Kohlraush’s Law

Kohlraush’s Law
F .W. Kohlraush (1875) determined the values of equivalent conductivity at infinite dilution for a large number of electrolytes and observed that the difference between the equivalent conductivity at infinite dilution of pairs of salts, having either a cation or anion in common, is constant at constant temperature.
For example, the difference between at 25°C for K and Na salts having a common anion is always found to be and that for chloride and bromide having a common cation is always . It is clear from the following table:
Electrolyte
A at C
Difference
NaBr
NaCl
128.51
126.45
2.06
KBr
KCl
151.92
149.86
2.06
LiBr
LiCl
117.09
115.03
2.06
KBr
NaBr
151.92
128.51
23.41
KCl
NaCl
149.86
126.45
23.41
144.66
121.25
23.41
From the study of above table, it may be pointed out that at infinite dilution, each ion makes a definite contribution towards the equivalent conductivity of electrolyte, irrespective of the nature of the other ion with which it is associated in solution. This important generalisation, called the law of independent migration of ions(also called (Kohlraush’s law, after the
discoverer) is strictly true at infinite dilution only where there is no mutual interaction between the different ions.
It may be stated as:
“The equivalent conductivity of an electrolyte at infinite dilution is the sum of two values, one depending only on the cation and the other only on the anion”.
Mathematically,
where ka and kc are the ionic mobilities or ionic conductivities of the anion and cation respectively. By the term ionic mobility of an ion we mean, ‘the conductivity of one equivalent of the ion when the solution containing that quantity of the ion is placed between two electrodes 1 cm apart.’
Applications:
(i) In calculating the equivalent conductivity at infinite dilution of weak electrolyte.
(ii) In explaining the independent motion of ions assumed in Arrhenius theory.
(iii) In calculating the absolute velocity of ion.
(iv) In calculating the ionic product of water.
(v) In determining the degree of dissociation of electrolytes.
(vi) In finding out the solubility of sparingly soluble salts.