Kohlrausch’s square root law

This relation is called Kohlrausch s square root law. It can be theoretically supported with the help of the Debye-Hiickel theory. The limiting molar conductivity A is impossible to measure directly because at infinite dilution, the solutimi does not conduct electricity. However, if A is plotted as a function of /c at concentrations that are not too high, we obtain a linear relation (Fig. 21.8) and A can be determined from extrapolation to the intercept of the straight line. 

The symbol A (or A°) represents the maximum theoretical value that the molar conductivity of an electrolyte will approach when diluted indefinitely with an inert solvent. At the beginning of this century Kohlrausch found that the molar conductivity of salts in very dilute aqueous solutions showed a linear relation with the square root of the concentration. This, Kohlrausch s square root law , was incompatible with the Arrhenius electrolytic dissociation theory (q.v.), but it has since been justified by the Debye-Hiickel-Onsager theory of interionic attraction effects, which have been shown to have a dependence. 

Ostwald s dilution law — Figure. Plot of Aeq vs. concentration c for aqueous solutions of various electrolytes, (see also - Kohlrausch square root law)... 

Kohlrausch s law states that the molar conductance of a strong electrolyte varies with the square root of concentration... 

The A, /c empirical relation found by Kohlrausch can be explained on the basis of the analogy of the gas and solution properties. According to the simple kinetic theory of gasesthe root-mean-square velocity /v is related (46) to /P by s/v = /3P7r where is the density of the gas. In dilute solutions, therefore, the conductivity (or the mobility) of the ions is proportional to /n or 7c. On the other hand, the Debye-Huckel-Onsager (D-H-0) limiting law,... 

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