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��218 ELECTROMOTIVE FORCE. chap.
Nernst's Calculation of the Electromotive Force at the Surface of Separation of Two Solutions of the Same
Salt (iJ).— We begin with salts which
consist of two monovalent ions. Suppose two
solutions in contact, in which each of the two
kinds of ions have the osmotic pressures pi
Fig 42 ^^^ ^ respectively (Fig. 42). Let us calculate
the work necessary to move the quantity of
electricity 96,500 coulombs through the surface of separation
G; this work corresponds with the electromotive force at
this surface. If the migration velocity of the cation C is w,
and that of the anion A is v, then equivalents of C
pass through the contact plane to the right, and
��u + V
equivalents to the left. The work done, expressed in heat units, is for the cation —
��IK = l-99r— - In ^-\
��and for the anion-
��?Fa = l-99r— i--ln^-'? u + V pi
��The total work must be equal to 23,0707r, where w is the required potential difference (expressed in volts) at G. Therefoi-e —
23,0707r = JF, + W^A = 199^--^^^ In^
or TT = 86T. 10-« 7 "^ In ^ = r99 . 10"^^ ""-- ~ log ^.
If + V JJi u -^ V ^ p^
These electromotive forces come into play in liquid elements in which the electrodes are so arranged that there ai-e no resulting electromotive forces between the metals and the liquids.
Thus, for instance, in the element —
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