Problem $1(35$ points$).$ An isothermal, first order liquid phase reaction:

$AB$

is carried out. $C_{A0}$ is $1\mathrm{.}0mo\frac{l}{L},k$ is $1mi{n}^{-1},$ and $v_0=30\mathrm{.}0\frac{L}{m}in$

The following reactors are available, and you can order up to three of each reactor, depending on

your budget.

a$)$ Select one reactor that is the most like an ideal CSTR$.$ What is its size? Use the ideal reactor

equations to solve for conversion in this reactor.

b$)$ Select one reactor that is the most like an ideal PFR$.$ What is its size? Use the ideal reactor

equations to solve for conversion in this reactor.

c$)$ Given the following reactor choices and prices, what are the reactor$($s$)$ you should choose to

achieve the greatest conversion assuming a budget of $$50,000?$ What conversion do you

achieve?

Hint: Use the tanks$-$in$-$series model to choose your reactor$($s$).$

Note: If you find that two reactor options are similar in performance, it is okay to select two

options or propose the one that is numerically the highest. Full credit will be awarded for either

answer.

d$)$ You can sell the molecule B for $$\frac{0\mathrm{.}02}{m}ol.$ The feed A is free because it comes from waste of

another process. How many days do you need to run the reactors, assuming only $$50000$ in

capital costs, to break even?