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I'm performing electrodeposition experiments with copper electrodes (anode and cathode) and a copper sulfate electrolyte solution. For my project, the cells assembled would need to be stored for a period of months. I was wondering if the copper sulfate can corrode the copper metal and how long it would take? The copper sulfate concentrations range from 5 mM to 100 mM.

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$\ce{CuSO4}$ will not corrode pure copper appreciably over a few months (though there is some dissolution and redeposition through random processes, such as density gradients and thermal motion, it might just reduce a mirror finish to slightly roughened).

However, if the electrodes or wires are brass, bronze or other alloy, or if there are other metals in contact, such as a tin-lead solder joint, there is a chance of some corrosion. In fact, copper sulfate is used to test passivation of stainless steel, and visible corrosion of iron can take place in minutes.

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