The dehydrogenation of ethanol $(C_2{H}_{5}OH)$ to acetaldehyde $(C_2{H}_{4}O)$ on metal surfaces occurs

via a sequence of elementary steps given by:

In which steps $1,3,$ and $4$ are quasi$-$equilibrated and ${(}^{**})$ and $(C_2{H}_5{O}^{***})$ are the most abundant

surface intermediates.

a$)$ Obtain a rate expression for the rate of $C_2{H}_{5}OH$ consumption. Obtain the equivalent rate

equation for the reverse of this reaction.

b$)$ What inequality $($in terms of only rate constants and reactant or product concentrations$)$

must be satisfied for the QE assumption of step $(1)$ to be valid?

c$)$ Propose experiments to show that:

i$.$ Step $1$ is QE

ii$.$ Step $2$ is irreversible