As a newly minted chemical engineer, you are tasked with describing the reaction mechanism of a new catalyst. You are told that you need to determine whether the surface reaction on the new catalyst follows a single site or dual site mechanism. Use the reaction below to answer the following questions:

$A(g)$catalystB$(g)+C(g)$

Questions:

Derive the following rate laws:

a$.$ Adsorption

b$.$ Surface reaction $($single site$)$

c$.$ Surface reaction $($dual site$)$

d$.$ Desorption

You are given the rate data for the surface reaction and calculate the concentration of the occupied sites $($Table $1).$ Determine whether the surface reaction follows a dual site or single site mechanism.

Table $1$: Surface Reaction Rate Data

$\backslash$table$[[,(\frac{\text{m}\text{o}\text{l}*T}{\text{k}\text{g}\text{c}\text{a}\text{t}*min})$