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My experiment is just the electrolysis of iron rust at different temperatures. It consists of a rusted iron cathode and an iron anode in a salt water solution. From my data, there is an approximately 0.032A increase in current per degree Celsius.

I understand that by increasing temperature, you increase the conductance of the electrolyte and thus the current and rate, but I don't quite understand how this increase in conductance outweighs the increase in resistivity of electrodes.

It would be good if there are any equations that describe the relationship between conductivity/conductance/current in salt water and resistivity of iron/iron rust, and temperature.

Thanks in advance

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    $\begingroup$ Resistivity of electrodes has negligible importance here. $\endgroup$
    – Poutnik
    Commented Jan 1, 2022 at 15:22

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The short answer as to why the rate of electrolysis increases with temperature likely relates to elevated efficiency. However depending on the nature of the cell, there can be an offset in the cell's corresponding longevity.

In case of the electrolysis of molten sodium chloride, for example, the ions are free to migrate to the electrodes of an electrolytic cell. At a high temperature the process is more efficient, in essence similar to the functioning of a good electrolyte.

Electrode surface area is also an important feature impacting the rate of reaction. To the extent that increased kinetic energy positively impact the electrodes performance, elevating temperature could be positive. However, in time this can be offset by an increase in electrode deterioration.

More technically per this source is a rise of efficiency from heating may be related to an electrode's particular overpotential, to quote:

Under conditions of electrolysis, the cell is operating away from its equilibrium (reversible) potentials determined from Thermodynamics. Certain electrode reactions are very fast and depart very little from the equilibrium potential. Such reactions are frequently referred to as reversible (see Figure 1). Other electrode reactions are inherently slow and require a potential, E, significantly greater in magnitude than the equilibrium potential to achieve a reasonable current density. This potential is called the overpotential, η (=E–Ee), and the electrode is the said to be polarized. Such reactions are referred to as irreversible (Figure 2). As overpotential is increased in magnitude (more negative for cathodic processes, more positive for anodic processes) current density increases, typically exponentially at high overpotentials. The relationship between current density and electrode potential is the subject of electrode kinetics.

And also, to answer the resistivity part of your question as altering the electrode coating likely elevates resistance but can address overpotential:

For example, in chlorine cells anode design has been revolutionized in the 1960s by the use of coated titanium electrodes (so-called dimensional stable anodes or DSAs) as replacements to carbon. The coating, based on ruthenium oxide, valve metals, precious metals and transition metals, gave significant reductions in overpotential (< 50 mV for chlorine generation). Such materials are widely used for many commercial electrolyses.

Lastly, in the particular case of a galvanic cell, the total chemical based source of electrons can be discharged sooner with a rise in temperature based on a corresponding increase in the reaction rate, a known function of temperature.

So some statistical curve fitting can be performed, but the time to failure of the cell for various reasons should also be noted at higher temperatures.

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