CO oxidation to $C{O}_2(CO+\frac{1}{2}{O}_{2}harrC{O}_2)$ is an important reaction that ensures that the

toxic $CO$ molecule is not released from combustion systems $($e$.$g$.$ cars, fossil fuel power

plants, etc.$).$ Over a Pd catalyst surface at atmospheric pressure and a $CO$:$O_2$ ratio of $70$:$30,$

the mechanism for this reaction, along with relevant kinetic information, can be written as:

Derive a rate law for this reaction by following the below steps.

a$.$ Write down each reaction and derive an elementary rate law for each reaction.

Label the reactions with the forward and reverse rate constants, accounting for unit

changes where needed by including partial pressures.

b$.$ Derive an overall rate law for $CO$ oxidation using the quasi$-$equilibrium

approximation and pseudo$-$steady state hypothesis as needed. Clearly state which

step you are assuming is rate limiting and why. Clearly state which species you are

assuming is short$-$lived and why. Based on a comparison of the relative rate

constants, state which steps $($if any$)$ you will consider reversible or irreversible.