Find the equilibrium constant

Question

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. For the reaction (below), ΔH_rxn° = 760.4 kJ and ΔS_rxn°= 1219.1 J/K. 

4CH₄ (g) + S₈ (s) --> 4CS₂ (g) + 8H₂ (g)

Calculate the equilibrium constant at 250.0 °C.

Calculate the equilibrium constant at 500.0°C.

Answer 1

ln K = ∆Hº/RT - ∆Sº/R (see below for derivation)

For 250ºC = 523 K:

ln K = 760.4 kJ/(0.008134 kJ/Kmol)(523K) - 1.219 kJ/K / 0.008314

ln K = 174.8 - 146.6

ln K = 28.2

K = 1.77x10¹²

(be sure to check the math)

Repeat above using 773K at the temperature

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∆Gº =-RT ln K

∆Gº = ∆Hº - T∆Sº

-RT ln K = ∆Hº - t∆Sº

ln K = ∆Hº/RT - ∆Sº/R