THE ELECTRICAL CONDUCTIVITY OF MIXED SALT SOLUTIONS1 A. KAY SMITH* AND R. A. GORTNER Division of Agricultural Biochemistry, University of Minnesota, St. Paul, Minnesota Received J u l y 86, 1958
An examination of the literature shows that few experimental studies have been made on the electrical conductivity of systematic mixtures of electrolytes. Two recent papers that do contribute directly to this subject are by Stern (1) and Ruby and Kawai (2). Stern examined the equivalent conductivity of systematic mixtures of the sodium and potassium halides from 0.1 M t o 4 M at 25°C. He compared his experimental values with values calculated on the assumption that the conductivity of the mixture is additive. He did not find this rule to hold true. Ruby and Kawai studied the various combinations of sodium chloride, potassium chloride, and hydrochloric acid for the purpose of “discovering the ‘nature of such solutions and to test the value of the methods of calculating the conductances of solutions of such mixtures of electrolytes.” They did not find their experimental values to fit into any of the known methods for calculating such data. I n addition t o these two papers, H. C. Jones and C. M. Stine (3) worked with a variety of salt mixtures but their concentrations, with few exceptions, did not go below 0.5 N . Pascoe (4) worked with mixed salt solution in a n attempt to correlate the conductivity of plant saps and of soils with their ionic concentrations. The present investigation was undertaken for the purpose of extending such conductivity data over a wider range of salts and into higher valence types in the hope of revealing the factor or factors that are responsible for their erratic behavior. MATERIALS
The salts used in this investigation, namely, sodium chloride, sodium sulfate, magnesium chloride, magnesium sulfate, copper sulfate, zinc sulfate and potassium chloride, and the hydrochloric acid used were all of a C.P. grade and no further purification was attempted except for the magnesium sulfate, which was recrystallized once, and the hydrochloric 1 Published as paper No. 1123, Journal Series, Minnesota Agricultural Experiment Station. 2 Guest of the University of Minnespta.
79
80
A. KAY SMITH AND R. A. GORTNER
acid, which was redistilled. The sodium chloride, potassium chloride, and sodium sulfate solutions were prepared by direct weighing of the dried salt; the hydrochloric acid was standardized according to the method of Hulett and Bonner ( 5 ) ; the other solutions were prepared by precipitating the sulfates as barium sulfate and the chlorides as silver chloride and weighing the respective precipitates. I n general, the dilute solutions were prepared from the more concentrated ones. Double-distilled water was used in the preparation of the solutions that had a specific resistance of approximately 5 X mhos and the solutions were preserved in Pyrex glass. The solutions were volume normal at 20°C. and burettes were used in proportioning them in the combinations desired. The combinations copper sulfate-sodium chloride, zinc sulfate-sodium chloride, sodium sulfate-sodium chloride, and magnesium sulfate-magnesium chloride were studied a t 0.01 N , 0.1 N , 1 N, and 2 N concentrations; the other combinations did not cover as wide a range of concentration. APPARATUS AND PROCEDURE
The usual Wheatstone bridge set-up was used in making the conductivity measurements, consisting of a Leeds and Northrup precision bridge with extension coil, a Leeds and Northrup precision resistance box, a type E Vreeland Oscillator a t 1000 cycles, a telephone tuned to 1000 cycles, and three conductivity cells of the Washburn (6) type. The cell constants were 2.544, 17.11, and 115.0. Since most of the measurements were made during the warm part of the summer, a higher temperature than usual was used in this work, namely 30.17"C. f 0 . 0 2 . The ratio of the bridge arms was determined and suitable corrections made in the calculations. The water correction was made in the Bolutions of 0.01 N concentration. All glassware was standardized and corrections were made, where necessary. RESULTS
The results are given in table 1, which includes the names of the combinations studied, the proportion of each compound in the mixture, the experimental values and An, the difference between the experimental value and that calculated on the assumption that the conductance of the mixture is additive. AA is given a positive sign when the calculated value is greater than the observed value, and a negative sign when less than the observed value. DISCUSSION
The data presented here do not show any decided regularity in their behavior. Such combinations as copper sulfate-sodium chloride, zinc sulfate-sodium chloride, sodium sulfate-sodium chloride, and potassium
81
ELECTRICAL CONDUCTIVITY OF MIXED SALT SOLUTIONS
TABLE 1 Conductivity data and AA, the difference between the calculated and experimental values
CONCENTRATION OF SOLUTION
NaCl.. . . . . . . . . . . . . . . . . . . 0.0100 N C U S O ~. . . . . . . . . . . . . . . . . . 0.0100 N VOLUME OF SOLUTION
A A I
Ratio NaCl : CuSOi
1oo:o 80: 20 60: 40 50: 50 40: 60 20:80 0: 100
0.1000 N 0.1000 N A
I A A I
0.9295 l'ooo N
I
2.000 N 1.859 N
-- -
A
AA
A
__-
131.2 127.1 121.0 116.6 111.8 101.5 * 90.8:
-4.0 -5.9 -5.6 -4.8 -2.6
119.0 110.1 -3.9 98.41 - 5 . 0 91.50 -4.5 84.87 -4.3 70.47 -2.7 55.01
95.50 83.82 71.55 65.18 59.00 46.40 33,55
-0.71 -0.83 -0.65 -0.67 -0.46
83.30 71.20 59.44 53.86 48.19 37.53 27.14
AA
0.87 1.40 1.36 1.41 0.84
-
T = 30.17"C. CONCENTRATION OF SOLUTION
NaCl., . . . . . . . . . . . . . . . . . . 0.0100 N ZnSOd. . . . . . . . . . . . . . . . . . . 0.0100 N VOLUME OF BOLUTION
Ratio NaCl : ZnSOh
1oo:o 80:20 60: 40 50: 50 40:60 20: 80 0: 100
A
AA
0.1000 N 0.1000 N A
AA
1.000 N 1.OOO N
2.000 N 1.859 N
A
A
AA
-
------130.9 128.2 121.7 117.7 114.0 104.8 94.21
-4.5 -5.5 -5.1 -5.1 -3.3
118.9 110.5 -3.7 99.32 -4.5 93.70 -4.9 87.80-5.1 73.52 -2.9 58.60
95.52 82.61 70.38 64.21 58.20 46.00 33.57
83.32 0.52 68.39 0.60 57.49 0.54 52.60 0.3147.49 0.04 37.35 26.74
AA
3.61 3.20 2.43 1.88 0.71
CONCENTRATION OF SOLUTION
NaCl. . . . . . . . . . . . . . . . . . . . 0.0100 N NazSO4. . . . . . . . . . . . . . . . . . 0.0100 N VOLUME OF SOLUTION
Ratio NaCl : Na2SOd
100: 0 80: 20 60: 40 50: 50 40:60 20: 80 0: 100
A
Ah
131.O 129.9 128.9 128.4 127.7 126.4 125.1
-0.1 -0.3 -0.3 -0.2 -0.1
0.1000 N 0.1000 N A
---
AA
118.9 115.5 -0.2 111.9 -0.3 109.9 -0.1 107.8 0.2 104.2 0 . 1 100.7 -
1.000 N
2.000 N 2.000 N
A
A
AA
82.09 75.39 68.98 65.98 62.97 57.56 52.36
0.75 1.22 1.25 1.28 0.75
1.000 N AA
--95.52 88.34 82.29 79.58 76.69 71.32 66.06
0.29 1.45 1.21 1.15 0.63
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A. KAY SMITH A N D R. A. GORTNER
TABLE 1-Continued
T
= 30.17"C.
CONCENTRATION OF SOLUTION
MgC19, . . . . . . . . . . . . . . . . . NazSOc, , . . . . . . . . . . . . . . . . VOLUME OF SOLUTION Ratio MgCla : Nazi304
A
AA
127.4 121.8 120.1 119.1 118.4 118.1 118.3 120.4
5.( 6.4 7. I 7.1 7.E 7.( 4.f
124.4
T CONCENTRATION OF BOLUTION
--
A
A
A.4
AA
110.9 106.3 103.3 101.1 98.09 96.37 95.40 95.04 96.57 98.16 99.93
3.50 5.41 6.51 8.42 9.04 9.28 9.18 5.55 2.87
80.85 77.72 75.39 71.94 69.80 67.97 66.76 66.53 66.00 66.43 66.92
64.38 1.74 2.67 4,73 5.48 5.92 5.73 4.47 3.71 1.88
59.78
2.2
55.78 54.07 53.07
3.8 4.3 4.1
52.02 52.16 52.36
2.7 1.4
= 30.17"C.
1
MgClr., . . . . . . . . . . . . . . . . . MgSOr, , , ., . . . . . . . . . . . . . .
-~
VOLUME OF SOLUTION
100:o 90: 10 80: 20 70: 30 60:40 50: 50 40:60 30: 70 20: 80 10: 90 0: 100
AA
A
2.000 N 2.000 N
0.9270 N 0.9315 N
- - ------
100:0 90: 10 80: 20 70: 30 60: 40 50: 50 40: 60 30: 70 20: 80 10: 90 0: 100
Ratio MgCla : MgSOi
0.0927 N 0.0932 N
0.0093 N 0.0093 N -
-~
0,0100 N 0.0100 N A
AA
128.9 121.1
1.7
115.0 112.0 109.2
1.7 1.7 1.4
103.5
1.1
98.46
0.0927 N 0.0930 N A
AA
111.9 105.5
1.66
95.70 90.85 86.18 81.78
1.97 2.08 2.01 1.67
72.59 68.59 64.48
1.37 0.63
0.9270 N 0.9295 N A
AA
80.57 75.96 71.60 66.99 62.17 58.06 53.58 49.52 45.45 41.52 37,89
0.34 0.43 0.68 1.23 1.17 1.38 1.17 0.98 0.64
83
ELECTRICAL CONDUCTIVITY OF MIXED SALT SOLUTIONS
TABLE 1- Continued
T
=
30.17"C.
CONCENTRATION OF BOLUTION
MgC12... . . . . . . . . . . . . . , . . ,
0.0927N 0.1000N
NaCl.. . . . . . . . . . . . . . . . . . , VOLUME OF SOLUTION
0.927N 1.000N
A
Ratio MgCh : NaCl
100:0
AA
109.8
90:10 80:20 70:30 60:40 50: 50 40:60 20:80 10:90 0: loo
AA
A
111.7
-0.1
114.1 114.9 116.0 117.8
-0.7 -0.5 -0.7 -0.7
80.46 81.89 83.56 84,90 86.65 87.74 89.17 92.11 93.57 94.68
118.9
-0.01 -0.26 -0.18 -0.41 -0.17 -0.25 -0.27 -0.31
CONCENTRATION OF SOLUTION
KCl. . . . . . , . . . . . . . . , . . ,
,
VOLUME OF SOLUTION
A
1oo:o 80:20 60:40 50:50 40:60 20:80 0 : 100
156.2 213.8 272.1 301.5 331.0 390.0 448.5
Ratio KC1 : HC1
I
0.0100N 0.0100N
,
HCl. . . , . . . . . . . . . . . . . . . , ,
M
A
AA
128.2 181.6 234.5 261.5 289.5 341.7 394.0
0.9 1.0 0.9 0.6 0.0
T
0.5000N 0.5000 N
-0.2 0.0
-0.4 -1.8 -1.9
= 0°C.
CONCENTRATION OF SOLUTION
NaCl. . . . . . . . . . . . . . . . . . . .
0.1OOON 0.1000N
cuso,.. . . . . . . . . . . . . . . . . . ~
VOLUME OF SOLUTION
Ratio NaCl : CuSOd
1oo:o 80:20 60~40 50:50 40360 20:80 0: 100
A
58.28 53.56 47.43 44.51 41.30 34.20 27.32
I
AA
-1.47 -1.53 -1.71 -1.60 -0.69
84
A. KAY SMITH AND R. A. GORTNER
TABLE 1-Concluded ~
T
=
~~~
30.17"C.
CONCENTRATION OF BOLUTION
cuso4... . . . . . . . . . . . . . . . .
0.0100 N 0.0100 N
ZnSOr. . . . . . . . . . . . . . . . . . . . VOLUME OF SOLUTION
Ratio CuSOr : ZnS04
1oo:o 80:20 60:40 50 :50 40:60 20:80 0: 100
A
90.55 91.93 92.62 93.45 93.66 94.38 94.16
I
an
-0.66 -0.63 -1.09 -0.95 -0.94
chloride-hydrochloric acid show positive, negative, and zero values for AA ; other combinations, such as magnesium chloride-sodium sulfate and magnesium chloride-magnesium sulfate, show only positive deviations for the concentrations studied. The results, as a whole, suggest, however, that when a sufficiently wide range of concentrations has been studied for any combination, they will show all three variations from the straight line curve. Table 2 is a tabulation of these deviations expressed qualitatively; the table also includes data taken from Stern (1) and from Ruby and Kawai (2). Our data are not strictly comparable with those of Stern and of Ruby and Kawai since they used weight-normal solutions, whereas we used volume-normal; the general trend of all three researches, however, is the same. No explanation is offered a t the present time for the apparently erratic behavior of these conductivity measurements. Stern used the theory of complex ion formation to explain his data; this requires a positive value for AA and that this value should increase with increasing concentration. Our measurements do not reasonably substantiate this theory, since all the AA values found for the combination magnesium chloride-sodium chloride are negative and likewise for the combination potassium chloridehydrochloric acid a t concentrations above 0.5 N . Even the combinations magnesium chloride-sodium sulfate and magnesium sulfate-magnesium chloride, which gave positive values for AA for all values studied, do not support the complex theory since the values a t 0.1 N concentration are larger than a t either higher or lower concentrations. If complex ions do occur in these solutions and contribute to the erratic behavior of their conductivities, then it is evident that their effect is less than some other superimposed phenomena.
85
ELECTRICAL CONDUCTIVITY OF MIXED SALT SOLUTIONS
In considering the problem of complex ions it should be kept in mind also that the studies of MacInnes (7), Dewey (8) and others on the transport numbers of the sodium and potassium halides have failed to find complex ions in these solutions. The inter-ionic attraction theory of Debye and Huckel (9) and its modificatidn by Onsager (10) in its present state cannot be applied to these data since it has been developed for systems containing only two ionic species. While Bennewitz, Wagner, and Kuchler (11) have extended Onsager's calculations to ternary ion mixtures it is still inapplicable, since
NORMAL CONCENTRATION
Combination: CuSO4-NaCl ZnS04-NaC1 CuS04-ZnS04 Na2S04-NaC1 MgClz-NanS04 MgCla-MgSO4 MgC12-NaC1 KCl-HCl KCl-HCl* NaCl-HC1' KC1-NaCl* KC1-NaClt KBr-NaBrt KI-NaIt
0.01
0.1
-
-
-
+ + +
0.5
-
+ +-
-
-
+ ++ + +
1
2
-
+ + + +
+ + + +-
+ + + + +
-
+ + + + +
4
-
+ + + +
Sign is negative when observed value is greater than calculated; positive the converse. * Taken from Ruby and Kawai. t Taken from Stern.
their method requires that one of the three ionic species shall be limited to a small concentration in comparison to the other two ions. The effect of solvation of the ions on their electrical conductivity is without a doubt a factor of considerable magnitude, but accurate information on solvation is too limited to be of much satisfaction. Attention should be called, however, to the similarity of our curves with those obtained by Jones and collaborators (3) wherein they measured the conductivity of salts in mixed solvents. Their data, which they obtained by varying the ratio of the solvent components and keeping constant the concentration of the salt, give curves that have essentially the same characteristics as those obtained by us. This permits the conclusion that the
86
A. KAY SMITH AND R . A. GORTNER
reaction between the solute and the solvent is of major importance in the interpretation of electrical conductivity data. REFERENCES (1) STEARN, A. E.:J. Am. Chem. SOC.44,670 (1922). (2) RUBY,C. E., AND KAWAI,J.: J. Am. Chem. Soo. 48,1119 (1926). H. C., AND STINE,C. M.: Carnegie Inst. Wash., Pub. No. 180 (1913). (3) JONES, (4) PASCOE, T.A.: M. S. Thesis, University of Minnesota (1926). Cited by R.A. Gortner in Outlines of Biochemistry, pp. 269-270. John Wiley and Sons, New York (1929). ( 5 ) HULETT,G. A,, A N D BONNER, W. D.: J. Am. Chem. SOC.31,390 (1909). (6) WASHBURN, E. W.: J. Am. Chem. SOC.38,2431 (1916). (7) MACINNEB, D. A.: J. Am. Chem. SOC.47, 1922 (1925). (8) DEWEY,JANE: J. Am. Chem. SOC.47, 1927 (1925). L: Z. 24, 185 (1923);24, 305 (1923); Trans. Faraday (9) DEBYEAND H ~ ~ C K EPhysik. SOC.23, 333 (1927). (10) ONSAGER:Physik. Z. 27, 388 (1926); 28, 277 (1927); Trans. Faraday SOC. 23, 341 (1927). (11) BENNEWITZ, WAGNER, AND KUCHLER: Physik. 8. 30, 623 (1929).
