A feed stock of pure n-butane is cracked at \(750 \mathrm{~K}\) and 1.2 bar to produce olefins. The following two independent reactions occur favouring the equilibrium conversions at these conditions:

\[ \begin{align*} & \mathrm{C}_{4} \mathrm{H}_{10} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{C}_{2} \mathrm{H}_{6} \tag{A}\\ & \mathrm{C}_{4} \mathrm{H}_{10} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6}+\mathrm{CH}_{4} \tag{B} \end{align*} \]

At \(750 \mathrm{~K}\) and \(1.2 \mathrm{bar}\), the equilibrium constants for the reactions (A) and (B) are \(K_{\mathrm{A}}=3.856\) and \(K_{\mathrm{B}}=268.4\). Determine the composition of the product gases at equilibrium.