# Catalysis:Mole Balance

To quantify the extent of reaction of a given system, at least one or more mole balances are required. For the general reaction

$aA+bB\rightarrow cC+dD$ 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

${\frac {dN_{A}}{dt}}=r_{A}V$ (Equation 3)

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

${\frac {1}{V}}{\frac {dN_{A}}{dt}}=r_{A}$ (Equation 4)

where the quantity

${\frac {N_{A}}{V}}=C_{A}$ = the concentration of species A

For a fixed volume reactor, this yields the result

${\frac {dC_{A}}{dt}}=r_{A}$ (Equation 5)

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.