The following equation represents the decomposition of a generic diatomic elemen

Question

The following equation represents the decomposition of a generic diatomic element in its standard state. 1/2 X_2 (g) rightarrow X(g) Assume that the standard molar Gibbs energy of formation of X(g) is 4.99 kJ middot mol^-1 at 2000. K and-51.88 kJ middot mol^-1 at 3000. K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature. At 2000. K, we were given: Delta G_f = 4.99 kJ middot mol^-1. What is K at that temperature? At 3000. K, we were given: Delta G_f = -51.88 kJ - mol^-1. What is K at that temperature?

Explanation / Answer

Using,

dGo = -RTlnK

with,

dGo = 4.99 kJ/mol at T = 2000 K

R = gas constant

we get,

4990 = -8.314 x 2000 lnK

K = 0.741

with,

dGo = -51.88 kJ/mol at T = 3000 K

R = gas constant

we get,

-51880 = -8.314 x 3000 lnK

K = 8.00

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