Kohlrausch square root law

See - conductance, - conductivity cell, -> conductometry, - Debye-Falkenhagen effect, -> Debye-Huckel-Onsager theory, - electrolyte, -> ion, -> Kohlrausch square root law, - mass transport. 

Kohlrausch square root law — (1900) A plot of equivalent conductiviy Aeq vs. square root of concentration c according to... 

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

According to Kohlrauschs square root law (research into conductivities of strong and weak... 

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. 

Subsequent theories of non-ideality have been mainly concerned with explaining the concentration and temperature dependences of Y and 0 (3,16). For a comparison with various other theories for the non-ideal part of free energy of solutions, see (14). The interionic attraction theory (3,5,16-18) formulated on the assumption of complete dissociation of strong electrolytes, predicted the InV vs /m linear dependence and explained the Jc dependence of A found empirically by Kohlrausch (3,14) for dilute solutions. Since the square-root laws were found to hold for dilute solutions of many electrolytes in different solvents, the interionic attraction theory gained a wide acceptance. However, as the square root laws were found to be unsatisfactory for concentrations higher than about 0.01m, the equations were extended or modified by the successive additions of more terms, parameters and theories to fit the data for higher concentrations. See e.g., (3,16) for more details. 

Equation (4.22) is of the same form as the empirical square root law (Equation 4.5)) found by Kohlrausch. 

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. 

Fig. 2.4 Dependence of molar conductivity of strong electrolytes on the square root of concentration c. The dashed lines demonstrate the Kohlrausch law (Eq. 2.4.15)...

Debye-Huckel-Onsager theory — (- Onsager equation) Plotting the equivalent conductivity Aeq of solutions of strong electrolytes as a function of the square root of concentration (c1/2) gives straight lines according to the - Kohlrausch law... 

This empirical relationship between the equivalent conductivity and the square root of concentration is a law named after Kohlrausch. His extremely careful measurements of the conductance of electrolytic solutions can be considered to have played a leading role in the initiation of ionics, the physical chemistry of ionic solutions. 

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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