Problem $3.$ A liquid$-$phase reaction with stoichiometry $AB$ takes place in a continuous well$-$

mixed $10\mathrm{.}0$ liter stirred$-$tank reactor. A schematic diagram of the process is shown below.

$11$ I $/$n

AlongrightarrowB, rate react $\frac{?}{(L*s)}$

The reactor may be considered perfectly mixed so that the contents are uniform and the

concentration of $A$ in the product stream equals that inside the tank. The tank is initially filled

with a solution that contains $2\mathrm{.}0$mol$\frac{A}{L}.$ The inlet and outlet streams begin to flow causing a

change in the concentration of $A$ in the tank with time.

a$)$ Write a balance on species $A$ in the tank and provide the initial condition.

b$)$ After the flows continue for a long period of time, the concentration of $A$ in the tank will

reach a new steady state concentration. Calculate the new steady$-$state concentration of A

in the tank $($the value approached as $t).$

c$)$ Solve the balance equation for $C_A(t).$ Check the solution by calculating $C_A(0)$ and $C_A().$

Answer: $C_A(t)=9\mathrm{.}6-7\mathrm{.}6e^{-0\mathrm{.}12t}(mol\frac{A}{L})$

d$)$ In Excel, use Euler's method to numerically approximate the solution to the differential

equation. You may need to vary your step size to get a good solution. Create a plot $($with

labeled axis$)$ comparing the analytical solution with your numerical approximation.