OUESTION $26$

The Deacon process for production of chlorine involves the gas$-$phase catalytic reaction:

$HCl+\frac{1}{4}{O}_2\frac{1}{2}C{l}_2+\frac{1}{2}{H}_{2}O$

Furusaki $(1973)$ studied the kinetics of this reversible reaction, with a $CuC{l}_2,KCl,SnC{l}_2-$on silica catalyst in differential and integral reactor. The rate of disappearance of $HCl$ could be correlated by the equation:

$r=\frac{k[C_{HCl}{C}_{O_2}^{\frac{1}{4}}-(\frac{1}{K})C_{C{l}_2}^{\frac{1}{2}}{C}_{H_{2}O}^{\frac{1}{2}}]}{[1+K_1{C}_{HCl}+K_2{C}_{C_2}{]}^2}$

$($i$)$ Devise a series of fundamental steps of adsorption and surface reaction which will give the above rate expression.

$($ii$)$ The rate data at $350C,$ obtained in the differential reactor with feed of $HCl$ and air $($no $C{l}_2$ or $H_{2}O),$ is as follows:

$\backslash$table$[[\backslash$table$[[$Rate