Question

Cracking of ethane is very big business, as can be seen from the construction of the Shell cracker plant just outside Pittsburgh. The basic reaction is

C₂H₆  = C₂H₄ + H₂

(a) Compute the heat of reaction and the Gibbs free energy of reaction and the equilibrium constant at standard conditions using the data in Koretsky

(b) Write down the expression for the equilibrium constant in terms of the extent of reaction and the system pressure, assuming ideal gas behavior. Assume you start with pure ethane as the feed.

(c) Based on the expression from part (b): State if it would be beneficial to run the reaction at higher or lower temperature in terms of maximizing the extent of reaction, clearly articulating your justification and reasoning. State whether it would be better to run the reaction at high or low pressure for maximizing the extent of reaction, clearly articulating your justification and reasoning.

(d) Estimate the equilibrium constant at temperatures of 200⁰C and 500⁰C using the van't Hoff equation.

(e) Calculate the equilibrium extent of reaction, xi, for an initial amount of 100 moles of ethane using an analytic expression (not a numerical solution, but an equation you can explicitly solve) for the following cases: (i) T = 200 ⁰C and P = 1 bar; (ii)  T = 500 ⁰C and P = 1 bar; (iii)  T = 500 ⁰C and P = 10 bar; (iv)  T = 500 ⁰C and P = 0.1 bar. Do your results follow your predictions from part (c)?

Answer 1