Thermal decomposition of n-butane can progress by three different gas-phase reaction pathways, forming ethylene, propylene, or 1-butene: 

(R1): C₄ H₁₀ ↔ C₂ H₄ + C₂ H₆ 

(R2): C₄ H₁₀ ↔ C₃ H₆ + CH₄

(R3): C₄ H₁₀ ↔ C₄ H₈ + H₂

1000 mol/hr of n-butane enter a reactor in which these three reactions occur simultaneously. The exiting stream is at equilibrium, with P = 1 bar. Use the rigorous method of accounting for the effect of temperature on equilibrium constants. 

A. Find the composition of the exiting stream if the reactor is at T = 500°C. 

B. Find the composition of the exiting stream if the reactor is at T = 1000°C. 

C. What temperature leads to the maximum yield of propylene?