Consider the following catalytic reaction mechanism. Gas reactants $A$&$B$ adsorb to a catalyst surface by molecular adsorption. These two adsorbed species on the surface participate in a dual site surface reaction that is nonreversible. The products are $C$ and $D,$ which are gas products that are never adsorbed on the surface.

Step $1$ adsorption: $A+SA*S$

Step $2$ adsorption: $B+SB*S$

Step $3$ surface reaction: $A*S+B*SC(g)+D(g)+2S$

Derive the catalytic rate expression from the reaction mechanism assuming that the surface reaction is the rate limiting step.