To quantify the extent of reaction of a given system, at least one or more mole balances are required. For the general reaction
one could write a mole balance on A, assuming it was the limiting reactant. For the specific case of batch reactor, with no net flow of moles into or out of the reactor
where dNA/dt is the accumulation of moles of A in the reactor, -rA is the rate of disappearance of species A, and V is the reactor volume.
This mole balances (in equation 3) can be rearranged as follows
where the quantity
= the concentration of species A
For a fixed volume reactor, this yields the result
where a suitable rate law expression can be substituted for the variable rA.
It is through a combination of a mole balance, a rate law, and appropriate stoichiometry that an accurate reaction engineering solution may be obtained.