Mass balances on components \(A\) and \(B\) in an isothermal batch reactor for the reaction \(A\rightarrow 2B\): \[\frac{dN_A}{dt}=-kc_A^nV\] \[\frac{dN_B}{dt}=2kc_A^nV\]where \(N_A\) and \(N_B\) are the number of moles of components A and B at time \(t\), \(k\) is the rate constant, \(V\) is the volume of the reactor contents, and \(c_A\) is the concentration of component A at time \(t\). These equations are solved using the starting conditions in the reactor: \[N_A=N_{A0}, N_B=N_{B0}\;\;at\;\; t = 0\]

\[N_A=c_AV\;\;\;\;N_B=c_BV\] \[X=\frac{(N_{A0}-N_A)}{N_{A0}}\]

where \(X\) is the fractional conversion.

Percent conversion \(=100X\)