Chapter 2: Conversion and Reactor Sizing
Derivation of Batch Reactor Design Equations
\(\frac{dN_{A}}{dt} = r_{A} V\)
\( N_{A} = N_{A0} - N_{A0} X \)
\( dN_{A} = 0 - N_{A0} \, dX \)
\(- N_{A0} \frac{dX}{dt} = r_{A} V\)
\( N_{A0} \frac{dX}{dt} = -r_{A} V \)
\(\frac{N_{A0} \, dX}{-r_{A} V} = dt\)
\(\text{at } t = 0, X = 0\)
\( t = N_{A0} \int_{0}^{X} \frac{dX}{-r_{A} V} \)