Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/403

 fact, by the law of Raoult, {{Wikimath|(p{{sub|0}}-p{{sub|1}}/p{{sub|0}}, is approximately equal to {{Wikimath|nv/V}}; so that the previous equation becomes {{c|$$p_0V(v^\prime - v) = nf^\prime (n/V)$$.}} Neglecting {{Wikimath|v}} in comparison with {{Wikimath|v&prime;}}, and making use of the equation of state of perfect gases (namely, {{c|$$p_0v^\prime = RT$$.}} where {{Wikimath|T}} denotes the absolute temperature, and {{Wikimath|R}} denotes the constant of the equation of state), we have {{c|$$f^\prime (n/V) = RTV/n$$,}} and therefore {{c|$$f(n/V) = RT \log (n/V)$$.}} Thus in the available energy of one gramme-molecule of a dissolved salt, the term which depends on the concentration is proportional to the logarithm of the concentration; and hence, if in a concentration-cell one gramme-molecule of the salt passes from a high concentration {{Wikimath|c{{sub|2}}}}, at one electrode to a low concentration {{Wikimath|c{{sub|1}}}} at the other electrode, its available energy is thereby diminished by an amount proportional to {{Wikimath|log c{{sub|2}}/c{{sub|1}}}}. The energy which thus disappears is given up by the system in the form of electrical work; and therefore the electromotive force of the concentration-cell must be proportional to {{Wikimath|log c{{sub|2}}/c{{sub|1}}}}. The theory of solutions and their vapour-pressure was not at the time sufficiently developed to enable Helmholtz to determine precisely the coefficient of {{Wikimath|log c{{sub|2}}/c{{sub|1}}}} in the expression.

An important advance in the theory of solutions was effected in 1887, by a young Swedish physicist, Svante Arrhenius. {{smallrefs}}