Complete the following for the reaction below. You may solve by hand, Excel, Mathematica, Matlab, or

any other program$($s$)$ of your choice. Your solution can be approximate $($i$.$e$.$ just like the examples in

chapter $9$ of the book$).$

$A(aq)R(aq)$

$G^{{?}_{298}}=-12k\frac{J}{m}ol$

$H_{298}^{}=-77k\frac{J}{m}ol$

$k_{0,1}=4\mathrm{.}5{10}^{6}mi{n}^{-1}$;$,E_1=40k\frac{J}{m}ol$

$C_{pA}=C_{pR}=$ constant $=C_{p{H}_{2}O\text{@}25C}$

a$)$ Plot the equilibrium conversion as a function of temperature $($like in Figure E$9\mathrm{.}2).$

APPROACH: This is a pretty straightforward relationship. The equation is given in chapter

$9$ and there is a near identical example.

b$)$ Estimate the minimum volume PFR required to achieve $30\%$ conversion of A $($like Example $9\mathrm{.}4).$ A

is fed into the reactor at $2\mathrm{.}0M$ and $1000mo\frac{l}{m}in.$

APPROACH: This is a bit more complex. Since the plot from example $9\mathrm{.}4$ does not apply, I

recommend the following steps to solving this:

Select specific conversions $($i$.$e$.x=0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}15,0\mathrm{.}2,0\mathrm{.}25,0\mathrm{.}3).$

Set$-$up the equation for $-r_A$ as a function of $T$ and $x$ using a stoichiometric table and

Arrhenius' equation.

For each conversion in step $1,$ calculate the $T$ that will maximize rate using something

like Wolfram Alpha. Keep in mind that this is an aqueous reaction.

This will give you a table of rates at each conversion. You can calculate the volume for

the PFR using the graphical approach described when we were originally covering ideal

reactors.

c$)$ What is the necessary inlet temperature for a minimum volume adiabatic CSTR operating at $30\%$

conversion?

APPROACH: Use the approach described above to determine the optimal temperature for

the CSTR$.$ Calculate the inlet temperature using the heat of reaction and specific heat as

described in chapter $9|$