The gas-phase decomposition of X₂ into X at 298 K follows the reaction: X₂ (g) ⇌ 2X (g). The standard Gibbs free energy change ΔG° for this reaction is positive. Initially, 1 mole of X₂ is present with no X. As the reaction progresses, β moles of X are formed, and βₑₓₑq represents the equi

Question

The gas-phase decomposition of X₂ into X at 298 K follows the reaction: X₂ (g) ⇌ 2X (g). The standard Gibbs free energy change ΔG° for this reaction is positive. Initially, 1 mole of X₂ is present with no X. As the reaction progresses, β moles of X are formed, and βₑₓₑq represents the equilibrium amount of X produced. The process occurs at a constant total pressure of 2 bar, assuming ideal gas behavior. (R = 0.083 L bar K⁻¹ mol⁻¹) What is the expression for the equilibrium constant Kₚ at 298 K in terms of βₑₓₑq?

Accepted Answer

8βₑₓₑq² / (4 − βₑₓₑq). The equilibrium constant Kₚ is derived using the partial pressures of the species at equilibrium. The total pressure is 2 bar, and the mole fractions depend on βₑₓₑq. Substituting these into the expression for Kₚ gives 8βₑₓₑq² / (4 − βₑₓₑq).

Solution

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