Batch Reactor: If a reaction is conducted in a batch reactor, then time, required to achieve conversion X_A, can be found as

and integrated solutions for a variety of reaction-types are provided below:

Batch Reactor, Constant Pressure:

Zero order reaction: -r_A = k

First order reaction: -r_A = kC_A

Second order reaction: -r_A = kC_A²

Third order reaction: -r_A = kC_A³

Second order reaction: -r_A = kC_AC_B

Third order reaction: -r_A = kC_A²C_B

Third order: -r_A = kC_AC_B²

Batch Reactor (Plug Flow Reactor), Constant Density:

For a constant volume case, ε = 0 and Equation 1.25 reduces to the following design equation

And integrated solutions are provided below:

Zero order reaction: -r_A = k

First order reaction: -r_A = kC_A

Second order reaction: -r_A = kC_A²

Third order reaction: -r_A = kC_A³

Second order reaction: -r_A = kC_AC_B

Third order: -r_A = kC_A²C_B

Third order: -r_A = kC_AC_B²

Third order: -r_A = kC_AC_BC_C