Consider the equilibrium C₂H₆(g) ⇋ C₂H₄(g) + H₂(g). At 1000.K and a constant total pressure of 1.00 bar, C₂H₆(g) is introduced into a reaction vessel. The total pressure is held constant at 1 bar and at equilibrium the composition of the mixture in mole percent is H₂(g): 26.0%, C₂H₄(g): 26.0%, and C₂H₆(g): 48.0%.

a. Calculate K_P at 1000.K.

b. If ΔH^o_R =137.0 kJ mol^-1, calculate the value of K_P at 298.15 K.

c. Calculate ΔG^o_R for this reaction at 298.15 K.