Propane is pyrolyzed by the following two independent gaseous reactions: [ begin{aligned} & mathrm{C}_{3} mathrm{H}_{8} ightarrow

Propane is pyrolyzed by the following two independent gaseous reactions:

\[ \begin{aligned} & \mathrm{C}_{3} \mathrm{H}_{8} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6}+\mathrm{H}_{2} \\ & \mathrm{C}_{3} \mathrm{H}_{8} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{CH}_{4} \end{aligned} \]

At \(1020 \mathrm{~K}\) and \(1 \mathrm{bar}\), the equilibrium constants for the reactions (A) and (B) are \(K_{\mathrm{A}}=\) 28.2 and \(K_{\mathrm{B}}=1.7\). Determine the composition of the equilibrium mixture. The reaction mixture is assumed to behave as an ideal gas.