned and Ehlers, THISJOURNAL, 65, 2179 (1933).
HERBERTS. HARNED AND CHARLES G. GEARY
2034
hydrochloric acid only by the amounts: -0.07, -0.13, -0.09, -0.06, -0.03, +O.Ol, 0.05, 0.1, 0.15, 0.18, 0.29 millivolts a t 0, 5, 10, 15, 20, 25, 30, 35, 40, 45 and 50°, respectively. This agreement is good since the present extrapolation involves an uncertainty due to the discontinuity in composition of the solutions. In the subsequent calculations, the values of Harned and Ehlers were employed.
+
+
+
+
+
The Ionization Constant of Water Since the equation of cell (A) may be written, EA
RT 2m RT YHYOH - EO + I n 2 = - InF 0.01 NF UH%O RT
NF In YHYCI - %In
K
(6)
K may be determined by plotting the left side against the ionic ~ t r e n g t h . ~ -The ~ values obtained are contained in Table 11. Along with these are given the independent determinations of K obtained by Harned and Hamer,2 Harned and M a n n ~ e i l e r and , ~ Harned and Donelson5 a t the temperatures designated. The first result seems to be somewhat high a t the lower temperatures as indicated by parentheses while our values of K from 0 to 10' inclusive are slightly low. At temperatures from 20 to 50' inclusive, the agreement is excellent with the exception of the result at 40' obtained from silversilver bromide electrodes. In the next to last column, the mean of the results with exception of those in parentheses is given. These values differ only a little from the mean of all the results. This is indicated by the numbers in parentheses following these values which represent the change which occurs in the last two places upon averaging all the results. In the last column is given the total deviation of the values of K calculated to millivolts, which is a good method of showing the accuracy. At the three lower temperatures, the spread is such as to show that the results in parentheses are in error. TABLE I1 THEIONIZATION (~ O N S T A N TOF WATERFROM 0 K X 10' t
Ref. 2,3 Ref. 4
0
10
(0.115) 0.1134 ( ,186) ,1850 ( ,293) .2!319
15
( ,432)
.4*;0;1
20
.6Xl 1.008 1 4il 2 088 2 916 4.016 5,476
,6806
5
25 30
35 40 45 50
1 007 1 470 2 091 ? 814
4.017 5.482
m
i
?.OR8 (2.891)
.... .. ..
(
I
.zsoo)
mo(1.v
.4500 ,6813
.4J03(07)
CIOU
1 466 2 090 2
wn
4.023 5.465
.68011
1.008 1 468 2 080 2 9ii(io) 4.018 5.474
If these be discarded, the maximum of the total deviation is about 0.1 mv. representing an error of * 0.05 mv. or 0.2%. The Activity Coefficient of Hydrochloric Acid in Barium Chloride Solutions Since the equation for the cell B is log
=
32~- E B + 51 log (0.01) (am4 + 0.01)
(7)
the activity coefficient of hydrochloric acid a t 0.01 M in barium chloride solutions may be obtained from the electromotive forces, E D . The reference values of y a t 0.01 2M derived from these results are 0.906, 0.906, 0.905, 0.905, 0.905, 0.905, 0.903, 0.903, 0.932, 0.901, and 0.900 a t 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50°, respectively. These agree with similar vahes of Harned and Ehlers" to within 0.001. For the sake of brevity, we have not included a table of these activity coeficients. They may be computed readily by equations ( 2 ) and (7) and the data in Table I. The Ionization and Ionic Activity Coefficient of Water in Barium Chloride Solutions The ionic activity coefficient product of water, Y H Y O H / a H 2 0 , was calculated by means of equation (6). The value of K determined by us, not the mean value as given in Table 11, was employed. This procedure was adopted to render the present calculations more self-consistent. The values of the activity coefficient of hydrochloric acid at 0.01 ;M in the salt solution were corrected slightly so that the values used in the calculation referred to zero concentration of the acid. Rather than construct a table of these results, we have resorted to a briefer method of expression. The thermodynamic equation for the ionization of water is
TABLE I11 THEIONIZATION OF WATERIN BARIUMCHLORIDE SOLUTIONS
TO
Ref. 5 This research Mean 0 . 1 1 3 ~ (n.iiz,g 0.1133(3:) ( ,1834) .1846(48) .1842
,4504 6806 1 007 1.467
Vol. 59
Constants of Equation (9)
50 O !J
Mv. 0 50 33 33 11 03
0.03 .05 .07 .1 .2 .
0.?I
09 03 26 04 .07
.7 I 2 3
A'
x
105
81929 81724 81587 81420 81042 80.509
B'
x
105
76.91 75.73 75.11 7 4 . lG 71.84
80:322 80 148
88 :is rj7.5G f;7.00
79939 79960
ti4.82 63.11
c' x
105
0.353 .372 ,336 ,316
,288 ,228 ,220 ,216 .168 .096
IONIZAT~ON OF WATERIN BARIUM CHLORIDESOLUTION
Oct., 1937
Knowing YHYOH/aH20 and K , m, was calculated, and it was found that this quantity may be expressed within the experimental accuracy by the equation -0.00039684 T log m, = A‘
AH = F [ ( A ’ - 298.1B’ f (298.1)’C’) - C’T2] = (A€€)o - C”T* (12)
Values of (AH),,and C” a t the designated concentrations are given in Table V.
+ B‘ (t - 25) + C‘ (t - 25)2
TABLE V THETOTAL HEATO F IONIZATION O F WATER Constants of Equation: AH = (A€€)o - C”T2
(9)
The values of A ’, B’ and C’ are given in Table 111. The Relative Partial Molal Heat Content of 0.01 M Hydrochloric Acid in Barium Chloride Solutions From the values of the electromotive forces O~ partial , molal of cells of type (B), ~ - B O .the heat content of 0.01 M hydrochloric acid in barium chloride solutions relative to its value in 0.01 M hydrochloric acid solution has been calculated. The results, valid from 0 to 40°, have been expressed by the equation
Fi
-
zo.01
=
(B-
$- cut
S0.01)o
+
Pt2
(10)
the constants of which are given in Table IV. ( H - Zo.ol)o, CY and @ are functions of E,”,, CY” and p” of equation (2). TABLE IV CONSTANTS OF EQUATION (IO)
(B - ao.o,)o
P
0.02 .03 .05 .07
.1 .2 .5 .7 1
2 3
a
- 18 -35 - 53 -69 -85 -95 -98 -92 -67 71 69
0.76 1.39 2.39 3.15 4.18 6.30 10.33 11.97 13.85 17.25 18.77
B
x
103
1.4 2.5 4.4 5.8 7.6 11.5 18.9 21.9 25.4 31.6 34.4
The Heat of Ionization of Water in Barium Chloride Solutions The total heat of ionization of water may be obtained from the equation
A€€
= RT2
d In rn?
dT
(11)
which upon combination with equation (9) and differentiation becomes
2035
c1
0.03 .05 .07 .10 .20
C”
AH)^
20839 21262 20535 20152 19651
,
x
104
814 858 775 729 664
fi
0.5 0.7 1 2
3
(AH)a
C” X 10‘
18536 18385 18301 17402 16067
526 507 498 387 221
To evaluate the heat of ionization a t zero salt concentration, an extrapolation was made using the limiting law of the Debye and Hiickel theory for the relative partial molal heat content. The results were in close agreement with those derived from similar cells containing potassium,2 sodium chlorides4 and lithium bromide5 except a t 0’. To illustrate, we obtained 14,230, 13,950, 13,730, 13,490, 13,180, 12,940 and 12,680, a t 10, 15, 20, 25, 30, 35 and 40’, respectively. Harned and Donelsons obtained 14,160, 13,940, 13,720, 13,480, 13,230, 12,980, and 12,730 at these temperatures. The agreement is good considering all the difficulties in obtaining heat data from free energy measurements, and the fact that the above two determinations require the measurements of four cells. Summary 1. The electromotive forces of the cells Hz I Ba(0H)z (0.005), BaClz (m) I AgC1-Ag HZI HCl (0.01), BaClz (m)I AgC1-Ag
have been measured a t 5’ intervals from 0 to 50’. 2. From these results, the standard electromotive force of the silver-silver chloride electrode, the ionization constant of water, the activity coefficient and the relative partial molal heat content of hydrochloric acid in barium chloride solutions, the ionic activity coefficient product, the ionization and the heat of ionization of water in barium chloride solutions have been calculated. NEWHAVEN,CONN.
RECEIVED AUGUST7, 1937
