When methanol-water (2M) electrolysis were carried out for 10 hours at constant current; how can we calculate how much methanol and water consumed theoretically?
Theoretically, you can use the Farady's Law in order to determine the amount of reactant consumed. However, it assumes that your current efficiency is 100%.
If you know, approximately, how much of your charge is used in each reaction you can approximate the results.
The current efficiency is the yield based on the electrical charge passed during electrolysis. From Faraday's law of electrolysis the current efficiency equal the charge consumed in forming product (wnF/M) to the total charge (q). So, by this relations you can find the amount of consumed reactants.Note that the total charge is a function and depend on the total electrolysis time and the current.
As mentioned above, application of Faraday's law requires the value of current efficiency. Perhaps, the easiest way would be to measure the concentration of methanol in the quote of solution after electrolysis (say, IR spectroscopy?).
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