A gas-phase decomposition reaction A(g) B(g) + C(g) takes place at 300 K . The standard enthalpies of formation ( H_f^ ) and standard absolute entropies ( S_m^ ) for the species are given below: Species H_f^ (kJ mol ⁻¹) S_m^ (J K ⁻¹ mol ⁻¹) A(g) -200 100 B(g) -150 120 C(g) -10 80 The standard free energy change ( G^ ) for the reaction in kJ mol ⁻¹ is ______.

Step-by-step solution

First, calculate the standard enthalpy of reaction ( H^ _ rxn ): H^ _ rxn = H_f^ ( products ) - H_f^ ( reactants ) H^ _ rxn = [ H_f^ (B) + H_f^ (C)] - H_f^ (A) H^ _ rxn = [(-150) + (-10)] - (-200) H^ _ rxn = -160 + 200 = 40 kJ mol ⁻¹ Next, calculate the standard entropy of reaction ( S^ _ rxn ): S^ _ rxn = S_m^ ( products ) - S_m^ ( reactants ) S^ _ rxn = [S_m^ (B) + S_m^ (C)] - S_m^ (A) S^ _ rxn = [120 + 80] - 100 S^ _ rxn = 200 - 100 = 100 J K ⁻¹ mol ⁻¹ Convert S^ _ rxn to kJ K ⁻¹ mol ⁻¹ to match the units of H^