Products
Rewards
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY

HOLOOLY
TABLES

All the data tables that you may search for.

HOLOOLY
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY
HELP DESK

Need Help? We got you covered.

## Q. 19.14

A reversible chemical reaction, $A \rightleftarrows B$, occurs in the isothermal continuous stirred-tank reactor shown in Fig. E19.14. The rate expressions for the forward and reverse reactions are

\begin{aligned}&r_{1}=k_{1} C_{A} \\&r_{2}=k_{2} C_{B}\end{aligned}

For the information given below, use a numerical search procedure to determine the value of $F_{B}( L / h )$ that maximizes the production rate of $C_{B}$ (i.e., the amount of $C_{B}$ that leaves the reactor, $mol B / h$ ). The allowable values of $F_{B}$ are $0 \leq F_{B} \leq 200 L / h$

Available Information

(i) The reactor is perfectly mixed.

(ii) The volume of liquid, $V$, is maintained constant using an overflow line (not shown in the diagram).

(iii) The following parameters are kept constant at the indicated numerical values:

\begin{aligned}V &=200 L & F_{A} &=150 L / h \\C_{A F} &=0.3 mol A / L & C_{B F} &=0.3 mol B / L \\k_{1} &=2 h ^{-1} & k_{2} &=1.5 h ^{-1}\end{aligned}

## Verified Solution

Material balance:

Overall : $\quad F_{A}+F_{B}=F$

Component B: $\quad F_{B} C_{B F}+V K_{1} C_{A}-V K_{2} C_{B}=F C_{B}$

Component A: $\quad F_{A} C_{A F}+V K_{2} C_{B}-V K_{1} C_{A}=F C_{A}$

Thus the optimization problem is:

$\max \left(150+F_{B}\right) C_{B}$

Subject to:

$\begin{gathered}0.3 F_{B}+400 C_{A}-300 C_{B}=\left(150+F_{B}\right) C_{B} \\45+300 C_{B}-400 C_{A}=\left(150+F_{B}\right) C_{A} \\F_{B} \leq 200 \\C_{A}, C_{B}, F_{B} \geq 0\end{gathered}$

By using Excel- Solver, the optimum values are

\begin{aligned}&F_{B}=200 l / hr \\&C_{A}=0.129 mol A / l \\&C_{B}=0.171 mol B / 1\end{aligned}