A possible mechanism for the reduction of $NO$ by $CO$ on Pt$-$based automotive exhaust catalysts

consists of four elementary steps. The most abundant surface intermediates are ${(}^{**})$ and $(C{O}^{**})$

when $O_2$ is present at low concentrations in the effluent. Steps $1-3$ are quasi$-$equilibrated, and

step $4$ is irreversible. The effluent contains a large amount of $C{O}_2$ compared with any amounts

generated by the NO reduction reaction.

a$)$ Obtain a rate expression for this reaction

b$)$ Simplify this equation for the case when $(C{O}^{***})$ is the MASI

c$)$ Would backmixing in the catalytic converter increase or decrease the rate of $NO$

reduction in the case above?

d$)$ Now let's consider the reaction is under lean burning condition, where there is residual

$O_2$ in the effluent and the quasi$-$equilibrated dissociative adsorption of $O_2($step $5,K_5)$

leads to $(O^{**})$ becoming a MASI in addition to ${(}^{**})$ and $(C{O}^{**}).$ Further, $(O^{**})$ reacts with

$(C{O}^{**})$ in an irreversible step to form $C{O}_2$ and $2^{**}($step $6,$ k$6).$

Obtain an expression for the selectivity $S,$ defined as the rate of $CO$ consumption in $NO$

reduction to the direct combustion of $CO$ to form $C{O}_2.$ Why does $O_2$ inhibit the $NO$ reduction

rate?

e$)$ How would you use experiments to confirm:

i$.$ The irreversible nature of the recombinative nitrogen desorption step $($step $4)?$

ii$.$ The non$-$dissociative nature of the $CO$ chemisorption step $($step $2)?$