Free Energy and K?

Question

Acetylene, C2H2, can be converted to ethane, C2H6, by a process known as hydrogenation. The reaction is:
C2H2(g) + 2H2(g) === C2H6(g)

Given the following, what is the Kp for the reaction?

C2H2(g): 209.2 ΔG˚f (kJ/mol)
H2(g): 0 ΔG˚f (kJ/mol)
C2H6(g): -32.89ΔG˚f (kJ/mol)

ΔG˚ = -RTlnK
ΔG = ΔG˚RTlnQ

Answer 1

? Under what conditions

For the reaction

C2H2 +2H2 <=> C2H6

ΔG0 = ΔG0f(C2H6) -(ΔG0f(C2H2) + 2ΔG0f(H2)) =
= -32.89-(209.2+2*0) = -242.09 kj


Kp= P(C2H6) /(P(C2H2)*P(H2)^2) and since P=CRT
Kp= [C2H6] / [C2H2][H2]^2 *(RT)^-2 = Kc / (RT)^2

But
ΔG0 = -RTlnKc =>
Kc= e^-(ΔG0/RT)

Thus

Kp= [e^-(ΔG0/RT) ] /(RT)^2

Substitute the value T that you want, ΔG0 from above and you're done; be careful to express R in kJ/K.mol if you express ΔG0 in kJ/mol