$(50$p$.)$ A proposed mechanism for the water$-$gas shift reaction on ferrochrome catalysts at

high $T$ is:

$H_{2}O+Sharr{H}_{2}O-S,r_1=k_l[H_{2}O]{}_S-k_{-1}{}_{H2O}S$

$H_{2}O-$Sha$\frac{r}{r}HO-S-H,r_2=k_2{}_{H2O-S}=k_{-2}{}_{HO-S-H}$

$HO-S-$HharrO$-S+H_2,r_3=k_3{}_{HO-S-H}-k_{-3}[H_2]{}_{O-S}$

$CO+O-$Sharr OCO$-S{r}_4=k_4[CO]{}_{O-S}-k_{-4}{}_{\text{O}\text{c}\text{o}-S}$

OCO$-SharrC{O}_2+S,r_5=k_5{}_{\text{o}\text{c}\text{o}-5}{k}_{-5}[C{O}_2]$

where $S$ is a surface site and $H_{2}O-S,HO-S-H,O-S$ and OCO$-$S are surface bound species

$($each molecule of a surface bound species is chemisorbed onto a single surface site$).$

$($a$)$ What are the units of each one of the ten rate constants? $(5$p$.)$

$($b$)$ Derive an expression for the rate of the overall reaction $(H_{2}O+CO{H}_2+C{O}_2)$

in terms of the gas phase concentrations, assuming that reaction $3$ is the rate

limiting step. $(15$p$.)$

$($c$)$ Derive an expression for the rate of the overall reaction assuming that $C{O}_2$

desorption is the rate limiting step. $(15$p$.)$

$($d$)$ Derive an expression for the rate of the overall reaction assuming that $H_{2}O$

adsorption is the rate limiting step. $(15$p$.)$