PIERRE VAN RYSSELBERGHE AND GOONLEE
2776
Our value, 2.68, is 25% smaller, and this difference is much greater than our experimental error which is about 27,. However, it should be remembered that carbonic acid is a peculiar acid in that the proton (or deuteron) must come exclusively from the water. Thus the hydration equilibrium plays an important role and it probably will not be the same in HzO and D2Q. This factor may account for the difference mentioned above. We are indebted to the Class of 1900 Fund for a
Vol. 60
grant which enabled us to purchase the deuterium oxide used in this work.
Summary The ratio of the first thermodynamic ionization constants of proto- and deuterio-carbonic acid has been determined potentiometrically using a cell without transference in which the electrodes were yuinhydrone and silver -silver chloride. Using 99.1% DzO the ratio, K w l K D ,has been found t o be 2.68 a t 23 '. WILLIAMSTOWN, MASS
RECEIVED JUNE 10, 1938
[CONTRLBUTION FROM THE DEPARTMENT OF CHEMISTRY, STANFORD UNIVERSITY ]
Conductivities of Con
Some Uni-, Di-, and
BY PIERRE VAN RYSSELBERGHE AND GOON LEE
As a further step in our investigation of the conductivity of concentrated mixtures of strong electrolytes1 we have studied a number of nitrates of uni-, di-, and trivalent cations at different total COlICentratiOnS raIl@ng fl-Om 1 to 5 1v. All possible types of binary mixtures have been included : two univalent cations, one uni- and one divalent cation, two divalent cations, one uni- and one trivalent cation, one di- and one trivalent cation, two trivalent cations. The method was essentially the same as in our previous work. The conductivities of the pure salts were found to be in close agreement with the existing standard data (I. C. T.; L. B. R.), except in three cases [LiNO3, Mg(NO&, Cr(NQ.&] for which the standard data seem to be somewhat in error. Moreover, some conductivities of pure salts are reported here for the first time. Others have been obtained for the first time a t 25". The results are recorded in Table I in which we give the conductivities of twenty anged in series corresponding uivdent concentration. We represent by x and 1-x the fractions of the total equivalent concentration corresponding to salts 1 and 2, salt 1 being the first in the title of the series. For each solutio give the specific and d the difference A h between the measured conductivity and that cal(1) Van Rysselberghe and Nutting, THISJOURNAL, 66, 1436 (1934); 69, 333 (1937), Van Rysselberghe, Grinnell and Carlsou % b i d .89, 336 (1937)
culated from the simple, uncorrected mixture rule: A = $Ai
-I-(1 - %)A2
~w~ series of miAures (19 and 20) contain nitric acid as one of the components, the maximum amount of nitric acid present being in both half the total normality. TABLE I CONDUCTIVTTIES OF CONCENTRATBD MIXTUFSSAT 25"
-
1.1 1
0
3/4
I/, 1/2
i/4
3/d
0
1
1.2 0
spccifie conductivity
1
2
'/4 '/2
'1 4
1
1.3 3
1
0
3/4
'14
'/z
'/z
'/4
3/4
0
1
Equivalent conductivity Cdcu'ated
N mixtures of KNOa + NaN03 0.09254 .08798 .oa24
92.54 87.98 83.24
,07973 ,07585
79 73 75.85
N mixtures of KNOa 0,15848 ,14993 ,14104
.13383 ,12617
79.24 74.97 70.52 66,92 63 09
-*A
88.37
0.39
80.02
.29
.85
+ NaN03 75.20 71.17 67.12
0 23 65 .%O
N mixtures of mas -+ NaN03 0.21042 .19996 .18413 .17222 ,16075
70.16 65.99 61.38 57.41 53.58
66.00 61.85 57.72
+
0.01 48 31
5 N mixtures of NaN03 LiNOa 0.19815 39.65 114 .I8944 37.89 38.28 0.39 '/e .I8167 36.42 36.72 .30 3/* .17511 35.02 35.27 .25 I 16910 33.52 2
0
Nov., 1938
MIXEDNITRATES
CONDUCTIVITIES OF
8
TABLE I (Continued) Compiodtion 1 x X
-
1
.
3.1 0
"4
1/4
'/2
1/2
'/4
3/4
0
1
1
3.2 0
'/2 '/4
0
3/4 '/2
1/4
0
1 "4 '/2 '/4
0
+ Cd(N03)2 79.56 69.78 61.56 53.89 47.44
3 N mixtures of 0 0.21019 1/4 .18973 '/Y .17035 a/4 .14966 1 .13446
63.75 57.44 51.13
KNOa 70.00 61.61 54.00 47.89 41.90
0
6.1 3 N mixtures of 0 0.14494 '/4 ,13504 '/a ,12613 3/4 .11741 1 .lo881
LiNOs 48.31 45.01 42.04 39.13 36.27
1
6.2 0
LiNOa 33.82 29.78 26.69 23.59 20.86
'/4
0
1
5.2 0
"4 '/2 '/4
0
1 3/4 '/2 1/4
5 N mixtures of 0.16910 '/4 .14894 '/2 .13345 3/4 .11797 1 .lo432
3/4
'/e 1/4
0
7 1 "4
'/2 '/4
0
4 N mixtures of 0 0.16168 '/4 .15711 '/2 .15277 3/4 ,14842 1 .14440
79.64 71.90 65.01 58.73 53.32
LiNOs 40.42 39.27 38.19 37.10 36.10
0 9.2
0.51 .66 .24
+ CU(NO~)~
0
1.16 1.47 1.17
+ CU(NO~)~
0
3/4
'/4
'/z
'/2
1/4
3/4
0
1
10.2
1 '/2
0 11 "4
'/2
1.37 1.95 1.04
+cd(N0~)~
0 1 "4
'/2 '/4
45.29 42.29 39.28
0.28 .25 .15
0 1 "4
+ Cd(NO&
'/2 '/4
30.57 27.34 24.10
0.79 .65
0
.51
1 3/4
+ Zn(NO&
'/2
1/4
39.33 38.26 37.18
0.06 .07 .OS
0 1 "4
0.10 .I3 .15
+
+ Cd(NO&
N mixtures of 0.13120 ,12420 .11875 .11373 .lo882
40.51 39.11 37.72
0.02 .02 -04
+
Mg(NOJ2 Cd(NO& 43.40 41.40 41.62 0.22 39.58 39.84 .26 37.91 38.05 .14 36.27
+
5 N mixtures of Mg(NO3)z Cd(N03)2 0.14555 29.11 '/1 .13102 26.20 27.05 0.75 .12119 24.24 24.99 .75 '/2 3/4 .11000 22.00 22.92 .92 1 .lo432 20.86
0
3/4
3/4
62.98 55.92 48.93
3
10.1
1
46.87 45.72 .44.56
3 N mixtures of Cu(NO& 0,12570 41.90 '/4 ,12146 40.49 '/z .11728 39.09 3/4 .11303 37.68 1 .IO896 36.32
1
'/4
73.06 b6.48 59.90
48.03 46.77 45.59 44.41 43.40
0
'/2
+ Zn(NO&
3 N mixtures of 0.21000 '/& .18482 '/2 .16200 "4 ,14368 1 .12570
'/¶
1
'/q
1.53 2.32 1.70
+
L i o ~ Mg(NO&
2 N mixtures of Cu(N0a)z Cd(N03)~ 0 0.10664 53-32 '/4 .lo369 51.85 51.91 0.06 .lo083 50.42 50.50 .OS '/2 3/4 .09805 49.03 49.08 .05 1 .09534 47.67
'/4
61.58 53.13 44.68
KNOa
'I4
9.1
'/2
+ Cd(N03)a
2 N mixtures of 0.15928 '/' .14380 '/2 ,13002 ,3/4 ,11746 1 ,10664
1
1/4
0
1
KNO3 70.06 63.24 56.78 49.89 44.82
5.1 0
3/4
'/z
"4
1.75 1.94 1.58
3 N mixtures of 0.14409 '/4 .14032 .13679 '/a 3/4 .13323 1 .13120
0
1
'/4
71.53 63.50 55.47
3.3 3 N mixtures of KN03 0 0.21009 70.03 '/4 .BO15 60.05 '/2 .15243 50.81 8/4 ,12895 42.98 1 .lo868 36.23 4
-AA
1 N mixtures of KNO, 4- Cd(NO8)l 0.09236 92.36 .08392 83.92 84.84 0.92 ,07522 75.22 77.33 2.11 ,06894 68.94 69.81 0.87 .06230 62.30
2 N mixtures of 0.15912 '/4 ,13947 '/2 .12313 3/4 .IO778 1 .09487
3/4
1
Specific Equivalent conductivity conductivity Measured Calculrted
2777
4 N mixtures of Zn(NO& 0.14440 36.10 l/4 .13549 33.87 '/2 .12683 31.71 3/4 .11808 29.52 1 .11068 27.67
+ Cd(N03)2
0
12 0
3 N mixtures of 0.21019 '/4 .19026 '/a .15467 3/4 .I2971 1 ,11045
KNOS 70.06 60.09 51.56 43.24 36.82
33.99 31.88 29.77
+ Al(NO.& 61.75 53.44 45.13
1.66 1.88 1.89
+ Al(NO&
4 N mixtures of LiNOs 0.16168 40.42 1/4 .14832 37.08 '/2 .13567 33.92 .12339 30.85 "4 1 .11276 28.19 14 2 N mixtures of KNOs 0 0.15857 79.29 '/4 .13537 67.69 '/2 .11395 56.98 3/4 .08986 44.93 1 .07198 35.99 15 3 N mixtures of Zn(NOa)2 0 0.13446 44.82 1/4 ,12701 42.34 13 0
0.12 .17 .25
37.36 34.30 31.25
0.28 .38 .40
+ Cr(NOJ3 68.46 57.64 46.81
0.77 .66 1.88
+ Al(NOJI 42.82
0.48
PIERRE: VAN RYSSELBERGHE AND GOONLEE
27'78
TABLE I (Concluded) Composition 1
T
-x
'/a
i/a
"4
dl,
il
1
16 1
Specific
Equivalent conductivity conductivity Measured CaIcuIated
12116 11334 11045
40 39 37 78 36 82
-Ai
40 82 38 82
4 LV mixtures of Cd(NO& 0 llOG8 27 67 lli20 27 80 '/4 1/2 11144 27 86 "4 11186 27 97 1 .I1276 28 19
43 1 04
+ Al(NO&
0
3/4
1/4
0
27 80 27 93 28 06
0 00 07
(19
+ Cr(NO&
2 V', mixtures of 0 09562 09034 ' i d 08498 It 07752 3/4 1 07119
Cd(NO& 47 81 45 17 42.49 38 76 35 60
17 2 4 A' mixtures of 0 0 11040 lln 11170 'I2 11181 ?ll 109633 I 10471
Cd(h'O& 27 60 27 92 27 95 27 43 26 18
tr
18.1 1 A' mixtures of 0 0 06264 05797 '/4 1/2 05349 j/C 048% 1 042ii0
Al(NOa)3 Cr(xO3)q A2 64 57 97 57 63 -0 34 53 49 52 62 - i l 48 28 47 61 - 67 42 tjo
1
18 2 2 0
17.1
0
1 "4
'/z '/4
0
1 3i4
112 1 j4
0
1 "4
'/z
"4
'14
1/2
'/2
1/4
3/a
0
1
1 3/a
1/2 '/g
0
19 0 '/z
2/.
3/6
1l4
11"
4/5
0
1
l / ~
'/P
I/
0
+ Cr(NO& 27 25 26 89 26 54
-0 67 -1 06 -0 89
Discussion In all the mixtures, except those of chromium nitrate with cadmium nitrate and of chromium nitrate with aluminum nitrate, the conductivity calculated according to the mixture rule is larger than the measured conductivity. As previously observed with other types of mixtures, the maximum difference between measured and calculated conductivities in a series of given total equivalent concentration follows the same trend as the difference between the conductivities of the pure salts. This is shown in Table I1 where the various groups of mixtures are classified according to the value of the difference X between the conductivities of the pure salts, AA being the largest departure from the mixture rule in the series. If one excludes the mixtures of chromium nitrate with cadmium and aluminum nitrates and those containing nitric acid, Table I1 could be combined with the corresponding tables of our previous papers. We note, however, that A h for 1 AT mixtures of KN03 NaN03 is larger than for the I molal mixtures previously studied.
+
i -
48 46 43 39 .35
24 04 09 99 68
+ Cr(N03)3 4q5 08 41 96 38 82
-0 96 -1 13 -1 17
+
Al(N03)a Cr(NO& 28 08 28 45 27.54 -0 91 28 53 26.99 -1 54 27 52 26.45 -1 07 25 90
2 N mixtures of HN03 (289 80) 0 36682 183.42 31319 156 59 25680 128 40 23726 118 63 ,13879 79 37
+ KNO? 184.59 163.54 131.97 121 44
1 17
6 95 3.57 2 81
+ Cd(NO&
2 N mixtures of HW03 (289.80) '/z 0.32599 163 00 3/5 .27131 135 66 3/4 20242 101 21 16 18164 90 82 1 09572 47 86
20 1
-0.41 - .78 - 11
+
of Al(h-Oa)s
0 09647 092U7' 08617 07997 f171t16
18 3 4 A' mixtures of 0 0 13232 11380 i/4 '/z ,11413 314 .llOlO 1 10361
1 '/z
2/,
N mivtiires
44 76 41 71 38 65
Vol. 60
0
168.83 144.63 108 30 96 24
5 83 8 97 7 09 5 42
N
2 2 2 3 3 2 1 3 2 3 1 1
3 2 5 2 4 2 3
4 5 3 3 5 2 3 3 4 4 4
4
x 241.94 210.43 43.30 33.80 33.24 32.12 30.06 28.10 26.32 25.24 20,04 16.69 16.58 16.15 12.96 12.56 12.23 12.21 12.04 8.43 8.25 8.00 7.13 5.83 5.65 5.58 4.63 4.32 2.18 1.42 0.52
-Ah
8 97 6.95 1.88 2.32 1.89 1 94 2.11 1.95 1.47 0.66
-
_I
.ii
85 .48 65 .79 -1.17 0.40 - .?8 .28 .25 .92 1.04 0.26 .39 . 08 .04
.15 . 08 -1.54 -1.06 0.09
Nov., 1938
CONDUCTIV~TIES OF MXED NITRATES
+
The behavior of the Cr(N03)3 Cd(N03)2 and Cr(N03)a Al(NO3)a mixtures seems abnormal, particularly in 4 N solutions where some mixtures exhibit larger conductivities than those of the two pure salts. We have noticed that the slope of the conductivity curve of Cr(N03)3is, at least in the range of concentrations here studied, appreciably smaller than the slopes for the other nitrates, these being all nearly equal. When the conductivities of Cr(N03)3 and of the other salt in the mixture are nearly equal, there is a positive A h due to this difference in the slopes. When the conductivities are quite different, as in the 2 N mixtures with KNOa, AA is negative because the effect of this difference is larger than that of the difference in the slopes. On account of the very large difference between the conductivity of pure nitric acid and that of KN03 or Cd(NOJ2 we would expect - A h to be much larger than is observed. We found in our previous work that, with salts, a difference of 100 in A corresponds to a A h of 14 to 16. The abnormal behavior of mixtures containing acids was pointed out in one of our papers and is evidently connected with the peculiar mechanism of proton conductivity. A common ion effect on the degree of ionization of nitric acid would tend to increase the lowering of the conductivity with respect to the mixture rule. Such an effect is to be expected, whether we accept Rao’s2 claim that nitric acid, alone among all nitrates, is incompletely dissociated, or whether we make the less drastic and more reasonable assumption that, a t these high concentrations, nitric acid is less completely dissociated than the salts. The
+
(2) Rao, Proc. R o y . SOC.(London), A191, 279 (1930).
2779
corresponding effect on the conductivity of mixtures containing nitric acid apparently is overshadowed to a certain extent by an effect in the opposite direction due to the adjustment of mobilities. Strong evidence for the incomplete dissociation recent analysis of nitrates is provided by Davie~’~‘ of Van Rysselberghe and Nutting’s data3bon the conductivity of mixtures of KNO3 with NaCl and of NaN03 with KC1. Davies gives a striking explanation for the fact that the calculated A’s are smaller than the experimental values in the former group of mixtures, and larger in the latter. On the basis of dissociation constants previously obtained for KNO3 and NaN03 he is able to calculate A h values in excellent agreement with the experimental ones.
Summary 1. Conductivities of twenty groups of binary mixtures of nitrates of uni-, di-, and trivalent cations have been measured a t total equivalent concentrations ranging from 1 to 5 N . 2. All mixtures studied, except those of chromium nitrate with cadmium and aluminum nitrates, exhibit conductivities lower than the values calculated from the simple mixture rule. The departure from the mixture rule is the larger the larger the difference of the conductivities of the pure salts. 3. The behavior of mixtures containing chromium nitrate and of those containing nitric acid is briefly discussed. STANFORD UNIVERSITY, CALIF. RECEIVED SEPTEMBER 26, 1938 (3) (a) Davies, J. Chem. SOC.,448 (1938); (b) Van Rysselberghe and Nutting, THISJOURNAL, 69, 333 (1937).
