The behavior of a plug flow reactor is typically described by the differential material balance equation. For a first-order reaction, the equation can be written as:
\[ \frac{dC_A}{dV} = -kC_A \]
where \( C_A \) is the concentration of reactant A, \( V \) is the reactor volume, and \( k \) is the reaction rate constant. This equation assumes that the reaction rate is proportional to the concentration of the reactant, and it can be integrated to determine the concentration profile along the reactor length.
