Problem $1$

In Applied Catalysis A $108(1994),7-19$ the selective hydrogenation of isoprene $($A$)$ over palladium

catalysts was described. In this study the gas phase reaction of isoprene $(2-$methyl$-1,3-$butadiene$)$

towards $2-$methyl$-1-$butene, $3-$methyl$-1$butene, $2-$methyl$-2-$butene $($collectively termed B$)$ and

isopentane $(C)$ is investigated.

The global reaction scheme is given as:

isoprene $$ isopentenes $$ isopentane

$($A$)$

$($B$)$

$($C$)$

In this reaction, a dual site catalyst is used, where two different sites $(*$ and $)$ are present. The

researchers suspect that the reaction mechanism consist of $5$ elementary steps $($see below$),$

where step $1-3$ are adsorption steps, which are considered very fast and in quasi$-$equilibrium while

the two reactions $($step $4$ and $5)$ are considered rate determining.

adsciption Step $1$: $A+*longleftrightarro{w}_{k_A}{A}^{*}$

Step $2$: $B+*longleftrightarro{w}_{k_B}{B}^{*}$

Step $3$: $H_2+2longleftrightarro{w}_{k_{H_2}}2H$

very fast quasi equilibrium

a$)$ Derive the rate expression for the conversion of isoprene $($A$).$

After further experiments, it became clear that the two reactions $($step $4$ and $5)$ were in fact

irreversible. Furthermore, it was experimentally observed that the conversion rate of A was first

order in hydrogen.

b$)$ Adjust the rate expression derived in $($a$)$ if steps $4$ and $5$ are considered irreversible.

c$)$ If the proposed reaction mechanism in $($b$)$ is correct, what can you conclude about the

adsorption strength of $H_2$ on a $$ site? $$