MIXTURES OF COLLOIDAL ELECTROLYTES WITH U NIUNIVALENT SALTS JAMES W. McBAIN AND JANET SEARLES Department of Chemistry, Stanford University, California
Received November 8, 1986
Owing to the dearth of information as t o the effect of mixtures of colloidal electrolytes and uni-univalent salts upon each other, the following data are instructive. One of the more interesting results of the study of colloidal electrolytes (1, 4, 5, 7, 9) is that the ionic strength principle does not apply to ionic micelles unless they are treated as uni-univalent electrolytes. Although ionic micelles are highly charged colloidal particles, their charges are spaced so far apart that thsy are effectively independent. In this respect, they are sharply differentiated from ordinary polyvalent ions in which the charges are coincident. The present data illustrate this in graphical form, both for freezing point lowering and for conductivity. MODE O F CALCULATION
For comparison with the observed data for mixtures, it is customary to make use of various simple additive rules (2, 8, 10, 11). We have used three. First (method 1) is the L‘classical”mixture rule, where the molar conductivity, both observed and calculated, refers to the specific conductivity multiplied by the number of cubic centimeters containing one gram-equivalent of the common ion. For example, for mixtures of potassium laurate with potassium chloride
where pKcltotal is the conductivity of a solution of potassium chloride alone of the same concentration of potassium ion as the total concentration in the mixture; whereas N K C ~ is the actual equivalent weight normality (molality or gram-equivalents per 1000 grams of water) of the potassium chloride present. The assumption is that each salt contributes toward the total conductivity in proportion to its actual concentration and t o its conductivity in a solution of the same total concentration as that of the mixture. The second basis of comparison (method 2) is likewise only a first approximation to the truth,for it assumes that each salt present is exhibiting 493 THE JOURNAL OF PHYBICAL CHEPIJTRY, VOL.
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JAMES W. MCBAIN AND JANET SEARLES
the same conductivity in the mixture which it would have if the other salt were absent. paurn = N K C l
x
pKC1,
+
NKL
x PKL,
This is compared with the observed conductivity of the mixture; that is, the observed specific conductivity multiplied by that volume which contains the stated number of equivalents of each of the two salts. It should be noted that for solutions containing much soap, the values of weight normality and volume normality may differ by as much as 30 per cent, owing t o the fact that soap solutions, in spite of the large weight of soap present, differ comparatively little in density from water. For this reason, application of the "classical" mixture rule to specific conductivities (method 3), that is, to equal volumes of solutions of the same total weight normality in common ion, leads again to a distinctly different result from the first method of comparison. All three provide some basis for examining the mutual effect of the constituents of the mixture. Data for pure substances were taken from International Critical Tables, published papers, or measured ad hoc. Freezing points of mixtures were compared by two methods of calculation. The first (method 4) corresponds to the second of those above mentioned, that is, simple addition of the freezing points exhibited by each salt at a weight normality equal to that which it possessed in the mixture. Bmixture
=
81
+ 02
Lastly (method 5), they were compared through the osmotic coefficient of the mixture g, = glm
x mdm + gz,
X mz/m
where glm is the osmotic coefficient of one constituent a t the total molality of the mixture. Bjerrum's osmotic coefficient g = 1 - j = O/vXm, where vX is the molal lowering at infinite dilution, obtained by diluting the mixture without changing the ratio between the two constituents. Thus
v
=
(vm
+ vzm2)/(m1 + m2)
where m = ml + m2 and X = 1.858'. All conductivity data refer to 25.00' f.O.Ol"C., measured with the usual precautions in water of conductivity 0.5 to 1.0 X 10-Oin an oil thermostat. Freezing point measurements were by the Beckmann method with undercooling 0.3' to 0.5'. The best available materials were employed and all instruments were standardized. The partial specific volumes of soaps above the concentration exhibiting minimum conductivity lie between 0.973 and 0.982 for lauryl- and myristyl-
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495
sulfonic acids, and 0.945 to 0.935 for the n-undecylsulfonic acid; that for potassium laurate as found by Bury and Parry (3)lies between 0.912and 0.917, but whereas the latter fell sharply in lower concentrations, the partial specific volumes of the straight chain sulfonic acids are slightly greater in more dilute solution. CONDUCTIVITY RESULTS
Figure 1 exhibits the first two methods of comparison of mixtures of 0.955N , potassium laurate with potassium chloride up to 1.235N,. It is observed that the conductivity of the mixture by both methods of com-
I80
t
20 40
I
o
-
-
-
-
-
-
a2 04 0.8 0.8 1.0 1.2
N, *KC/
FIG.1. Molar conductivity of 0.955 N,(m) potassium laurate containing potassium chloride. #, observed, referred to 1 mole of total K; A, 8 u m of constituents (method 2); 0 , observed, referred to total K in 1000 g . of water; 0 ,sum of constituents (method 1).
parison is definitely less than the calculated value. The same result follows from comparison of specific conductivities. I n contrast to this, figure 2, for mixtures of 0.1 N , undecylsulfonic acid with hydrochloric acid up to 1 N,, shows fairly close agreement between calculated and observed values, the latter being generally even higher. Similarly, if, according to the third method of calculation, observed conductivity is plotted against total molality (N,) for true mixtures and separate constituents, the curve of observed values in every case lies slightly
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but definitely higher even than the calculated values. This may be largely attributed to increased formation of ionic micelle. A mixture, 0.1016 N , with respect to laurylsulfonic acid and also with respect to hydrochloric acid, calculated by the first method, gave an equivalent conductivity with respect to total acid of 53.67 mhos as compared with the calculated value 54.6. From the foregoing it may be concluded that the conductivity of the mixtures of soaps with electrolytes does not depart very much from simple additive rules,
0
0.2 0.4 0.6
0.8
1.0
1.2
Mw . HCI FIG. 2. Molar conductivity of 0.1 N , undecylsulfonic acid containing hydrochloric acid. A, observed, referred to 1 mole of total H; 0 , sum of constituents (method 2 ) ; X , observed, referred t o total acid in 1000 g. of water; 0 , sum of constituents (method 1). FREEZING POINT RESULTS
Figure 3 exhibits the data for mixtures of 0.1 N , undecylsulfonic acid with addition of hydrochloric acid up t o 1 N,. It will be seen that well within the error of experiment the total lowering is the sum of the constituents. Figure 4 shows that the osmotic coefficient of the mixture is definitely even greater than that calculated froin the constituents, for a mixture0.1016 N , laurylsulfonic acid containing 0.1016 N , hydrochloric acidexhibited a freezing point lowering of 0.440', as compared with 0.420' for the sum of the constituents and an osmotic coefficient of 0.583 as com-
TOTAL
m
PIG.3. Freezing point lowering ( 0 ) of 0.1 N , undecylsulfonic acid containing hydrochloric acid. 0 , observed values; A, calculated values (method 4); X, International Critical Tables values for hydrochloric acid alone; 0,Miss Betz’ values for C11HzaSOsH alone.
I.a
0.9
0.0 0.7 0.6
0.5 0.4
0.3 0.2 0.1
I . . . a2 0.4 0.6 OB TOTAL
.
.
0.1
1.2
m
Fro. 4 Osmotic coefficients (g) of 0.1 N , undecylsulfonic acid containing hydrochloric acid. A, observed values; 0 , calculated values (method 5 ) ; 0, International Critical Tables values for hydrochloric acid alone; ,. Miss Betz’ values for CltHoaSOaH alone. 497
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JAMES W. MCBAIN AND JANET SEARLES
pared with predicted 0.551. Thus again the observed values are higher than those calculated from the constituents. This result applies equally to ordinary soaps. Quick (6), for example, found the following dew point lowerings a t 18'C.: 1 N , potassium laurate, 0.22'; 1 N , potassium chloride, 0.50'; mixture 1 N , with respect t o each, 0.77', as compared with the sum of the constituents, only 0.72'. I n these strong soap solutions, the increased lowering is presumably due t o hydration of the soap. It is evident that presence of ionic micelle does not exert any great effect toward suppression of conductivity or freezing point lowering as had been assumed by a number of writers.' Sodium salts of dibasic organic acids carry upon the anion charges which are far apart. The following mixtures were studied, concentration being expressed in molality, m ; the values of freezing point lowering in brackets are for the respective constituents, and the sum of t h e s e : 4 . 1 sodium chloride, 0.1 sodium oxalate (0.348', 0.445', 0.793"), 0.787"; 0.2 sodium chloride, 0.1 sodium oxalate (0.685', 0.445', 1.130'), 1.130"; 0.1 sodium chloride, 0.1 sodium succinate (0.348', 0.532', 0.880'), 0,885'; 0.2 sodium chloride, 0.1 sodium succinate (0.685', 0.532', 1.217'), 1.233'; 0.5 sodium chloride, 0.486 sodium succinate (1.675', 2.545', 4.220'), 4.305'; 0.1 sodium chloride, 0.1 sodium tartrate (0.348', 0.476', 0.824'), 0,803'; 0.2 sodium chloride, 0.1 sodium tartrate (0.685', 0.476', 1.161°), 1.141'; 0.5 sodium chloride, 0.5 sodium tartrate (1.675', 2.002', 3.677'), 3.626"; 0.230 sodium chloride, 0.115 sodium phthalate (0.775', 0.731', 1.506'), 1.475";0.5 sodium chloride, 0.247 sodium phthalate (1.675', 1.561', 3.236'), 3.510"; 0.270 sodium chloride, 0.137 sodium isophthalate (0.925', 1.400', 2.325'), 2.450'; 0.5 sodium chloride, 0.266 sodium isophthalate (1.675', 2.814', 4.489'), 4.464"; 0.230 sodium chloride, 0.113 sodium terephthalate (0.775', 0.780', 1.555'), 1.633"; 0.450 sodium chloride, 0.2315 sodium terephthalate (1.510', 1.980', 3.490'), 3.475". In every case it is seen that the observed lowering is, within experimental error, equal to that of the sum of the lowerings caused by the two constittuents independently. For the tartrates, succinates, and o-phthalates, osmotic coefficients could be calculated and were likewise within a few per cent of those observed. SUMMARY
Mixtures of ordinary electrolytes with ordinary alkali soaps or with hydrogen soaps, like mixtures of sodium chloride with sodium salts of organic acids, exhibit conductivities and freezing point lowerings in sub1
G . W. Fuller in this laboratory has found that the electrometric titration curves
of these hydrogen soaps show the normal form and position for a moderately strong univalent acid. A similar observation on gum arabic was made by Thomas and Murray (J. Phys. Chem. 32, 696 (1928)).
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499
stantial agreement with the simple additive mixture rules. In all these cases, the charges on the polyvalent ion or micelle are spaced so far apart as to be effectively independent. Hence the ionic strength of colloidal electrolytes resembles that for a uni-univalent electrolyte. REFERENCES (1) BJERRUM, N.:Z.physik. Chem. 104, 147; 108, 219 (1923). (2) BRAY,W. C., AND HUNT,F. L.: J. Am. Chem. SOC.33, 781 (1911). (3) BURY,R. C., AND PARRY, G. A,: J . Chem. SOC.1936, 626. (4) MCBAIN,J. W.:J. Am. Chem. SOC.60, 1633 (1928). (5) ~MCBAIN, J. W.,AND BETZ,M. D.: J. Am. Chem. SOC.87, 1912 (1935). (6) QUICK,W. C.: J. Chem. SOC.127, 1405 (1925). (7) SCATCHARD, G., AND KIRKWOOD, J. G.: Physik. Z. 33, 297 (1932). (8) SHERRILL, M. S.: J. Am. Chem. SOC.32, 741 (1910). (9) SIMMS,H.S.: J. Phys. Chem. 32, 1121 (for corroboration by Debye, see footnote 11, p. 1124), 1495 (1928);J. Am. Chem. Soo. 48, 1244 (1926); J. Gen. Physiol. 11, 613 (1928). (10) STEARN,A. E.:J. Am. Chem. SOC.44, 670 (1922). (11) VAN RYBSELBERGHE, P., AND NUTTING,L.: J. Am. Chem. SOC. 66, 1435 (1934).
