Final answer:
To calculate the standard Gibbs free energy change (ΔG°) at 298 K, we use the formula ΔG° = ΔH° - TΔS° with the provided values to obtain ΔG° = 130.0 kJ/mol, suggesting the reaction is nonspontaneous at this temperature.
Step-by-step explanation:
The standard Gibbs free energy change (ΔG°) at 298 K for a reaction can be calculated using the formula:
ΔG° = ΔH° - TΔS°
where ΔH° is the standard enthalpy change, T is the temperature in Kelvin (K), and ΔS° is the standard entropy change. Using the given values:
ΔG° = 177.8 kJ/mol - 298 K * (0.1605 kJ/K mol)
Substitute the values into the equation:
ΔG° = 177.8 kJ/mol - (298 K * 0.1605 kJ/K mol)
The calculation gives:
ΔG° = 177.8 kJ/mol - 47.83 kJ/mol = 129.97 kJ/mol or approximately 130.0 kJ/mol
The positive value of ΔG° indicates that the reaction is nonspontaneous under standard conditions at 298 K and favors the reactants.