Page:Text-book of Electrochemistry.djvu/242

 The electric work which can be obtained from this is n. 96,500 . TTo, where tto is the electromotive force at the surface of contact ; therefore when p =p% (see p. 218) —

RT .P 86.r.l0-«, P 71.96,500 p n '^^pi'

This applies to the pole at which the zinc dissolves ; at the other pole (where p =: ^1) an electromotive force in the opposite direction is set up, and this, consequently, has the opposite sign. We have, therefore —

86.r.io-*, P

TTa =. m -.

n pi

The sum of tto and W2 is —

86.T.10-' - pi 1-99. T. 10-*, pi

which is the same expression as we found above.

Planck's Formula. — Nernst only developed the expres- sion for the electromotive force at the contact surface between two solutions of the same electrolyte at different concen- trations. Planck (19), taking a more general view of the problem, has deduced a formula for the electromotive force at the contact surface between any two electrolytic solutions. If—

U = up + uipi + VriPi +. . . and — V =^ vq + Viqi + v^q^ +. ..

where u, ui, u^, etc., are the transport numbers of the positive ions ; v, Vi, V2, etc., those of the negative ions ; p, pi, p%, etc., and q, ji, ja, etc., the osmotic pressures of these ions ; and if € is the total concentration of all the positive ions, and there- fore of all the negative ions, provided that all the ions are monovalent, then we have to find expressions for Ui and C/^,

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