112
J. Phys. Chem. 1981, 85,112-115
c
i
0 - 0 0 4
0.8
0.4
1.2
Flgure 9, The Vrij-Overbeek plot of micelle molecular weight. The
points from left to right are in the following order: NaF, NaCI, NaBr, NaSCN, and NaI.
increment at constant salt concentration directly measurable, (dfi/dc)c8, by means of eq A-3. Equation A-3 is ( d i i / d ~ ) , = (dii/dc)c, (dii/dC,), (dC,/d~), (A-3)
+
converted into eq A-4, where
rs = Ml(dC8/dc),,
is the
amount of preferential adsorption of added salt on SDS micelle, on a molar basis. Equation A-4 is introduced into eq A-1. Then we have eq A-5, which relates the apparent micelle molecular
M1/2 = Mw1/2(1+ l?s(dfi/dCs)c=o/ [Ml(dii/dc)c8])
(A-5)
weight with the true micelle molecular weight. Figure 9 shows the relation of M1l2 with (dii/dC,),[M1. ( d i i / d ~ ) for ~ ~ SDS ] micelles in 0.80 M sodium halide so-
lutions. It is found that a straight line can be drawn through the three points for NaC1, NaBr, and NaI solutions in such a way as given by eq A-5 with constant adsorption. The deviation of the two points for NaF and NaSCN solutions from this straight line might be related to the reasons as mentioned in the text. The intercept of the straight line gives the true molecular weight of the rodlike micelle, 236 000, which corresponds to the aggregation number, 819. Its slope leads to the amount of preferential adsorption of the salt, 0.25 mol of salt per mole of SDS, or 205 salt molecules per SDS micelle. That is, ca. four salt molecules are adsorbed on a cross-sectional molecular layer of the rodlike micelle. Then these sodium halide salts are adsorbed on the rodlike micelle positively. On the other hand, in 0.80 M NaSCN solutions the adsorption of the salt is negative, and it amounts to -0.19 mol of NaSCN per mole of SDS, or -156 NaSCN molecules per SDS micelle, if the micelle molecular weight is common to that in the other sodium halide solutions. Huisman observed negative adsorption of NaF, NaC1, NaBr, and NaI on SDS micelle at lower concentrations of salt, and he ascribed it to the effects of electrostatic repulsion and excluded volume of the spherical micelle. If Huisman's explanation for the negative adsorption is accepted, the actual positive adsorption of salt at the high salt concentration must be even higher than that observed directly, by the amount of the negative adsorption. However, the conclusion of the large positive adsorption of sodium halides should be considered with severe reservation, since it is based on the postulate of constant molecular weight of the rodlike micelle in 0.80 M sodium salt solutions, irrespective of the co-ion species of salt. We do not have any guarantee for this postulate in the case of the rodlike micelles of SDS in 0.80 M sodium halide solutions, especially because we observe that even the apparent micelle molecular weight changes largely with the halide species of the added salt.
Conductance of Hydrochloric Acid and Potassium Chloride in Supercooled Dilute Aqueous Solution M. Nakahara,* N. Takisawa, and J. Osugl Department of Chemistry. Faculty of Science, Kyoto University, Kyoto 606, Japan (Recelved: June 24, 1980)
Conductance measurements were carried out on dilute aqueous solutions of HCl and KC1 at low temperatures; the limiting equivalent conductances were determined at 5 , 4 , 2 , 0 , -2, -4,-6, and -8 "C. The excess proton conductance at infinite dilution (AO(HC1)- AO(KC1))decreases with decreasing temperature without any anomaly around 0 "C, and its relative contribution to the total proton conductance slightly increases. The decreasing rate of the excess proton conductance is somewhat smaller than that of the inverse of the rotational correlation time in pure water; the difference is ascribed to the effect of the electrostatic field of the HS0' ion on the water rotation controlling the excess proton conductance. Introduction The abnormally high conductance of the proton in hydrogen-bonded solvents has attracted many researchers in this century.12 The mechanism of the anomalous
(excess) conductance of the proton in water was discussed by Conway et al.; 3*4 rotation of a water molecule in the vicinity of the H30' ion Was concluded to be the ratedetermining step. According to this mechanism, the excess
(1)T.Erdey-Grdz and S. Lengyel, Mod. Aspects Electrochem., 12, (1977). ( 2 ) F. H. Stillinger, Theor. Chem.: Adu. Perspect., 3, 178 (1978).
(3) B. E. Conway, J. O M . Bockris, and H. Linton, J. Chem. Phys., 24, 834 (1956). (4)B. E.Conway, Mod. Aspects Electrochem., 3, 43 (1964).
0022-3654/81/2085-0112$01 .OO/O
0 1981 American Chemlcal Society
Conductance of HCI and KCI in Supercooled Solution
proton conductance measured by the difference in conductance between HC1 and KC1 can be utilized as a probe to investigate the dynamic aspect of the water structure under various conditions. I t turned out in previous papers5t6that the acceleration by pressure of the water reorientation increased as water was cooled from room temperature to 0 "C. The effects of pressure and temperature were interpreted by considering hydrogen bonds in water to be distorted and weakened by an increase in pressure and/or temperature. The lower the temperature the more significant the water structure. Accordingly, it is interesting to study the excess proton conductance in supercooled water. In the famous monographs on electrolyte solutions,7v8no limiting equivalent conductance in water is given below 0 "C. Noticing that the conductance data below 10 "C was scarce, Horne et al. measured the conductivity ( K ) of KC19 and HCllO in the temperature range of 10 to -1 "C in order to obtain the activation energies near the freezing point. Laying stress on the unusual trends of the activation energies below 4 "C and taking account of the enhanced structure of water, they proposed some special mechanisms of the hydrodynamic and nonhydrodynamic transport processes of the ions in cooled water. Therefore, it is desired to confirm the temperature coefficients of the limiting equivalent conductances of HC1 and KC1 over a temperature range as wide as possible where the expansivity of water is abnormal and negative, before we accept the proposed mechanisms. Experimental Section Concentrated aqueous hydrochloric acid solution and potassium chloride salt of high quality were supplied by Merck. The concentrations of the dilute HC1 solutions at 5 "C were determined by conductance, applying the Fuoss-Onsager equation to the data given by Owen and Sweeton." Dilute solutions of KC1 were prepared by the usual method, and their concentrations were determined by weight. Conductivity water was obtained by passing distilled water through an ion-exchange resin; the conductivity at 0 "C was in the range of 5 X 10-'-8 X lo-' 3-1 cm-l. Variation with temperature of solution densities was assumed to be equal to that of the water density. The conductivity cell used was of the syringe type,12the capacity and inner diameter being 3 cm3 and 1 cm, respectively. The cell constant was determined at 0 "C by using a standard solution,13and its temperature dependence was negligibly small in the temperature range studied here. A calibrated bridge (Yanagimoto MY 8) was employed to measure the resistance. The conductivity cell was put in a bath containing a silicone oil of low viscosity and surrounded by a large amount of methanol in a refrigerator. The temperature was regulated to fO.O1 "C and measured relative to 0 "C by means of a few Beckmann thermometers. The conductance data obtained in this way had a maximum deviation of f0.15%. (5) M. Nakahara and J. Osugi, Reu. Phys. Chem. Jpn., 47, 1 (1977). (6) M. Ueno, M. Nakahara, and J. Osugi, J. Solution Chem., 8, 881 (1979). (7) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions", Reinhold, New York, 1958.
(8) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions", Butterworths, London, 1959. (9) R. A. Horne and R. A. Courant, J . Phys. Chem., 68,1258 (1964). (10) R. A. Horne and R. A. Courant, J . Phys. Chem., 69,2224 (1965). (11) B. B. Owen and F. H. Sweeton, J . Am. Chem. Soc., 63, 2811 (1941). (12) M. Nakahara, Y. Kumo-oka, and J. Osugi, Bull. Chem. SOC.Jpn., 53, 68 (1980). (13) G. Jones and B. C. Bradshow, J . Am. Chem. SOC.,55,1780 (1933).
The Journal of Physical Chemistry, Vol. 85, No. 1, 198 1
113
TABLE I : Properties of Water from 5 to - 8 "C ~~
5 4 2 0 -2 -4 -6 -8
0.999 9 6 0.999 97 0.999 94 0.999 84 0.999 67 0.999 4 1 0.999 08 0.998 65
1.519 1.567 1.671 1.787 1.915 2.057 2.216 2.394
85.93 86.32 87.12 87.92 88.73 89.55 90.37 91.20
Most of the properties of supercooled water have been measured by means of the capillary method or emulsification techniques.14 The capillary method has not been attempted here, because it is stated that the conductivity measured through solutions in capillaries is composed of the bulk and surface ones.16J6 In the case of dilute aqueous solutions of electrolytes, the extent of supercooling is limited by the dissolved ions which may cause heterogeneous nucleation; the freezing-point depression amounts only to 3.7 X O C at the highest concentration M) in the present work. The aqueous solutions studied here could be supercooled to -8 "C but rarely to -10 "C. A rapid expansion due to sudden freezing always damaged the conductivity cell. The physical properties of water used in the present work are listed in Table I. The density p is taken from ref 17; the values of p are extrapolated ones from the data above 0 "C, which agree sufficiently well with the experimental values by Zheleznyi.18 The viscosity 7 is calculated from the eq 1,19where t is temperature in "C; eq 1is based log 9 = 1301/[998.333 + 8.1855(t - 20) 0.00585(t 20)2] - 3.30233 (1) on the viscosity data in the range from 0 to 20 "C and can reproduce within 2% the experimental values in the supercooled region.20 The dielectric constant e is due to the eq 2,21which fits the static dielectric constant measured log 6 = 1.94409 - 1.9g1 X 10-3t (2)
+
between 0 and 40 "C; the extrapolated values are only 0.3-1.5% larger than those m e a ~ u r e d . ~ ~ * ~ ~ Results and Discussion The equivalent conductances (A/ (C1 cm2 equiv-')) of HC1 and KC1 from 5 to -8 "C were determined in the concentration ranges of 0.32-15 and 1-10 mM after solvent corrections of 0.03-3 and 1-3%, respectively. The data of A summarized in Table I1 (see paragraph at end of text regarding supplementary material) were analyzed by the Fuoss-Onsager conductance theoryz4 which can be expressed as eq 3, where C is the molar concentration (M) A = Ao - SC1J2+ EC log C JC (3)
+
and S, E , and J have the usual meaning. (14) D. H. Rasmussen and A. P. MacKenzie, J. Chem. Phys., 59,5003 (1973). (15) A. J. Rutgers and M. de Smet, Trans. Faraday SOC.,43, 102 (1947). (16) J. A. Schufle and N. T. Yu, J. Colloid Interface Sci., 46, 395 (1968). (17) G. S. Kell, J. Chem. Eng. Data, 12, 66 (1967). (18) B. V. Zheleznyi, Zh. Fiz. Khim., 43, 2343 (1969). (19) R. C. Hardy and R. L. Cottington, J. Res. Natl. Bur. Stand. ( U S . ) , 42, 573 (1949). (20) J. Hallett, Proc. Phys. SOC.,London, 82, 1046 (1963). (21) R. L. Kay, G. A. Vidulich, and K. S. Pribadi, J . Phys. Chem., 73, 445 (1969). (22) J. B. Hasted and M. Shahidi, Nature (London),262,777 (1976). (23) I. M. Hodge and C. A. Angell, J. Chem. Phys., 68, 1363 (1978). (24) R. M. Fuoss and F. Accascina, "Electrolyte Conductance", Interscience, New York, 1959.
114
The Journal of Physical Chemistty, Vol. 85, No. 1, 1981
TABLE 111: Limiting Equivalent Conductances
Nakahara et al.
( a-' cm2 equiv-' ) and Related Parameters from 5 to - 8 " C
HC1
t/"c 5 4 2 0 -2 -4 -6 -8
KC1
A0
S
E
J
A0
297.9 291.4 278.5 265.8 253.0 240.5 227.9 215.4
101.3 98.64 93.44 88.39 83.40 78.55 73.80 69.16
136.3 133.0 126.6 120.3 114.1 108.0 102.0 96.07
359 352 330 308 292 271 249 228
94.44 91.80 86.69 81.77 76.89 72.15 67.51 62.99
94.23 91.67 86.62 81.67 76.80 72.04 67.39 62.82
S
E
J
56.12 54.39 51.05 47.82 44.68 41.65 38.72 35.90
35.36 34.29 32.25 30.31 28.40 26.56 24.78 23.05
75.0 73.8 71.2 67.6 66.6 63.0 60.2 59.4
F r o m eq 4 . TABLE I V : Limiting Ionic Equivalent Conductances ko and Excess Proton Conductances haE ( a cm2 equiv-' )
t/"C 5 4 2 0 -2 -4 -6 -8
K+
c1-
H'
koE
46.79 45.51 43.02 40.63 38.25 35.94 33.67 31.46
47.65 46.29 43.67 41.14 38.64 36.21 33.84 31.53
250.3 245.1 234.8 224.7 214.4 204.3 194.2 183.9
203.5 199.6 191.8 184.1 176.2 168.4 160.5 152.4
koEE/ho(H+)
0.813 0.814 0.817 0.819 0.822 0.824 0.827 0.829
The limiting equivalent conductances AO(HC1) and Ao(KC1) at each temperature are listed in Table I11 together with their related parameters. The present value of Ao(HC1) at 5 "C, 297.9,25is in good agreement with 297.68 or 297.5,' and that at 0 "C, 265.8, is between 265.1 (extrapolated from eq 4) and 266.4.6 The values of Ao(KC1),94.44 a t 5 "C and 81.77 at 0 "C, agree sufficiently well with the literature ones: 94.26 and 81.7, respectively. Both AO(HC1) and AO(KC1) diminish with decreasing temperature without any singularity around 0 "C. To represent the temperature dependence of ionic equivalent conductance at infinite dilution above 5 "C, Harned and Owen' have proposed the cubic equation in the temperature X o ( t ) = XO(25) + a(t - 25) + b(t - 25)' + ~ (- t25)3 (4) where t is temperature in "C, and a, b, and c are 1.43262, and -3.183 X for K+ and 1.54037,4.6500 4.0563 X X and -1.285 X for C1-, respectively. The quantities of AO(KC1) computed by eq 4 agree fairly well with the present results even in the supercooled region as seen in Table 111, while the parameters in eq 4 are based on the conductance and transference-number data from 55 to 5 "C. The transference numbers of aqueous potassium chloride solution have been studied at 1 and 10 "CZ6 and 15, 25, 35, and 45 "C." The limiting cation transference numbers t+O above 0 "C can be represented within the standard deviation of kO.000 13 by the empirical equation t + O = 0.49685 - 2.99 X 10-4t + 1.9 X lo+%' ( 5 ) Equation 5 is used over the entire range of temperature to obtain the ionic equivalent conductances at infinite dilution listed in Table IV. According to Robinson and Stokes: Xo(Cl-) = 47.51, Xo(K+)= 46.75, and Xo(H+)= 250.1 at 5 "C, and Xo(C1-) = 41.0, XO(K+)= 40.7 and XO(H+)= 225 at 0 "C. These are in accordance with the corresponding values in Table IV within the experimental uncertainty. (25) The original data" analyzed by the Shedlovsky equation give a slightly smaller value of 297.6. (26) R. L.Kay and G. A. Vidulich, J. Phys. Chem., 74, 2718 (1970). (27) R. W. Allgood, D. J. LeRoy, and A. R. Gordon, J. Chern. Phys., 8, 418 (1940).
-8
0
-4
4
t/'C
Flgure 1. The Arrhenius activation energies of the transport properties against temperature: (a) from ref 19; (b) at 0.1 M from ref 9; (c) at 0.01 M from ref 10.
The excess proton conductance due to proton jump XoE is expressed by the quantity2s XoE = hO(HC1) - XO(KC1) = Xo(H+)- Ao(K+) (6) where the translational mobility of the H30+ ion is approximated by that of the K+ ion because of their similarity in size. The values of XoE and the ratios of XoE to Xo(Hf) are shown in Table IV. The excess proton conductance monotonically diminishes and its relative contribution to the overall proton conductance slightly increases with decreasing temperature. The temperature dependence of the excess proton conductance will be discussed in detail below, paying attention to rotation of a water molecule which controls the conductance process. To compare the present results with those by Horne and co-workers,SJOwe calculated the Arrhenius activation energies (E,) with eq 7, where R is the gas constant, T is E, = -R d In X/d(l/T) (7) temperature, and X is Ao, XoE, or 7-l. As seen in Figure 1, the phenomenological activation energies are not constant but increase considerably with decreasing temperature like those for other dynamic properties in water. The activation energies for the equivalent conductances of HC1 and KC1 are independent of the concentration (
