The equilibrium 3Fe(s) + C(s) $\rarr$Fe₃C(s) is established in a solid solution. For such a solution, one can write an equilibrium constant expression in the usual way except that the concentrations that refer to solids in the solid solution are included. Determine the equilibrium constant for the formation of cementite from iron and carbon at 680^$\circ$C. (Given: for this reaction at 25^$\circ$C, $\Delta$H^$\circ$= 21 kJ/mol and $\Delta$S^$\circ$ = 20.4 J/mol.K)

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The equilibrium constant for the formation of cementite from iron and carbon at 680°C can be calculated using the van't Hoff equation:ln(K2/K1) = -ΔH°/R(1/T2 - 1/T1)where K1 is the equilibrium constant at 25°C, K2 is the equilibrium constant at 680°C, ΔH° is the enthalpy change of the reaction, R is the gas constant, and T1 and T2 are the temperatures in Kelvin.Substituting the given values into the equation, we get:ln(K2/0.75) = -21 kJ/mol / (8.314 J/mol.K) * (1/953 K - 1/298 K)Solving for K2, we get:K2 = 0.82Therefore, the equilibrium constant for the formation of cementite from iron and carbon at 680°C is 0.82.

The Equilibrium 3Fe(s) + C(s) →\rarr→ Fe3C(s) Is Established in a Solid Solution

The Equilibrium 3Fe(s) + C(s) $\rarr$ Fe₃C(s) Is Established in a Solid Solution