Specific and Equivalent Conductivities in Terms of Ionic Mobilities

Specific and Equivalent Conductivities in Terms of Ionic Mobilities 

Let the fundamental expression for the drift velocity of ions [Eq. (4.151)] be substituted in Eq. (4.157) for current density. One obtains 

Several conclusions follow from this atomistic expression for specific conductivity. First, it is obvious from this equation that the specific conductivity t of an electrolyte cannot be a concentration-independent constant (as it is in the case of metals). It will vary because the number of moles of ions per unit volume c can be varied in an electrolytic solution. 

Second, the specific conductivity can easily be related to the molar and equivalent A conductivities. Take the case of a z z-valent electrolyte. With Eqs. (4.161), (4.136), and (4.138), it is found that 

What does Eq. (4.163) reveal It shows that the equivalent conductivity will be a constant independent of concentration only if the electrical mobility does not vary with concentration. It will be seen, however, that ion-ion interactions (which have been shown in Section 3.3.8 to depend on concentration) prevent the electrical mobility from being a constant. Hence, the equivalent conductivity must be a function of concentration. 

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