Page:Text-book of Electrochemistry.djvu/155

 HO CONDUCTIVITY OF ELECTROLYTES. chap.

Kohlrausch's Law. — Since X^ for potassium chloride evidently represents the sum of the transporting powers of = 64*67 to the potassium. These numbers refer to the temperature 18°, and are termed the mobilities (or migration velocities) of the chlorine and potassium ions respectively. From the determinations of the conductivities X^ of salts and the transport numbers it has been possible to ascertain the mobilities ofr other ions. The mobility of an ion, e.g, the chlorine ion, can evidently be obtained from the investigation of any chloride, and all the results must be the sama It is better, perhaps, to calculate the transport numbers from the mean value of the ionic mobilities, and see how the results agree with experiment. This is the method by which Kohlrausch proceeded to show the connection between transport numbers and conductivity.

Kohlrausch (<^) stated the law that the molecular conductivity of an electrolyte (at infinite dilution) can be calculated as the sum of two numbers, one of which depends only on the cation and is independent of the anion, whilst the other depends on the anion and is independent of the cation with which it is combined in the original salt. Kohlrausch, however, could only prove this for certain groups of similarly constituted electrolytes, e.g. for those with two monovalent ions (so that 96,500 coulombs are transported per gram-ion). It appeared as if a chlorine ion, when present with a potassium ion, possessed a different mobility from that when it was the dissociation product of the barium salt the cation of which is divalent, i.e. is charged with 2 x 96,500 coulombs per gram-ion. The difference in the mobilities of the SO4 ion was held to be much greater when it occurred with a mono- valent than when with a divalent cation. At first it was not expected that the relationships would be so complicated; the presumption that the relationships are quite simple was afterwards confirmed, and so the general form given above was associated with the law. The connection expressed

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