The kinetics of the following reaction was investigated over $Cu\frac{O}{C}{r}_2\frac{O_3}{S}i{O}_2$ catalyst at temperatures of

$225C$ to $285C$ and a pressure of $10$atm.

$C{H}_{3}C{H}_{2}OHharrC{H}_3$CHO$+H_2$

AharrB$+C$

The possible rate law to describe the data obtained is given by:

$-r_{CO}=\frac{k[P_A-\frac{(P_B{P}_C)}{K_e}]}{[1+k_A{P}_A+k_B{P}_B{]}^2},\frac{\text{m}\text{o}\text{l}}{\text{m}\text{i}\text{n}\text{.}\text{k}\text{g}\text{c}\text{a}\text{t}}$

where $k_A=0\mathrm{.}1,k_B=0\mathrm{.}02$ and $K_e=20.$

Develop a mechanism and rate$-$limiting step that is consistent with this experimental observation.

Prove that the mechanism developed will yield the rate law given above.

Suggest a reaction system, a PBR$,$ fluidized CSTRs and reactors in series that will maximize the

production of $C{H}_3$CHO. Consider both isothermal and non$-$isothermal $($but adiabatic$)$ operation

of the reactor$($s$).$ The feed of pure $C{H}_{3}C{H}_{2}OH$ enters at $225C$ and a pressure of $10$atm.