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

$\frac{dN_A}{dt} = r_AV$        (Equation 3)

where dN_A/dt is the accumulation of moles of A in the reactor, -r_A 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 r_A.

It is through a combination of a mole balance, a rate law, and appropriate stoichiometry that an accurate reaction engineering solution may be obtained.