I need all parts answered. The following equation represents the decomposition o

Question

I need all parts answered.

The following equation represents the decomposition of a generic diatomic element in its standard state. 1/2X2(g) rightarrow X(g) Assume that the standard molar Gibbs energy of formation of X(g) is 5.23 kJ- mol-1at 2000. K and -63.28 kJ - mol-1 at 3000. K. Determine the value of K (the thermodynamic equilibrium constant) at each temperature. K a I 2000. K = K at 3000. K = Assuming that delta H degree rxn is independent of temperature, determine the value of delta H degree rxn from these data . delta H degree rxn =

Explanation / Answer

1/2 X2(g) => X(g)

Molar gas constant R = 8.314 J/mol.K

Temperature T = 2000 K

Delta Gf = -RT ln K = 5.23 kJ/mol = 5230 J/mol

K at 2000 K = exp(-Delta Gf/RT)

= exp(-5230/(8.314 x 2000))

= 0.7301 = 0.730

Temperature T = 3000 K

Delta Gf = -RT ln K = -63.28 kJ/mol = -63280 J/mol

K at 3000 K = exp(-Delta Gf/RT)

= exp(63280/(8.314 x 2000))

= 12.64

van't Hoff equation: ln(K2/K1) = -DH/R x (1/T2 - 1/T1)

ln(12.64/0.7301) = -DH/8.314 x (1/3000 - 1/2000)

DH = 142241 J/mol = 142 kJ/mol

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