In the decomposition of limestone to lime, the values of H^o and S^o are +179.1 ~kJ ~mol ⁻¹ and 160.2 ~J ~K ⁻¹ ~mol ⁻¹ . Calculate the temperature above which conversion of limestone to lime will be spontaneous, if values of H^o and S^o remain unchanged with temperature. [Assuming pressure 1 bar ]

Step-by-step solution

The reaction for the decomposition of limestone is CaCO₃(s) CaO(s) + CO₂(g) . For a reaction to be spontaneous, the Gibbs free energy change G^ o must be less than zero. The relationship between G^ o , H^ o , and S^ o is given by G^ o = H^ o - T S^ o . Setting G^ o H^ o S^ o . Given H^ o = +179.1 kJ mol ⁻¹ = 179100 J mol ⁻¹ and S^ o = 160.2 J K ⁻¹ mol ⁻¹ . Substituting the values into the inequality: T > 179100 J mol ⁻¹ 160.2 J K ⁻¹ mol ⁻¹ T > 1117.977 K Rounding to the nearest whole number, the temperature above w