(Solved): Problem 8-6 (Level 2) Methyl cyclohexane (MCH) is being dehydrogenated to toluene (T) in a catalyt ...

Problem 8-6 (Level 2) Methyl cyclohexane (MCH) is being dehydrogenated to toluene $(\mathrm{T})$ in a catalytic, fluidized-bed reactor. The feed to the reactor is a $2/1$ (molar) mixture of ${\mathrm{H}}_2$ and $\mathrm{MCH}$ at a temperature of $500^{?}\mathrm{C}$ and atmospheric pressure. The feed rate of $\mathrm{MCH}$ is $2.0\mathrm{lb}?\mathrm{mol}/\mathrm{s}$. The reactor contains 20.0 $\mathrm{lb}$ of catalyst and operates adiabatically. For the purpose of this analysis, assume that the reactor is an ideal CSTR. The following table contains some kinetic and thermodynamic data pertaining to the reaction. Kinetic and thermodynamic data for methyl cyclohexane dehydrogenation Methyl cyclohexane Toluene ${}^6$ Provided that the mixture results from an initial composition of $1\mathrm{mol}$ of toluene and $1\mathrm{mol}$ of ${\mathrm{H}}_2$. Heat of reaction $?+54.3\mathrm{kcal}/\mathrm{mol}$ (you may assume that $?H_{\mathrm{R}}$ is constant even though $?v_i{c}_{p,i}?=0$ ) Equilibrium constant (based on pressure) $\ln K_{\text{eq }}?53.47?(27,330/T){\mathrm{atm}}^3$, where $T$ is in $\mathrm{K}$ Heat capacities (cal/mol-K) Rate equation $?r_{\mathrm{MCH}}=k{\mathrm{C}}_{\mathrm{MCH}}\left(1?\frac{p_T{p}_{{\mathrm{H}}_2}^3}{p_{\mathrm{MCH}}{K}_{\mathrm{eq}}}\right)$ $p_i$ denotes partial pressure of species " $i$ ", and $C_{\mathrm{MCH}}$ is the concentration of $\mathrm{MCH}$. $k=3.35\times 10^{24}\left(\frac{{\mathrm{ft}}^3}{\mathrm{s}?\mathrm{lb}?\mathrm{cat}}\right){\mathrm{e}}^{?E/RT}$ $E=70.0\mathrm{kcal}/\mathrm{mol}$ The ideal gas law is valid. 1. At what temperature and fractional conversion of $\mathrm{MCH}$ does the reactor operate? 2. Based only on the slopes of the $G(T)$ and $R(T)$ curves, is the operating point stable or unstable?