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

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from Faraday to J. J. Thomson

383

fact, by the law of Raoult, {{Wikimath|(p₀-p₁/p₀, is approximately equal to $nv / V$ ; so that the previous equation becomes

$p_{0}V(v^{\prime }-v)=nf^{\prime }(n/V)$ .

Neglecting $v$ in comparison with $v'$ , and making use of the equation of state of perfect gases (namely,

$p_{0}v^{\prime }=RT$ .

where $T$ denotes the absolute temperature, and $R$ denotes the constant of the equation of state), we have

$f^{\prime }(n/V)=RTV/n$ ,

and therefore

$f(n/V)=RT\log(n/V)$ .

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 $c 2$ , at one electrode to a low concentration $c 1$ at the other electrode, its available energy is thereby diminished by an amount proportional to $log c 2 / c 1$ . 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 $log c 2 / c 1$ . The theory of solutions and their vapour-pressure was not at the time sufficiently developed to enable Helmholtz to determine precisely the coefficient of $log c 2 / c 1$ in the expression.^[1]

An important advance in the theory of solutions was effected in 1887, by a young Swedish physicist, Svante Arrhenius.^[2]

↑ The formula given by Helmholtz was that the electromotive force of the cell is equal to $b (1 - n) v log(c 2 / c 1)$ , where $c 2$ and $c 1$ denote the concentrations of the solution at the electrodes, $v$ denotes the volume of one gramme of vapour in equilibrium with the water at the temperature in question, $n$ denotes the transport number for the cation (Hittorf's $1/ n$ ), and $b$ denotes $q \times$ the lowering of vapour-pressure when one gramme-equivalent of salt is dissolved in $q$ grammes of water, where $q$ denotes a large number.
↑ Zeitschrift für phys. Chem. i (1887), p. 631. Previous investigations, in which the theory was to some extent foreshadowed, were published in Bihang till Sveuska Vet. Ak. Förh. vii (1884), Nos. 13 and 14.

[1] The formula given by Helmholtz was that the electromotive force of the cell is equal to $b (1 - n) v log(c 2 / c 1)$ , where $c 2$ and $c 1$ denote the concentrations of the solution at the electrodes, $v$ denotes the volume of one gramme of vapour in equilibrium with the water at the temperature in question, $n$ denotes the transport number for the cation (Hittorf's $1/ n$ ), and $b$ denotes $q \times$ the lowering of vapour-pressure when one gramme-equivalent of salt is dissolved in $q$ grammes of water, where $q$ denotes a large number.

[2] Zeitschrift für phys. Chem. i (1887), p. 631. Previous investigations, in which the theory was to some extent foreshadowed, were published in Bihang till Sveuska Vet. Ak. Förh. vii (1884), Nos. 13 and 14.

[1]

[2]