A treatise on the theory of solution including the phenomena of electrolysis . s of increase and decrease of the ^ functions for thetwo phases will be given by the partial differential coefficientso^i/dm and d^^l^m and the condition of equilibrium is that dm dm The common values of these differential coefficients give theamount of work necessary to introduce unit mass of eachsubstance into any of the phases or states under the condi-tions of the system, and are termed by Gibbs the chemical 1 Trans. Conn. Acad. vol. in. 1877, translated Thermodynamische Studien,Leipzig, 1892, and Equilibre des
A treatise on the theory of solution including the phenomena of electrolysis . s of increase and decrease of the ^ functions for thetwo phases will be given by the partial differential coefficientso^i/dm and d^^l^m and the condition of equilibrium is that dm dm The common values of these differential coefficients give theamount of work necessary to introduce unit mass of eachsubstance into any of the phases or states under the condi-tions of the system, and are termed by Gibbs the chemical 1 Trans. Conn. Acad. vol. in. 1877, translated Thermodynamische Studien,Leipzig, 1892, and Equilibre des Systemes Cliiniiques, Paris, 1899. 26 SOLUTION AND ELECTROLYSIS [CH. I potentials or the potentials of the substances in the givenphases or states. A graphical method, due to van Rijn van Alkemade^enables us to treat the subject in a simple manner. Let the abscissae (Fig. 7) denote the number of gram-molecules of solvent in which one gram-molecule of the solidis dissolved, and the ordinates be proportional to the value ofthe f function for unit mass of the phase Fig. 7. First consider the curve for the liquid phase, which givesthe value of ^ for unit mass of the phase as the amount ofsolvent containing one gram-molecule of solute changes fromzero to infinity. When m vanishes, ^ has the value corre-sponding to the solute in its liquid form: a fused salt, forexample. The direction of the curve is determined by thegradient d^/dm. When m is small, and the concentration ofthe water in the fused salt is therefore small, the amount ofwork required to introduce a further small quantity of waterwill be given by an expression analogous to that which holdsfor a gas, which is essentially only a dilute system (see p. 4).The value of d^/dm will therefore be of the form a + log bmwhere a and b are independent of m. When m is zero this 1 Xcits. 2>li>j>iiloil. Chcm. u. 289, 1H93. CH. l] THERMODYNAMICS 27 expression becomes — oo , and therefore the curve must at firsttouc
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