Page:Text-book of Electrochemistry.djvu/243

 2 28 ELECTROMOTIVE FORCE. chap.

Vi and Fa, Ci and c^, which are applicable to each of the solutions which are in contact.

Planck found that the electromotive force at such a surface of contact can be expressed by —

TT = 1-99. 10-\r. log £, where 5 is given by the equation —

S^Ja - Ui _ __ci gca - ci

^^"^^^"in^ + lng'^"^'^'

m

When two solutions of the same electrolyte are ex- amined —

Ui = tici ; Il2 = ttC2; Vi = vci ; V^ =s vc^

«

and by introducing these values into Planck's formula, we obtain that of Nemst (see p. 218) —

7r= 1'99.10-\T^^^ log^^.

A further simplification occurs when Ci = ca, i,e. when the total concentration is the same on both sides of the contact surface. In this case we have —

. ^ l ^ + F a and— TT = 1-99. lO"* . T. log ^M^ •

Ki + U%

For a solution of one electrolyte, Ui = up, and Fi = vp ; and for that of another electrolyte, U^ = u\p, and Fi = t;ip. Several combinations of this type were examined by Nemst, and his results, as well as those calculated by Planck's formula, are contained in the following table : —

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