The performance of a PFR can be described by the differential mass balance equation: \[ \frac{dC_A}{dV} = -r_A \] where \(C_A\) is the concentration of reactant A, \(V\) is the reactor volume, and \(r_A\) is the rate of reaction for A. For a first-order reaction, \(r_A = kC_A\), the equation becomes: \[ \frac{dC_A}{dV} = -kC_A \] Solving this differential equation provides the concentration profile of reactant A along the length of the reactor.
