Methyl ethyl ketone $($MEK$)$ is an important industrial solvent that can be produced

dehydrogenating butan$-2-$ol $($Bu$)$ over a zinc oxide catalyst $[$Ind$.$ Eng. Chem. Res., $27.,$

$272050(1988)]$:

$Bu$MEK$+H_2$

The following data giving the reaction rate for the production of MEK were obtained in

a differential reactor at $490C.$

Based on the data in this table, the appropriate speed equation is as follows:

$-r_A=r_B=\frac{k_1{P}_A}{(1+k_2{P}_A{)}^2}$

According to the value of $>0,$ the Ergun differential equation should be used as follows

shape:

Sea $y=\frac{P}{P_0},$ entonces: $\frac{dy}{dW}=-\frac{(1+x)}{2y}$

Taking into account the previous information, solve the following:

a$)$ Determine the value of the rate constants, $k1$ and $k2,$ using the data

experimental $($it is suggested to linearize the kinetic equation$).$

b$)$ Graph $\frac{P}{P_0}$ and $x$ as a function of the weight of the catalyst throughout the reactor, using a

incoming molar flow of pure butan$-2-$ol of $10mo\frac{l}{m}in$ at a temperature of $490C$ and a

inlet pressure of $10$atm. Consider a Wmax$=23$ kg taking into account the fall of

pressure and $=0\mathrm{.}03kg-1.$ Plot P$/$P$0$ and

reactor.

c$)$ Determine the weight of catalyst needed to achieve a $90\%$ conversion.

Remember that

$\frac{dx}{dW}=-\frac{r_A}{F_{A0}}$

$C_A=C_{A0}(\frac{1-x_A}{1+x_A})(\frac{P}{P_0})(\frac{T_0}{T})$

For this isothermal process with pressure drop:

$P_A=P_{A0}(\frac{1-x_A}{1+x_A})y$

It is suggested to use polymath to solve this problem.