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Self-Diffusion of , and Iodide in - Mixture

E. Hawlicka* Institute of Applied Radiation , 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 at 35 ± 0.01 °C have been measured in their dependence on the 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 with a Nal(Tl) scintillation crystal water-organic solvent solutions, data on of the -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 -solvent interactions. mixtures. The molarity of the 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 ( 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 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 )

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Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung This work has been digitalized and published in 2013 by Verlag Zeitschrift in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der für Naturforschung in cooperation with the Max Planck Society for the Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Advancement of Science under a Creative Commons Attribution Creative Commons Namensnennung 4.0 Lizenz. 4.0 International License. 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 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 . 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 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 . 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 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 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 -bonded Water 4.60 3.93 0.81 - 0.14 ones. Methanol 4.60 3.27 0.34 + 0.99 In (9) the first term results from viscous friction Ethanol 4.60 3.29 0.25 + 1.06 forces, assuming sticking, and the second from nBu4N+ dielectric friction forces; the meaning of the third Water 5.0 4.80 0.81 -0.60 term ry, however, is not so clear. To find a proper Methanol 5.0 3.86 0.34 + 0.80 Ethanol 5.0 3.85 0.25 + 0.90 value of ry, Gill [15] has examined the limiting conductance of tetra alkylammonium ions in several (Ionic conductances in from [16].) organic solvents and organic solvent mixtures. These ions have been assumed to be unsolvated, and the parameter ry has been calculated as the difference between the crystallographic radii of these ions and the real value of the ionic radius and may reflect the values resulting from the hydrodynamic and variations of the ionic solvation arising from dielectric terms of (9). changes of the solvent. The following discussion of Based on the data given in Table 1 and putting the influence of the solvent composition on the ionic ry= 1.13 A (cf. [13]), the ionic radii have been solvation is based on the rj values calculated from calculated from (9). The results are pressented in (9), because this equation seems to be more accurate Figure 3. As can be seen, the influence of the by its dielectric term. solvent composition on the ionic radii is similar, but For all studied ions the dependence of rx on xM is the values calculated from (9) are greater than those found to be non-linear; first the rx values decrease from (8), and this difference becomes smaller with from pure methanol to ca. 75 mol% of methanol, increasing methanol content. This discrepancy can where they become constant for a certaint .vM range. result from the lack of a proper ry value for aqueous This non-linearity might indicate that the com­ solutions. In order to solve this problem we petition the water and methanol molecules in the examined in a similar way as has been done by Gill solvation shells of the ions plays an important role [15] the conductances of tetraalkylammonium ions only if the concentration of water is too small to in aqueous and alcoholic solutions. The results are create a pure hydration shell. Thus one can assume presented in Table 2. Unfortunately we did not find a preferential hydration of Na+, Cl" and I- in the proper value of ry and we noticed that the value methanol-water solutions. of ry equal 1.13 A does not fit the ionic radii in Additionally, in the case of sodium and chloride methanol and ethanol solutions. The discussion ions a minim um of rx has been observed at .y m about presented above leads to the conclusion that there 0.15. It is known [17] that the structure of aqueous does not exist a proper equation to calculate a real solutions of methanol and other alcohols becomes ionic radius. more ordered at .\M about 0.12-0.15. One can As can be seen from Fig. 3, the variations of the rx suppose that the creation of a typical solvation shell values obtained from (8) and (9) with the variations of ions in a more ordered solvent is obstructed, of the composition of the solvent are similar. Thus which may result, as it has been suggested by one can suppose that the rx value is proportional to Feakins [18], from a disagreement between the E. Hawlicka • Self-Diffusion of Sodium in Methanol-Water Mixture 943

spherical structure of the hydrated ions and the for sodium ions, because usually the hydration shell structure of the solvent. Such a conclusion is con­ of Na+ is assumed to be more pronouced [19] than firmed by the fact that the minimum of r{ is deeper that of Cl-.

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