(Solved): 3. Hydrogen and toluene (T) react over a solid catalyst to form methane (M) and benzene (B). C6 ...

3. Hydrogen and toluene (T) react over a solid catalyst to form methane (M) and benzene (B). ${\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{CH}}_{3(g)}+{\mathrm{H}}_{2(g)}?{\mathrm{C}}_6{\mathrm{H}}_{6(g)}+{\mathrm{CH}}_{4(g)}$ The mechanism of the reaction is as follows: Adsorption: $\begin{array}{lll}\text{ Adsorption: }& {\mathrm{T}}_{(\mathrm{g})}+\mathrm{S}?\mathrm{T}.\mathrm{S}& \left({\mathrm{K}}_{\mathrm{T}}=\text{ adsorption equilibrium constant }\right)\\ \text{ Surface reaction: }& {\mathrm{H}}_{2(\mathrm{g})}+\mathrm{T}.\mathrm{S}?\mathrm{B}.\mathrm{S}+{\mathrm{M}}_{(\mathrm{g})}& (\mathrm{Ks}=\text{ surface reaction equilibrium constant })\\ \text{ Desorption: }& \mathrm{B}.\mathrm{S}?\mathrm{B}(\mathrm{g})+\mathrm{S}& \left({\mathrm{K}}_{\mathrm{B}}=\text{ benzene adsorption equilibrium constant }\right)\end{array}$ (i) Assuming surface reaction is rate limiting, derive: $?r_T=\frac{k{P}_{H2}{P}_T}{\left(1+K_B{P}_B+K_T{P}_T\right)}$ (ii) Determine the model parameters $\mathrm{k},{\mathrm{K}}_{\mathrm{B}}$, and ${\mathrm{K}}_{\mathrm{T}}$ using computer and attach the result with the help of Table 10-5 (Fogler). (iii) What is the fraction of vacant sites at $60\%$ conversion?