Reaction in an Isothermal CSTR

 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, CA,0, the volumetric flow rate and the rate constant k. Select the reaction order with respect to A using the "1st" or "2nd" button. 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 FA,0], the feed concentration CA,0, the outlet molar flow rates FA, FB and the outlet concentrations CA, CB. Note that the outlet concentrations are identical to the concentrations in the reactor. The reactor residence time τ=V/v is also calculated.   Download the CDF file to view the simulation using the free Wolfram CDF player.

Details
The constant-density, liquid-phase reaction takes place in an isothermal CSTR: A → B, with reaction rate -rA = rB = kCAwhere CA is the concentration of component A, ri 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: FA,0 - FA + rAV = 0
component B: FB,O - FB + rBV = 0

Mass balances in terms of volumetric flow rates and concentration:
component A: CA,0v  - CAv + rAV = 0
component B: CB,0v - CBv + rBV= 0
Fi,0 is the molar flow rate of component i at the inlet, Fi is the molar flow rate of component i at the outlet. Ci,0 and Ci 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 solution to these mass balances for first- and second-order reactions are:
first order:
CA(τ) = CA,0 - CA,0e-kτ
CB(τ) = CB,0 + (CA,0 - CA,0e-kτ)
second order: CA(τ) = CA,0 - [(1/CA,0) + kτ]-1
where τ = V/v is the residence time in the reactor.