UNPUBLISHED FRAGMENTS.
431
Integrating from one point to another in the electrolyte,
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The evaluation of these integrals which denote the resistance and electromotive force for a finite part of the electrolyte depends on the distribution of the ions in the cell. For one salt with varying concentration,
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or, since and ,
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The resistance depends on the concentration throughout the part of the cell considered, but the electromotive force depends only on the concentration at the terminal points ( and ).
For and we may write and , where and are the "valencies" of the molecules. This gives
for(circuit open).
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I think this is identical with your equation () when your ions have the same valency.
Planck's problem is less simple.[1] We may regard it as relating to a tube connecting the two great reservoirs filled with different electrolytes of same concentration, i.e., . I use (0) for an y ion, (1) for any cation, (2) for any anion. [The accents () and () refer to the two reservoirs.]
The tube is supposed to have reached a stationary state and dissociation is complete. The number of ions is immaterial, but they all must have the same valency .
Now by equations (3) and (4), since ,
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- ↑ [Planck, Wied. Ann., vol. xl (1890), p. 561.]