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Why does the current increase over time in an electrolytic cell with a $\ce{CuNO3}$ electrolyte. The current increased about $2~\mathrm{A}$, and the temperature increased during the experiment to around $55\ \mathrm{^\circ C}$.

I’m not sure whether the formation of hydrogen and oxygen gas at the electrodes would decrease the internal cell resistance causing the current to increase. Or is there something else causing this?

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The electrolyte conductivity is dependent on the temperature of the electrolyte. Higher temperature increases ions mobility, thereby increasing electrolyte conductivity. The conductivity increases around 2% per degree (assuming linear increase of conductivity). More info here.

As Burak Ulgut mentioned, temperature increase is due to ohmic (Joule) heating. This can be estimated accordingly: $Q=V \cdot I \cdot t$

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  • $\begingroup$ Temperature will increase due to resistance. $\endgroup$ – Ben Norris May 10 '15 at 10:36
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As the reaction proceeds, your electrodes will get rougher since the surfaces will be etched. This will in turn result in an increased electroactive surface area increasing the current.

The temperature effect mentioned by Jaroslav Kotowski is there, but the growing electrode area is also a contributing factor.

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  • $\begingroup$ Thanks this clears it up because there were some anomie in my data where a higher temperature didn't always result in a higher current. $\endgroup$ – Jonathan May 11 '15 at 10:58

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