94
JAMES W. MCBAIN AND 0. E. A. BOLDUAN
The best value (from Levy) for the dissociation constant of the acid R(IH+)I\'HzFCOO-, is and Greenstein gives 10-9"0 for Ka. L13 turns out to be 4.16 X lo4,a figure which is consistent with the characteristics of figure 1. Lais L13 X 4.52, or 1.45 X 10'. A comparison of the constants calculated by Levy and those given in this paper is given in table 4. In every case in which comparable values are reported, the agreement of the values calculated by the authors with those given previously is quite satisfactory. SUiMMARY
The polarimetric method has been applied to the study of the equilibria between histidine and formaldehyde. Contrary to previous reports, evidence is presented to show that each of the three ionic forms of histidine reacts with first one, and then another mole of formaldehyde. The calculation of the values of five equilibrium constants which characterize these reactions has been described. The values of these constants are in good agreement with the comparable values which have been reported previously. REFERENCES (1) D U X N hf. , S., FRIEDEN, E. H., STODDARD, M. P., A N D BROWN, H. V.: J. Biol. 144, 487 (1942). (2) FRIEDEN, E. H., D U N N hl. , S., ASD CORYELL, C. D.: J. Phys. Chem. 46, 215 (3) FRIEDEN,E. H., DUNS, M. S.,AND CORYELL, C. D.: J. Phys. Chem. 47, 10 (4) FRIEDEN, E. H., D U N N M. , S., AND CORYELL, C. D.: J. Phys. Chem. 47, 20 (5) GREENSTEIN, J. P.: J. Biol. Chem. 93, 479 (1931). (6) LEVY,M.:J. Biol. Chem. 99, 767 (1933).
Chem. (1942). (1943). (1943).
(7) LEVY,M.: J. Biol. Chem. 109, 365 (1935).
OSMOTIC PROPERTIES OF SOLUTIOKS OF SOME TYPICAL COLLOIDAL ELECTROLYTES' JAMES W. McBAIN
AND
0. E. A. BOLDUAN
Department o j Chemistry, Stanjord Cniversity, California Received December
4,1948
Colloidal electrolytes are characterized by the replacement of an ion by conducting colloidal particles or micelles. Hence, the osmotic activity of colloidal electrolytes is correspondingly diminished (6), while their conductivity may remain comparatively high, owing to the other free ion and the conductivity of the charged colloidal micelles. Although much has been published on the electrical behavior, few data have been supplied during the last twenty years on the thermodynamic or osmotic behavior (3) of colloidal electrolytes. 1 Presented a t the Nineteenth Colloid Symposium, which was held a t the University of Colorado, Boulder, Colorado, June 18-20, 1942.
4
OSMOTIC BEHAVIOR OF COLLOIDAL ELECTROLYTES
95
We here present data for a series of Aerosols, a Tergitol, two potassium soaps and several lower members of the same homologous series, and sodium triisopropylnaphthalenesulfonate, thus including straight- and branched-chain and aromatic derivatives and also a polycyclic compound, sodium dehydrocholate. Most of the higher soaps and detergents become too insoluble a t 0°C. to be studied by means of freezing-point lowering. EXPERIMENTAL
The purest available materials were used in each case. The precise freezingpoint equipment modeled after that of Scatchard was used, except where a modified B e c h a n n method is specially indicated. The calibration of the thervolts per degree Centigrade, as compared with mometer gave 8.840 X Johnson’s previous value (2) of 8.831 X Concentrations are expressed in molality, m, that is, weight normal N , or moles per 1000 g. of water. The freezing-point lowering is expressed in terms of the Bjerrum osmotic coefficient g = 0/(2 X 1.858m), where 0 is the number of degrees lowering, and it is assumed that at infinite dilution there is complete dissociation into two ordinary ions. The osmotic coefficient is, therefore, the ratio of the actual lowering to that for completely ideal behavior, represented as unity for all concentrations. The straight line on the graphs is the limiting Onsager slope for an idealized univalent electrolyte, g = 1 - 0.32 6. THE AEROSOLS
LiAerosol”is the trade name of a group of sulfosuccinic esters, of which there are over a million possible members. They have become very familiar as wetting agents. We have measured four of them in solution: namely, OT or the dioctyl (2-ethyl-1-hexanol) ester of monosodium sulfosuccinate; MA or the dihexyl (methylamyl) ester; AY or the diamyl (mixture of 2-methyl-I-butanol and 3-methyl-1-butanol) ester; and IB or the diisobutyl ester. All of these esters were supplied in pure form by the American Cyanamid Corporation. Of them, Aerosol OT is the least soluble, but it is solubilized by admixture with Aerosol MA, and this mixture was also measured. Thus, the solubility of OT a t 0°C. is increased from about 0.01 m to 0.035 m by the presence of 0.09 m MA. Similarly, 15 per cent of urea is required to raise it to 0.09 m OT. The freezing point of this latter solution is about the same as that of the urea solution alone, showing that the osmotic coefficient of the Aerosol OT is very slight. For a mixed solution which is 0.315 m MA and 0.067 m OT (total 0.382 m), the freezing-point lowering is 0.35”C. and the mean osmotic coefficient, g, is 0.252. On the other hand, as may be seen from figure 1, the osmotic coefficient for the 0.3153 m MA alone is 0.34. Hence, we have the interesting result that the solubilized Aerosol OT actually lowers the g value of the MA in solution with it. In a duplicate experiment with 0.3165 m MA and 0.0674 m OT, the mean g value was again 0.255.
96
JAMES W. MCBAIN AND 0. E. A . ROLDUAN
The measurements for the Aerosols are given in table 1 and are shown graphically in figure 1. Figure 1 is very interesting because it not only shows that the aerosols are unmistakably colloidal electrolytes, but it also exhibits the effect of decreasing molecular weight in requiring much higher concentrations for the formation of micelles. Likewise, it illustrates the general rule that the formation of micelles is progressive over at least a tenfold range of concentration after their initial appearance. Most of the ions or colloidal electrolytes added throughout this region where the value of g falls so rapidly go into micelles without greatly increasing their
00 08
'
01 06
05 04
03
02
1
O.'
GY
FIG.1. Osmotic coefficient, g, of Aerosols OT, MA, AY, and IB
number. The freezing point is definitely, although only slightly and progressively, lowered,-otherwise the liquid would separate into two layers. However, one of the most striking and characteristic properties of colloidal electrolytes is that this process comes to an almost abrupt end and thereafter the value of the osmotic coefficient g remains nearly constant and may even increase. In other words, the lowering of freezing point suddenly becomes proportional to the added substance, after being almost independent thereof. This outstanding phenomenon has never been adequately explained. As soon as the osmotic coefficient .g falls below the value 0.5, it is a neoessary consequence that the average particle (average of all particles, such as ions, complex ions, ion pairs, and colloids) must contain both anions and cations within the particle Recently the conductivities of the aerosols have been determined by Haffner, Piccione, and Rosenblum (1). They observe the same effect of increasing
AEPOSOI.
OT . . . , , . . . . . . . . . . . . .
MA ...................
AY . . . . . . . . . . .
. . ... ...
IB. . , , , , . . . . . . . . . . ....
OT and MA ... . . . . . . . .
1
m
B
moles per 1000 g. watt?
dcgtccs
g
0.003598 0.003834 0.004606 0.006602 0.00760 0.01046
0.01281 0.01346 0.01479 0.01697 0,01775 0.01978
0.958 0.945 0.864 0.692 0.629 0.509
0.8902 0.5553 0.400 0.300 0.1995 0.1001 0. 0501
0.699 0.543 0.446 0.388 0.325 0.259 0.168
0.211 0.263 0.300 0.348 0.438 0.697 0.m2
1.0020 0.8008 0.6017 0.4810 0.3970 0.3006 0.2006 0.1002 0.0498
0.958 0.827 0.706 0.627 0.584 0.506 0.442 0.338 0.175
0.257 0.278 0.316 0.351 0.396 0.453 0.593 0.908 0.945
0.5989 0,5014 0.4003 0.2995 0.2008
1.479 1.381 1.226 1.919 0.680
0.665 0.741 0.824 0.899 0.912
0.382 0.3839
1
0.35 0.364
1
0.252 0.255
POTASSIUM SALTS OF SATURATED FATTY ACIDS
Potassium laurate ((212) We have measured here the freezing-point lowering of solutions of potassium laurate. Table 2 and figure 2 give the results for potassium laurate, the molecule of which contains twelve carbon atoms. The figure includes four results inde-
98
JAMES W. MCBAIN AKD 0. E. A. BOLDUAN
pendently obtained by A. P. Brady, which agree excellently with our curve. It is very interesting that the osmotic coefficient, g, unmistakably passes through a minimum in nearly normal solution. This must be due to hydration. The TABLE 2 Values of the osmot'c coeficzent, g, of potasszuni laurate m
I
moles $e? I000 g water
I
. B
1.113 0.826 0.592 0.389 0.219 0.194 0.176 0.158 0.151 0.148 0.0684
1 700 1 331 1 001 ~
0 651 0 3015 0 2629 0 2031 0 1518 0 1015 0 0508 0 0203
00
I
I
05
g
degrees
10
.Jm FIG.2 Osmotic coefficient, g, of potassium laurate
0.1762 0.1668 0,1592 0.1608 0,196 0.199 0.233 0.281 0.402 0.788 0.906
L 0.5 I. 0
00
4%FIG.3. Osmotic coefficients of potassium caprate. potassium butyrate, and potassium caprylate
hydration was measured by McBain, Kawakami, and Lucas (4), who found it t o amount t o at least 10 moles of water per mole of dissolved potassium laurate. This would remove nearly one-fifth of the water in a molar solution. McBain, Laing, and Titley (5) published some results obtained by the Beck-
99
OSMOTIC BEHAVIOR OF COLLOIDAL ELECTROLYTES
mann method which are somewhat higher, but their results for the Richards method agree rather well with our curve. One should note that the asterisks denoting which solutions were turbid were omitted by the printer in their tables ( 5 ) .
Potassium caprate (GO) Potasslum decylate, although in the transition region of the homologous series, is still definitely a soap. This is well shown by the data of figure 3 and table 3, where it is seen that the value of the osmotic coefficient falls from about 0.94 TABLE 3 Values of the osmotic coeflcient, g, of potassium caprate
l
m
e
moles per I000 g. wafer
degrees
0.9348 0.7009 0.4999 0.3003 0.2002 0.1002 0.0400
0.877 0.747 0.668 0.612 0.573 0.351 0.142
I
E
0.253 0.287 0.350 0.548 0.770 0.943 0.954
TABLE 4 Values of the osmotic coeficient, g, of potassium butyrate m
R
moles )w I000 8. water
degrees
0.7 0.5 0.45 0.4 0.3 0.0912
2.756 1.890 1.696 1,494 1.094 0.315
in decinormal solution to 0.25 in normal solution,-again concentration.
E
1.om 1.018 1.013 1.@I3 0.90 0.929
a tenfold range of
Lower homologs The osmotic coefficient for potassium caprylate, with eight carbon atoms, begins to fall at about 0:7 N , where that for potassium heptylate, C,, still retains its full value. At 0.93 m potassium octoate, the value of g is approximately 0.73. The data for potassium butyrate are given in table 4 and are included with those for the decoate and the octoate in figure 3. It is at once evident that potassium butyrate is not a colloidal electrolyte. Hydration causes its osmotic coefficient to rise well above unity in concentrated solution.
100
JAMES W. MCBAIN AND 0. E. A. BOLDUAN
Potassium propylsulfonate has a g value a t 0.1 m of 0.90 and at 0.7 m of 0.86, showing that it is only an electrolyte, like potassium methyl xanthate, the g value of which is 0.90 a t 0.7 m. The free propylsulfonic acid has a g value of 0.975 for 0.1 m and of 1.02 for 0.7 m, while amylsulfonic acid has a g value of 1.01 a t 0.8 m. These high values of g, around unity, may be contrasted with g equalling only 0.118 for 0.197 m sodium oleate. McBain, Laing, and Titley TABLE 5 Values of the osmotzc coeficzent, g, o j sodaurn dehydrocholate
1
m
moles
$8”
I
0
8
degrees
I000 g. waler
0.2815 0.m 0.1008 0.0504 0.0195
0.781
0.718
0.556 0.504
0.748 0.813 0.903 0.980
0.189 0.071
8. 0.5
I 0.0
+__-___1
0.0
05
10
K FIG.4. Osmotic coefficients of sodium deoxycholate and sodium dehydrocholate
0.5
6
FIG.5. Osmotic coefficient of Tergitol No. 4
(5) obtained 0.128 for 0.2 m and 0.098 for 0.4 m sodium oleate, values comparable with those more recently obtained by S. A. Johnston for potassium oleate, using the precision method.
Bile salts Sodium dehydrocholate differs from other very closely related bile salts in not exhibiting appreciable solubilieing action either for a dye or for propylene,
101
OSMOTIC BEHAVIOR OF COLLOIDAL ELECTROLYTES
and by not affecting living cells (2), whereas the closely related deoxycholic acid is an excellent solubilizer. This behavior is reflected in the osmotic coefficient, which shows a much diminished tendency towards formation of colloid, as is seen in table 5 and figure 4. The latter includes for comparison Johnston’s results for the deoxycholate. A TERGITOL (NO. 4) Tergitol No. 4 is 7-ethyl-2-methyl-4-undecanolsodium sulfate, and therefore has a much-branched tetradecyl chain attached to the sulfate group. We are indebted to the Carbide and Carbon Chemicals Corporation for a supply of the almost pure waxy substance containing 90.1 per cent of Tergitol, 0.5 per cent of sodium sulfate, 2.22 per cent of sodium chloride, and 7.2 per cent of water, as determined by our own analysis, in good agreement with the total electrolyte content indicated by them. The data for the freezing point were corrected in the only available manner ,by subtracting from the total lowering the Debye-
TABLE 6 Values of the osmotic coefficient,
g,
of T iitol No. 4
m molcr par 1000 g. wale?
0.02112 0.02371 0.0523 0.0786 0.1093 0.1649 0.2m1
P
dagrcsr
0.0704 0.0746
0.099 0.103 0.121 0.153
0.224
0.891 0.846 0.510 0.363 0.298 0.260 0.241
.
Huckel values for the small amounts of electrolytes taken alone. The results so corrected are given in table 6 and figure 6 , in which they are plotted against the square root of m. This shows that a tergitol is definitely a colloidal electrolyte. SOME OTHER DETERGENTS
Sodium triisopropylnaphlhalenesulfonate:This is another wetting and penetrating agent which is definitely a colloidal electrolyte, since the g value for 0.08 m is 0.80 and for 0.15 m is 0.69, thus coming between the values for Aerosol AY and Aerosol MA, but having a less steep slope. Alronol: This is mainly a non-electrolytic detergent containing a little substituted ammonium salt. Its g value remained constant at 0.43 from 0.1 to 0.6 m. Solubilities: A number of other detergents which would be interesting to study have a very low solubility a t the freezing point of water. Thus, glycerol dioleate, lauric ethanol amide, and pyridonium cholesteryl sulfate and sodium
102
JAMES W. MCBAIN AND 0. E. A. BOLDUAN
TABLE 7 A . Activity coeficients .Tor Aerosol O T
m . . . . . . , . . , . . . . . , . , ,~ 0.004 .fa... . . . . . . . . . . . . . , , , 0.880
1
0.005 0.775
1 ~
0.006 0.684
0.007 0.607
~
0.008 ~
0.546
0.010 0.452
0.009 ~
0.494
i
3. Activity coeflcients j o y Aerosols A Y , M A , and I B I
m
AEROSOL MA
AEROSOL
0,784 0.564 0.323 0.230 0.160
0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.o
AY
0.760 0.340 0.271 0.225 0.193 0.171 0.153 0.139 0.128
0.150 0.129 0.113 0.100 0.090 0.062
m. .........
1
0.02 0.823
. .... . . . .
0.05 0.452
~
, ~
0.10 0.237
0.730 0.697 0.624 0.548 0.484
0,475
.
C. Activity coeficients of Tergitol N o .
fa.
I8
AEROSOL
~
0.15 0.168
4 ~
0.20 0.134
0.25 0.113
~
D. Activity coeficients of potassium laurate and potassium caprate m
POTASSIUM L A U U T E
POTASSILW CAPRAIE
0.6258 0.3302 0.1735
0.837 0.801 0.623 0.333 0.232 0.181 0.151
0.05 0.1 0.2 0.4 0.6 0.8 1.o 1.2 1.4 1.6
0.1150 0.0806 0.0634 0.0527 0.0450 0.0398 0.0358
decyl sulfonate are practically insoluble. Values for some other detergents are as follows:
.
.
.
.
Damol, , , . , . . , , , . . , , . , , , , , , , , . , , , , , , , , , , , , , , . , , , , , , . . . . . . . . . , . Potassium octyl sulfoacetate.. . . . Sodium dodecyl sulfate.. . . , . . . . . ,. . . . .. Sodium tetradecyl sulfate. , . . . . . Cetylpyridinium chloride. . . . , . . . . , . , , . . , , , , , . . . , , . . , , . , , , , . . . . . . . , . . . , . . . . . .. . Laurylpyridinium iodide.. . . Cetyltrimethylarnmoniumbr .................................... , ,
,
.. .
,
0.026 m
0.104 m 0.082 m 0.053 m 0.069 m
OSMOTIC BEHAVIOR OF COLLOIDAL ELECTROLYTES
103
Activity coefficients, f8, were calculated in the usual way from the equation:
where the integral is evaluated graphically from a plot of
asa d/55.51N ,
function of d -. In the very dilute concentration range, it is assumed that these substances behave like potassium chloride and that the limit of
d 5 r n is 0.32, as given by the Debye-Huckel
thkory.
Values for the substances studied here may be tabulated as in table 7. SUMMARY
Freezing-point data have been provided for solutions of many colloidal electrolytes of different types. Following the very dilute region, in which practically only ions are present, there is a range in which the concentration increases tenfold while the freezing point is only slightly but progressively lowered. During this range, the average composition of the micelles is progressivelychanging. After the osmotic coefficient precipitously falls off throughout at least a tenfold increase in concentration, the process comes to an abrupt end; thereafter, the osmotic coefficient remains nearly constant at a low value, and may even pass through a minimum, the lowering of the freezing point being then approximately proportional to the concentration. This outstanding property of colloidalelectrolytes (g ceasing to fall in moderate dilution) has received as yet inadequate attention and explanation. REFERENCES
(1) HAFFNER, F. D., PICCIONE,G. A,, AND ROSENBLUM, c.: J. Phys. Chem. 46,662 (1942). (2) H ~ B E RR., , AND H ~ B E RJ.: , J. Gen. Physiol. 26, ill (1942). (3) MCBAIN,J. W., LAING,M. E., DYE, W. B., AND JOHNSTON, S. A.: J. Am. Chem. SOC. 61, 3210 (1939). MCBAIN,J. W., AND JOHNSTON, S. A , : Proc. Roy. SOC.(London), communicated in 1942. MCBAIN,J. W.,AND BETZ,M. D.: J. Am. Chem. SOC. 67,1909 (1935). MCBAIN,J. W.,AND WILLIAMS, R. C.: J. Am. Chem. SOC.66, 2250 (1933). RALSTON, A. W.,HOERR,C. W., AND HOFFMAN, E. J. : J. Am. Chem. SOC.83,2576 (1941). ROEPKE,R . R., AND MASON,H. L.: J. Biol. Chem. 195,103 (1940). (4) MCBAIN,J. W.,KAWAKAMI, Y., AND LUCAS,H. P.: J. Am. Chem. SOC. 68, 2762 (1933). A. F.: Trans. Chem. SOC.116, 1289 (1919). (5) MCBAIN,J. W.,LAING,M. E., AND TITLEY, C. S.: J. Am. Chem. soc. 42, 426 (1920); Proc. Roy. SOC. (6) MCBAIN,J. W., AND SALMON, (London) 97A,44 (1920). MCBAIN,J. W., LAING,M. E., AND TITLEY,A. F.: Trans. Chern. SOC.116, 1219 (1919).
