Question

An elementary reaction of A + B ? C + D takes place in a 60 L semibatch reactor. The rate constant is 2 L/(mol-s). The reactor initially has 6 L of a liquid solution containing A at 0.1 mol/L. A stream of B containing 0.06 mol/L is fed in at 0.05L/s. Plot Ca, Cb, Cc, Cd and reactor liquid volume vs. time until the reactor is full.

Please note the problem is meant to set up a system of equations, supporting equations, and parameters for an ODE solver

Answer 1

Firstly, the time required to fill the reactor completely = (60 - 6)/(0.05) = 1080 s

This will be the time range for solving the ODE's.

Converting in minutes form, feed rate = 0.05 L/s

We have, dV/dt = v_o,    with V(0) = 6 and v_o=0.05 ---- (1)

We have

-r_A = -r_B = k C_aC_B                  ---(2)

For semibatch reactors,

dt dt

Substituting eq(1) and eq(2) in the above design equations, we can obtain C_A and C_B. For C_C and C_D, use eqns:

UC dt dC dt OCD

Using Polymath, the equations entered are:

Differential equations as entered by the user [1] d(CaVd(t) --kCa*Cb (0.05/(6+0.05*t))*Ca [21 d(CbVd(t) --kCa*Cb + (0.05/(6+0.05*t)*(Cbo [3] d(CC)/d(t) k*Ca*Cb-(0.05/(6+0.05*t))"Co [4] d(Cdid(t)-kCach-(0.05/(6+0.05*t))*Cd Cb) Explicit equations as entered by the user 1] Cbo 0.06 [2] k 2

Concentration profiles:

0.10 Ca Cb Co Cd Concentration profiles 0.07 0.08 0.05 0.04 0.03 0.02 0.01 0.00 0.00 108.00 218.00 324.00 432.00 40.00 848.00 758.00 84.00 972 00 050.00

The graph for reactor liquid volume was not plotted since when plotted in the same graph, it would make the concentration volumes look negligible. Nevertheless, its just a straight line with start at 6L and slope 0.05.