For a voltaic cell, the chemistry is spontaneous. Therefore once the cell is connected the chemistry drives electrical current through the external circuit.
The amount of chemistry can be quantified by measuring the current over time. Typically, the current might change over long periods of time, but for short periods, it would likely be constant. Therefore we can relate the current and time to the total charge that has passed between the anode and the cathode. Knowing the charge, we can figure out how many moles of electrons there were. Knowing how many electrons will tell us about how many moles of reactants have been consumed and how many moles of product are formed.
In a typical alkaline battery the half-reactions are
\[\rm{Zn(s) + 2OH^-(aq) \rightarrow ZnO(s) + H_2O(l) + 2e^-}\]
\[\rm{2MnO_2(s) + H_2O(l) + 2e^- \rightarrow Mn_2O_3(s) + 2OH^-(aq)}\]
Note: the batteries are called alkaline because they have a basic pH not because they use alkali metals. Also, the liquid water and hydroxide are not really a "liquid solution" as they are typically in a more solid suspension.
Assuming you had such a battery and used it to power your wireless mouse. This device might draw 1 mA of current (I think personally that is a bit high, but maybe you are really active with your computer mouse). You can run a typical AA battery at this current level for 2000 hours. If you ran your battery at a constant 1 mA for 2000 hours, how many grams of Zn would be consumed?
Well first, we need to convert current to charge. Current is charge per time. So charge is current multiplied by time. 2000 hours = 7.2 × 106 seconds. 1 mA = 10-3 A. So the total charge is (10-3 C s-1)(7.2 × 106 s) = 7200 C.
How many electrons is this? We need to use Faraday's constant.
Moles of electrons = 7200 C / 96,485 C mol-1 = 0.0746 moles of electrons.
Looking at our oxidation half reaction, we see that for every mole of zinc there are two moles of electrons. So the moles of Zn = moles of electrons/ 2 = 0.0746/2 = 0.0373 moles of Zn. The grams of Zn is then just this number of moles times the atomic mass of Zn. Grams of Zn = 0.0373 mol × 65.4 g mol-1 = 2.44 g