Final answer:
The change in free energy (ΔG°) for the reaction at 298 K is calculated to be -120.31 kJ/mol, indicating a spontaneous reaction at this temperature.
Step-by-step explanation:
To calculate ΔG° for the reaction at 298 K, we use the equation ΔG° = ΔH° - TΔS. The provided enthalpy change (ΔH°) is -187.78 kJ/mol, and the entropy change (ΔS°) is -226.3 J/(mol·K). First, convert the entropy to kJ by dividing by 1,000: -226.3 J/(mol·K) × 1 kJ/1,000 J = -0.2263 kJ/(mol·K). Then substitute the values into the equation:
ΔG° = (-187.78 kJ/mol) - (298.15 K)×(-0.2263 kJ/(mol·K))
ΔG° = -187.78 kJ/mol + 67.47 kJ/mol
ΔG° = -120.31 kJ/mol
The change in free energy ΔG° for the reaction at 298 K is therefore -120.31 kJ/mol, indicating that at 298 K, the reaction is spontaneous since the ΔG° value is negative.