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I'm analyzing the current output of a galvanic cell with aluminum electrode in aluminum sulfate solution and platinum electrode in acetic acid solution.

What I am confused about is whether molar conductivity will account for current resistance in the cell even though the electrons are being transferred through the metallic electrodes. Or is it just the metallic conductivity that accounts for current resistance?

If molar conductivity is also one of the reasons for current resistance in the cell, how is it?

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The resistance you'll find in your system basically corresponds to that of the solution (plus some charge-transfer resistance if your kinetics are somewhat sluggish).

Remember that for current to circulate, you need a closed loop; so the movement of electrons from anode to cathode is only part of the big picture. An equal ammount of current will be transported in the solution by ions approaching/leaving the electrode's surface. So, if you want to minimize your resistance effects, two intuitive approaches come to mind: i) make your ions move faster and/or ii) have a lot of ions moving at the same time. That means that the diffusion coefficient and the concentration of your ions (hence, the molar conductivity) will have direct effect on the solution resistance.

Since metals/alloys are, normally, excellent electronic conductors when compared to electrolytes (which, in turn, have ions as charge carriers), the overall cell resistance is pretty much due to the latter.

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