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The following equation represents the decomposition of a generic diatomic element in its standard state.

1/2 X_{2} (g) → X (g)

Assume that the standard molar Gibbs energy of formation of X (g) is 5.14 kJ • mol^{-1} at 2000 K and -51.10 kJ • mol^{-1} at 3000 K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature.

Assuming that ΔH°_{rxn} is independent of temperature, determine the value of ΔH°_{rxn} from these data.