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

How are these two related?

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  • $\begingroup$ I'm in the middle of understanding the relation since it's a question made by my professor at the university. There is no data to compare yet although I would be glad to provide a much more detailed question to help others who may read this. $\endgroup$ – Tonakis2108 Feb 3 at 17:28
  • $\begingroup$ I've asked a follow-up question: Is there an electronic component to water conductivity? $\endgroup$ – uhoh Feb 4 at 0:42
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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.

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

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