The variation of standard Gibbs free energy change ( G^ ) with temperature ( T ) for a reversible reaction is represented by a straight line. The line intersects the G^ axis (y-axis) at +40 kJ mol ⁻¹ and the temperature axis (x-axis) at 500 K. Assuming standard enthalpy ( H^ ) and standard entropy ( S^ ) changes are independent of temperature, the value of the equilibrium constant K at 500 K and the standard entropy

Step-by-step solution

The relationship between standard Gibbs free energy change, enthalpy change, and entropy change is given by the Gibbs-Helmholtz equation: G^ = H^ - T S^ This is the equation of a straight line ( y = mx + c ), where y = G^ , x = T , slope m = - S^ , and y-intercept c = H^ . From the given information, the y-intercept is +40 kJ mol ⁻¹ . Therefore, H^ = 40 kJ mol ⁻¹ = 40000 J mol ⁻¹ . The line intersects the temperature axis at 500 K, which means at T = 500 K, G^ = 0 . Using the relation G^ = -RT K , when G^ = 0 , we