A Conductance Method for the Determination of the Diffusion Coefficients of Electrolytes

Abstract

The possibility of employing conductance measurements for determining the diffusion coefficients of electrolytes has obviously occurred to many physical chemists, but this method has never been carefully exploited nor extensively used. As early as 1892, Niemoller' measured the change in conductance through a capillary tube containing a solution of a diffusing electrolyte. HaskelP measured the conductance a t various heights of an electrolyte diffusing in a tube 50 cm. long and 5 cm. wide. More recently, Lamms has employed conductance to determine diffusion constants of electrolytes in dilute solutions by a method which differs somewhat in principle from the one which we shall describe. In our preference for utilizing measurements in the later stages of the diffusion process we agree with Lemonde4 whose procedure in other respects bears little resemblance to ours.The most important characteristic of thc method developed in this study consists in measuring vertical diffusion in a closed cell, hy means of conductance measurements, between pairs of electrodes a t suitable positions near the top and bottom of the cell. The idea of utilizing the difference of conductances between the bottom and the top of the cell was suggested by Professor Lars Onsagcr, sonic years ago, a t which tiine hc dewloped the theory of the method and computed the dimcnsions of a cell suitable for ineasurcinents in dilute solutions. A few preliminary cxpcriments werc made a t Yale by Drs. Gosta Akerlof and Oliver A. Short which indicated promise of success. But difficulties arose due to control of temperature and convection, and to cell construction, which, in large part, have been eliminated as a result of this study. THEORY OF CELL AND MEASUREMENTThe simplest form of cell for an electrolyte diffusing vertically upwards is a rectangular parallelopipcd of height, a, and with electrodes 1~iem611er, A. Ann. der Phys. und Chem. 47: 694. 1892. 'RsrkeU, a. Phys. Rev. 07: 145. 1908. * L a m , 0 . 4Lemondo, H. Ann. de physlque (11) 9: 539. 1938.

The electrical conductivity of sodium polysulfide melts

“…Consequently; the number of independent equations (2-1) is one less than the number of species. 2F Xe (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) Do denotes the activity of sulfur in the melt. and Xe denotes the mole fraction of sodium sulfide in phase ~.…”

“…Xe dlnlle+Xodlnao =0, and equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), the term of In lle in equation can be expressed in terms of dVI· On the other hand, let us apply the definition of the electrolyte molality, and the chain rule to the term of din m on the right side of equation . Consequently, equation can be rewritten as…”

“…If the electrolyte is a dilute solution with an excess supporting electrolyte and only one depleting component is present in the overall electrode reaction, the diffusion impedance (also called the Warburg impedance) can be obtained using equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22). Zw = 1JJi =cr(l-j)/Yro , where As shown in this equation, the higher the frequency is, the smaller the Warburg impedance is.…”

“…With an excess supporting electrolyte, conductivity variations are negligible. Therefore, for dilute solutions with an excess supporting electrolyte, the above equation becomes (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) The last term can be neglected since it is on the order of the reactant concentration divided by the at a-y2 (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) Y is the distance from the surface. In this case, the movement of the species due to migration and convection is neglected, and the diffusion coefficient is assumed to be independent of concentration.…”

“…Let us apply this concentration equation in equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) to obtain the concentration overpotential for dilute solutions with an excess electrolyte.…”