Please help with this problem. Question 1 to 4.

If C. S. T. Richfield is successful in capturing the methane from the cows, it will be necessary to convert methane to a more valuable product such as methanol as the price of methane is historically low.

The methanol synthesis reaction is CH 4 + 0.5 O 2 CH 3OH with a rate constant of k 1.

Assume that this reaction is first order in methane, zero order in oxygen, zero order in methanol and that all species are present as ideal gases. The feed is stoichiometric. The total pressure of the inlet stream is P total. The temperature of the reactor is T. Dr. Richfield has found a large tank on the farm which he plans to use as a CSTR for this reaction.

1. What is the rate law expression of for this reaction in terms of the concentrations of the species involved? Assume that the rate constant is k 1.

2. Write an expression for the concentration of CH 4 as a function of the conversion of methane, X, and other given/known values assuming that the reactor is isothermal and isobaric.

3. Write an expression for the residence time of the reactor, , as a function of the conversion X and other constants given in the problem statement. Assume that the reactor is isothermal and isobaric.

4. Assume now that this reaction is reversible, but still isothermal and isobaric. Write an expression for the equilibrium constant, K, as a function of the initial concentration of methane and the equilibrium conversion, X Eq . Does the value of the equilibrium conversion change if a PFR is used instead of a CSTR?