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The decomposition of a generic diatomic element in its standard state is represented by the equation 12X2(g)āŸ¶X(g) Assume that the standard molar Gibbs energy of formation of X(g) is 4.84 kJĀ·molāˆ’1 at 2000 . K and āˆ’61.53 kJĀ·molāˆ’1 at 3000 . K. Determine the value of the thermodynamic equilibrium constant, K , at each temperature. At 2000 . K, Ī”????f=4.84 kJĀ·molāˆ’1 . What is K at that temperature?

Respuesta :

dsdrajlin

Answer:

At 2000 K. K: 0.747

At 3000 K. K: 11.79

Explanation:

Let's consider the decomposition of a generic diatomic element in its standard state.

1/2 Xā‚‚(g) āŸ¶ X(g)

The relation between the equilibrium constant (K) and the standard Gibbs energy (Ī”GĀ°) is:

[tex]K = e^{-\Delta G Ā \Ā° / R.T}[/tex]

where,

R is the ideal gas constant (8.314 Ɨ 10ā»Ā³ kJ/mol.K)

T is the absolute temperature

At 2000 K (Ī”GĀ° = 4.84 kJĀ·molā»Ā¹)

[tex]K=e^{-4.84kJ.mol^{-1}/8.314 \times 10^{-3} kJ.mol^{-1}.K^{-1} \times 2000 K } =0.747[/tex]

At 3000 K (Ī”GĀ° = āˆ’61.53 kJĀ·molā»Ā¹)

[tex]K=e^{61.53kJ.mol^{-1}/8.314 \times 10^{-3} kJ.mol^{-1}.K^{-1} \times 3000 K } =11.79[/tex]

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