Page:Text-book of Electrochemistry.djvu/228

 gram-molecule of copper sulphate from the concentrated solution to the more dilute one. The electrical work amounts to —

dA=:2x 23,070 d real.,

or, in general, when the electrolyte used contains n gram- equivalents per gram-molecule —

dA =nx 23,070 d V cal.

This work may be used to re-establish the old conditions of concentration, which is done by separating so much of the dilute solution as contains (1 — m) mol of copper sulphate, and evaporating water partly from this and partly from the concentrated solution at constant temperature until the old concentration is reached. This quantity of water vapour is now compressed until it reaches the same concentration as the vapour over the dilute solution, and it is then forced into this solution. The only work done in this process is used in the compression of the water vapour at low pressure over the concentrated solution to the high pressure over the dilute solution. This was the method used by Helmholtz in his deduction.

The same result can be attained more simply by making use of semi-permeable membranes, which allow water, but not salt, to pass through. Let the concentration of the solution to the left, which contains 1 mol of copper sulphate, be c, its

osniotic pressure tt, and its volume ^ = -, and let this be

separated from the solution to the right by a semi-permeable membrane, Mi ; further, let the characteristics for this second solution be c + dc, TT + dw, and v - dv. Another semi-perme- able membrane, Jfa, is used to separate from the remainder such a quantity of the dilute solution as contains (1 - 7n) gram-molecule dissolved copper sulphate. The arrangement can then be expressed by the following scheme : —

dll. 80I. M2 dll. Bol. Ml cone. sol.

I c, TT, t; I (1 - m)CuS04 \c + dc,v + dir, v -dy |.

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