In this Demonstration, the liquid-phase reaction A ⟶ B takes place in an isothermal, continuous stirred-tank reactor (CSTR). Use the sliders to set the feed concentration of A, C_A,0, the volumetric flow rate v, and the rate constant k. Use the buttons to select the reaction order with respect to A (first, second). The rate constant has the same numerical value when the reaction order changes, but its units are different. The figure shows the feed molar flow rate F_A,0, the feed concentration C_A,0, the outlet molar flow rates F_A, F_B, and the outlet concentrations C_A, C_B. Note that the outlet concentrations are identical to the concentrations in the reactor. The reactor residence time τ = V/v is also calculated.

The constant-density, liquid-phase reaction takes place in an isothermal CSTR: A → B, with reaction rate

−r_A = r_B = k C_A^m,

where C_A is the concentration of component A, r_i is the rate of reaction of component i, m is the order of reaction with respect to A, and k is the rate constant.

Mass balances on each component:

component A:  F_A,0 − F_A + r_AV = 0,

component B:  F_B,0 − F_B + r_BV = 0.

Mass balances in terms of volumetric flow rates and concentrations:

component A:  C_A,0v − C_Av + r_AV = 0,

component B:  C_B,0v − C_Bv + r_BV = 0.

F_i,0 is the molar flow rate of component i at the inlet; F_i is the molar flow rate of component i at the outlet; C_i,0 and C_i are molar concentrations of component i at the inlet and outlet, respectively; and v is the volumetric flow rate, which is equal at the inlet and outlet for constant-density reactions.

The solutions to these mass balances for first- and second-order reactions are:

first-order:  C_A(τ) = C_A,0 / (1 + kτ),   C_B(τ) = C_B,0 + C_A,0 − C_A(τ),

second-order:  C_A(τ) = [−1 + √(1 + 4kτC_A,0)] / (2kτ),   C_B(τ) = C_B,0 + C_A,0 − C_A(τ),

where τ = V/v is the residence time in the reactor.

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Neil Hendren. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.