Decrease in temperature of an aqueous salt solution decreases conductivity

Question

Why does the conductivity of a water solution drop as the temperature decreases?

How are these two related?

Answer 1

According to the Stokes-Einstein-Debye theory, and assuming the ionic composition remains constant (say for a fully dissociated salt), the main factor accounting for the response of the conductivity to temperature is the change in the viscosity of the solvent.

In the SED theory the frictional drag coefficient $f$ of a charged particle is proportional to the viscosity $\eta$: $$ f \propto \eta$$ As a result the electrical mobility $\mu$ of an ion of charge $q$ is inversely proportional to the viscosity, since $$ \mu =q/f\propto \eta^{-1}$$ and since the specific conductance $ \kappa$ depends linearly on the mobilities (approximately, at constant ionic strength), $$ \kappa \propto \eta^{-1}$$ Since the viscosity usually increases with decreasing temperature, the conductivity decreases.

Answer 2

Decrease in temperature has two effects, both attributing to lower electrolytic conductivity:

• decreases the mobility of the charge carriers (e.g. $\ce{H3O+}$ and $\ce{OH-}$ for pure water);
• suppresses auto-ionization of water (higher $\mathrm{p}K_\mathrm{w}$), reducing the total number of charge carriers.