How to find the Kp values?

Question

4) Carbon disulfide is a foul smelling solvent that dissolves sulfur and other nonpolar substances. It can be made by heating sulfur in an atmosphere of methane.

4CH4 (g) + S8 (s) ⇔ 4CS2 (g) + 8 H2 (g)

Starting with the following data, calculate the values of Kp for the reaction at 25 °C and
500 °C. ∆H° f= 115.3 kJ/mol, ΔS°= 237.8 kJ/mol ⋅ K, and ∆G° f = 65.1 kJ/mol

Answer 1

Assuming that the ∆Sº is indeed J/mol-K and not kJ/mol-K as stated, and assuming that the given values of ∆Gf and ∆Hf are at 25ºC, then, since there are 4 moles CS2(g) formed, the ∆Grx = 4x65.1 = 260.4 kJ. Also recall that ∆Gf for CH4, S8, and H2 are zero.

At 25ºC = 298ºK
K = e^-∆G/RT = e^-260.4/(0.008314 kJ/mol)(298) = e^-105 = 2.5x10^-46

At 500ºC = 773ºK
∆G = ∆H - T∆S = 4x115.3 - (773)(4x237.8) = 461.2 kJ - 735,278 J = 461.2 kJ - 735 kJ = -274 kJ

K = e^-∆G/RT = e^-(-274)/(0.008314)(773) = e^+42.6 = 3.3x10^18