Page:Text-book of Electrochemistry.djvu/270

 evident evolution of gas. Since the gas must have a^pressure at least equal to the external pressure in order to be able to leave the electrode in the form of bubbles, it is clear that the electromotive force, as in Meyer's concentration element, will be the greater the higher the external pressure is. Helmholtz {11) investigated the relationship by varying the pressure from Po = 10 mm. of water to Pi = 742 mm. of mercury. The ratio of these pressures is 1 : 1000, therefore

log ^ = 3. The concentration of the gas in the liquid must

be in the same ratio, according to Henry's law, and the difference in the electromotive force for the hydrogen electrode will be (see the formula on p. 211)—

rf^ = i. 23^^ ^"^ ^^^^ " ^*^^'^^-

A molecule of hydi'Ogen (Ha) contains two equivalents (H), therefore in the formula n = 2.

For the oxygen the corresponding difference dE\ is only half as great (for n = 4), and we therefore obtain —

dE + dEi = 00879 + 0-0440 = 01319 volt,

whilst Helmholtz actually found that the electromotive force of polarisation rose from 1*635 volt to 1*805 volt ; dE + dEi was, therefore, 017 volt, which is in tolerable agreement with the requirement of the theory.

If the electromotive force of polarisation is known for a certain pressure, we may evidently calculate how great the partial pressure of the hydrogen and of the oxygen must be in order that the polarisation may become zero. Now, since the concentration of hydrogen and oxygen in water is regulated by Henry's law at a given external pressure, and the absorption coefficients of the two gases are known, we may easily calculate what quantities of the gases are con- tained in unit volume of the liquid when the electromotive force is zero, assuming that the hydrogen and oxygen are present in equivalent quantities. If we are below this limit, the back electromotive force is negative, i.e. by the

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