Self-Diffusion of Sodium, Chloride and Iodide Ions in Methanol-Water Mixture E. Hawlicka* Institute of Applied Radiation Chemistry, Technical University, Wroblewskiego 15, 93-590, Lodz, Poland Z. Naturforsch. 41 a, 939-943 (1986); received April 25, 1986 The self-diffusion coefficients of Na+, C l- and I- in methanol-water solutions at 35 ± 0.01 °C have been measured in their dependence on the salt molarity in the range 1 • 10-4— 1 • 10-2 mol dm -3. The ionic self-diffusion coefficients in infinitely diluted solutions have been computed. The influence of the solvent composition on the solvation of the ions is discussed. A preferential hydration of Na+, Cl - and I “ ions in water-methanol mixtures has been found. In spite of the great interest in the porperties of aqueous solution with a Nal(Tl) scintillation crystal water-organic solvent electrolyte solutions, data on of the well-type (2 x 2"). the ionic mobilities in such systems are scarce. For the self-diffusion measurements the open-end Usually the ionic mobility is calculated from the capillary method was used. The details of the equivalent conductance and the transference num­ experimental procedure have been described in [6], ber. Ionic transference numbers have been reported The labelling of the sodium ions with 22Na or for water and 17 organic solvents [1], but only for a 24Na and the iodide ions with i25I or 1311, respective­ few water-organic solvents mixtures. ly, did not make any difference in the results. Similar information can be obtained from the ionic self-diffusion coefficients, which have been reported for a few water-organic solvent systems Results [2-5], The aim of the present work was to determine the All self-diffusion experiments have been carried self-diffusion coefficients of sodium, chloride and out at 25.0 ± 0.05 °C. The measurements have iodide ions in water-methanol mixtures and to study covered the whole composition range of the solvent the ion-solvent interactions. mixtures. The molarity of the salts was varied between 1.0 • 10-4 and 1.0 • 10-2. Some concentration dependences of the ionic self­ Experimental diffusion coefficients are presented in Figure 1. All values have been calculated from 9 independent Methanol (spectroscopy grade, Merck), Nal experiments obtained for 3 different diffusion times (suprapur, Merck), NaCl (suprapur, Merck) and ranging from 10 to 72 hrs. The statistical error of the double distilled, degassed water were used to D-values is less than 1%. prepare the solutions. 22Na, and N a 36 from the The D-values have been used to compute the USSR, and 24Na, N a125 and ,31I from Poland were limiting self-diffusion coefficients D x, i.e. the used as radioactive tracers. The radioactivities of coefficients in the infinitely diluted solutions. 24Na, 36C1 and l25I were measured in toluene- Taking into account the relaxation effect in the ethanol solutions of 2,5-diphenyloxazole (PPO) with self-diffusion process of ions, Robinson and Stokes a liquid scintillation counter, whereas the radio- [8] proposed the following equation, which describes acitivites of 22Na and 131I were determined in the influence of the salt molarity m on the ionic self­ diffusion coefficient D x of an ion i for a 1:1 elec­ trolyte: 2.801 • 103 , , ' * Present address and reprint requests to Max-Planck- Di = D f 1.5 - l/d O i ) ) V™ . (1) Institut für Chemie, Saarstraße 23, D-6500 Mainz. («oT ) 0340-4811 / 8 6 / 0700-0939 $ 01.30/0. - Please order a reprint rather than making your own copy. 940 E. Hawlicka • Self-Diffusion of Sodium in Methanol-Water Mixture Fig. 1. Dependence of the ionic self­ diffusion coefficients on the square root of the salt molarity, csa[t, for two solvent compositions (xM mole fraction of meth­ anol): a) .vM = 0.31; b) .ym = 1.00. where T, e0 and m denote the temperature, the static simultaneously the two mean square deviations dielectric constant of the solvent and the molarity of Oi = V[D{(cal) - D,(exp)]2 (6) the salt, respectively. d(//j) is a function of the mobilities of both ions. This function has been for i = cation and i = anion. The computed D 00 defined as values for the sodium, chloride and iodide ions are given in Table 1. As it was expected, the same d (00=7(1+2/?), (2) limiting self-diffusion coefficients of the sodium where rf and = 1 — /f are the transport numbers ions resulted from the experiments with NaCl and of the ion under study and its counterion, respective­ Nal. The influence of the solvent composition on ly, at infinite dilution. the D(° values is presented in Figure 2. As it can be The value can be expressed by the limiting self-diffusion coefficients of the ions: Table 1. The limiting self-diffusion coefficients of sodium, chloride and iodide ions in water-methanol mixtures. .vM is DI the mole fraction of methanol in the solvent. t? = (3) D f + D f /)§-• 105 b o D&. • 105 "8 *M 2 -1 Introduction (3) into (2) yields cm2 s~' cm2 s_1 cmz s 1 NaCl Nal B, + 3 d (//j) = ---------- (4) 0.000 1.328 1.325 a 2.064 2.094a 4 ( ^ + 1 ) 0.100 1.178 1.180 a 1.672 1.741a 0.229 1.021 1.025 1.271 1.303 a 0.310 0.902 0.902 1.105 1.139 with Z?j = D^/D-0, and from (4) and (1) follows 0.400 0.814 0.814a 1.062 1.101 a 0.471 0.810 0.809 a 1.079 1.140 a 2.8 0 - io6 /. y Bi + 3 0.551 0.810a 1.111 1.237a 1 - |/m D\ = D? 1.5 0.641 0.925 0.927 1.178 1.315 (£oT) 0.690 0.973 1.201 1.378 0.817 1.097 1.099 a 1.286 1.501 a (5) 0.900 1.156 1.152 1.329 1.582 1.000 1.222 1.218 a 1.378 1.678 a To calculate the Dj30 and Z)j°° values from (5), a computer program has been written to minimize Recalculated results from Ref. [7], E. Hawlicka • Self-Diffusion of Sodium in Methanol-Water Mixture 941 DC|-x1Q D7- *10 cm s Fig. 2. The dependence of the limiting self­ diffusion coefficients D ^a+ (a), j- (b) and Df- (c) on .vM. 0 r Na* i k «■V A ' Ä K 5.0 - 5.0 - 5.0 - A.O 4 £.0 ’ 4.0 ,___ ✓ / S * r J 3.0 3.0 3.0 „„ »' J 2.0 2.0 2.0 Fig. 3. Ionic radii calculated from Eq. (8) (o) 1.0 1.0 1.0 and Eq. (9) (x). (The viscosity of methanol- water mixtures from [10, 11], the dielectric i i .. ... constants from [12].) 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 Xu XM Xu seen, all functions are similar and pass through a self-diffusion of pure solvents. In our case of ionic minimum. The smallest values of Dg- and are self-diffusion one can assume, however, that the found at xM = 0.4 and that of Dfa* at = 0.5. solvated ions are much greater than the water or methanol molecules. Then the hydrodynamic radius of the ion i, i\, can be calculated from the equation Discussion kT (7) In order to discus the solvation of ions one can Tißrj0 D? compute hydrodynamic ionic radii. The simplest where r/0 is the viscosity of the solvent and ß a approach, frequently used for such calculations, is parameter resulting from the solute-solvent bound­ based on the Einstein-Stokes equation, which inter­ ary condition. For perfect sticking ß = 6 , whereas relates the self-diffusion coefficient with the solu­ for perfect slipping ß = 4. A detailed examination of tion viscosity. The applicability of this equation is, solute-solvent boundary condition by Ravel et al. [9] however, one of the most controversial questions in indicated slipping to be more appropriate for ionic diffusion studies. These controversies result from self-diffusion. Thus based on the data given in the fact that this equation was derived for diffusing Table 1 the ionic radii shown in Fig. 3 have been species large enough for a solvent to be treated as a computed from the equation continuum. It is obvious that such a condition is not fulfilled if the sizes of the diffusing particles and kT ( ) the solvent molecules are similar, as for example in 4 Ti rj0 D? 8 942 E. Hawlicka ■ Self-Diffusion of Sodium in Methanol-Water Mixture Recently Gill [13], following Zwanzig’s theoretical Table 2. Results of examination of (9) for tetraalkyl­ ammonium ions (rc = crystallographic radius, r = ionic attempt [14], has proposed a modification of Stokes’ charge, F = Faraday’s constant, N = Avogadro’s number, law to calculate an ionic radius from an ionic /.f = limiting conductance). conductance. Taking into account the relation z F2 between the ionic conductance and the ionic self­ Solvent rc 0.0103 e0 ry = re- {a + 6nrj0n diffusion coefficient. G ill’s equation can be re­ + 0.0103 £q) written as A A Et4N+ Water 4.00 2.82 0.81 + 0.37 Methanol 4.00 2.49 0.34 + 1.17 where ry is a parameter dependent on the solvent Ethanol 4.00 2.59 0.25 + 1.16 properties, equal to 0.85 A for nonassociated sol­ nPr4N+ vents and 1.13 A for associated or hydrogen-bonded Water 4.60 3.93 0.81 - 0.14 ones.