Why does the molar conductivity decrease with increasing charge density?

Question

This is a question in a problem sheet I have been set. Is it do do with the following equation: $\Lambda=\Lambda_0-a\sqrt c$? Surely charge density is proportional to concentration so therefore molar conductivity would decrease linearly with the square root of concentration (and $c$ $\alpha$ charge density?). Also, what is the physical origin of this equation; my lecture notes simply say that the ions interact with each other, is it as simple as that?

The second part to this question asks "Does the actual conductivity decrease?". Presumably by "actual conductivity", he means $\kappa$ where $\kappa=\Lambda c$. I have no idea about this part so any help would be much appreciated.

Answer 1

The molar conductivity is the conductivity per mole: if you increase the concentration, you increase the number of charge carriers so the conductivity increases. If the number of ions scaled exactly with concentration of electrolyte, the molar conductivity would be constant. However, the conductivity per ion goes down as the ions don't behave as fully independent charge carriers: they combine, and the rate at which they do so will increase as there are more of them. This behavior results in Kohlrausch's Law (that's the law you stated at the beginning of your question), and it is valid for strong (fully dissociated) electrolytes only.

The association of ions can be described by a simple equilibrium equation:

$$A^+ + B^− \rightleftharpoons A^+B^−; K=\frac{[A^+][B^−]}{[A^+B^−]}$$

[source]

As the concentration of ions increases, the fraction of non-dissociated ions will go up - and you can see where that square root relationship comes from.

For the second part, the actual conductivity will increase - you will have more ions in total, so greater conductivity. Just that every mole you added will add a smaller number of ions than the previous one.

There's more information at that wikipedia article I linked above.