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The 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 5.41 kJ⋅mol − 1 at 2000. K and − 52.48 kJ⋅mol − 1 at 3000. K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature. K at 2000. K = K at 3000. K =

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Answer:

[tex]K(2000K)=0.722\\K(3000K)=23.5[/tex]

Explanation:

Hello,

In this case, in terms of the Gibbs free energy of the given reaction, the equilibrium constant is computed as shown below:

[tex]K=exp(-\frac{\Delta G }{RT} )[/tex]

In such a way, since the given Gibbs correspond to formation of X, they will equal the Gibbs free energy of those reactions. Thus, at each temperature we obtain:

[tex]K(2000K)=exp(-\frac{5410J/mol}{8.314J/(mol*K)*2000K} )\\K(2000K)=0.722\\\\K(3000K)=exp(-\frac{-52480J/mol}{8.314J/(mol*K)*3000K} )\\K(3000K)=23.5[/tex]

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