For a reversible reaction X Y , the standard enthalpy change ( H^ ) is 400 kJ mol ⁻¹ and the standard entropy change ( S^ ) is 800 J K ⁻¹ mol ⁻¹ . Assuming H^ and S^ are independent of temperature, the temperature in ^ C at which the equilibrium mixture contains equal moles of X and Y is:

Step-by-step solution

For the reaction X Y , the equilibrium constant is K = [ Y ] [ X ] . When the equilibrium mixture contains equal moles of X and Y , their concentrations are equal, meaning K = 1 . The standard Gibbs free energy change is given by G^ = -RT K . For K = 1 , G^ = 0 . Using the Gibbs-Helmholtz equation G^ = H^ - T S^ , we have: H^ = T S^ Given H^ = 400 kJ mol ⁻¹ = 400000 J mol ⁻¹ and S^ = 800 J K ⁻¹ mol ⁻¹ . Solving for temperature T in Kelvin: T = H^ S^ = 400000 800 = 500 K Converting the temperature to Celsius: T ( in