In this exercise we propose to study the kinetics of the formation of methane from hydrogen and carbon monoxide over a nickel catalyst. \mathrm{CO}+3 \mathrm{H}_{2} \leftrightarrow \mathrm{CH}_{4}+\mathrm{H}_{2} \mathrm{O} The use

of a differential reactor gave the following rate expression: \mathrm{r}_{\mathrm{CH} 4}^{\prime}=\frac{0.0183 \mathrm{P}_{\mathrm{HZ}}^{1 / 2} \mathrm{P}_{\mathrm{CO}}}{1+1.5 \mathrm{P}_{\mathrm{H} 2}} The following mechanism has been proposed: \mathrm{H}_{2}+\mathrm{S} \longleftrightarrow \mathrm{k}_{1} \longrightarrow \mathrm{H}_{2} . \mathrm{S} \mathrm{H}_{2} . \mathrm{S}+\mathrm{S} \leftrightarrow \mathrm{k}_{2} \longrightarrow \mathrm{H} . \mathrm{S}+\mathrm{H} . \mathrm{S} \text { H.S }+\mathrm{CO} \leftrightarrow{ }_{4} \longrightarrow \mathrm{CHO} . \mathrm{S} \text { CHO.S + H.S\longleftrightarrow } \stackrel{k_{4}}{\longrightarrow} \text { C.S }+\mathrm{H}_{2} \mathrm{O}+\mathrm{S} \mathrm{C.S}+2 \mathrm{H}_{2} \stackrel{\mathrm{k}_{5}}{\longrightarrow} \mathrm{CH}_{4}+\mathrm{S} (1) Show that the mechanism is consistent with the proposed rate expression. You will assume that reaction 3 is the rate determining step and that reaction 5 is irreversible. Also, the equilibrium constant for reaction 1 is several orders of magnitude greater that the equilibrium constant of reaction 2. Make appropriate assumptions (and justify them) when needed.where Ki =k-1/k-1; K2 = k/k-z; K3 = k/k-3; Ka = kak4 (2) The feed consists of 75% Hz and 25% CO at a pressure of 10 atm. Determine the fraction of sites covered by H2. What do you conclude?