Problem $2.$ Development of a Catalytic Reaction Rate Expression

Consider the catalytic reaction $AP.$ A possible reaction mechanism is given below where $s$

denotes an active catalytic site.

Chemisorption of $A$:$A+sAs$

Surface reaction: $,$ As $$ Rs

Desorption of $R$:$,RsR+s$

Derive expressions for the reaction rate for the following two cases:

$($a$)$ Step $1($Chemisorption of specie A$)$ is rate controlling

$($b$)$ Step $2($Surface reaction$)$ is rate controlling

Derive the linearized from of the rate equations for the above two cases that would be

used to obtain initial estimates of the rate and adsorption equilibrium parameters from

experimental data on the initial rates, partial pressures of specie A and R$,$ and the

overall thermodynamic equilibrium constant.