For a chemical reaction at 300 K , the standard enthalpy change ( H^ ) is -20 kJ mol ⁻¹ and the standard entropy change ( S^ ) is -50 J K ⁻¹ mol ⁻¹ . What is the value of the standard Gibbs free energy change ( G^ ) for the reaction, and what does it imply about the equilibrium constant ( K )?

Step-by-step solution

First, calculate the standard Gibbs free energy change ( G^ ) using the equation: G^ = H^ - T S^ Given: H^ = -20 kJ mol ⁻¹ = -20000 J mol ⁻¹ S^ = -50 J K ⁻¹ mol ⁻¹ T = 300 K Substituting the values: G^ = -20000 J mol ⁻¹ - (300 K )(-50 J K ⁻¹ mol ⁻¹) G^ = -20000 J mol ⁻¹ + 15000 J mol ⁻¹ G^ = -5000 J mol ⁻¹ = -5 kJ mol ⁻¹ Next, relate G^ to the equilibrium constant ( K ) using the equation: G^ = -RT K Since G^ is negative ( -5 kJ mol ⁻¹ ), the term -RT K must be negative. This implies that K must be positive ( K > 0