Final answer:
To calculate the standard Gibbs free energy change (ΔG°) at 298 K, use the equation ΔG° = ΔH° - TΔS°, applying the values for ΔH° and ΔS°, where ΔS° is derived using the 'products minus reactants' rule from the standard molar entropy values of reactants and products.
Step-by-step explanation:
To calculate the standard Gibbs free energy change (ΔG°) at 298 K for a reaction, you need to know the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) of the reaction. At 25°C (or 298 K), you can use the following equation:
ΔG° = ΔH° - TΔS°
Where ΔG° is the standard Gibbs free energy change, ΔH° is the standard enthalpy change, ΔS° is the standard entropy change, and T is the temperature in Kelvin. Calculate ΔS° for the reaction from the absolute molar entropy values given for the reactants and products using the "products minus reactants" rule:
ΔS°reaction = ΣS°products - ΣS°reactants
For the given example reaction H₂(g) + O₂(g) → H₂O₂ (l) at 25°C, given:
ΔH° = -187.78 kJ/mol
S°(H₂O₂) = 109.6 J/(mol·K)
Sᵒ(O₂) = 205.2 J/(mol•K)
S°(H₂) = 130.7 J/(mol•K)
Calculate ΔS° using the entropies provided:
ΔS° = S°(H₂O₂) - (S°(H₂) + S°(O₂))
ΔS° = 109.6 J/(mol·K) - (2*130.7 J/(mol·K) + 205.2 J/(mol·K))
Then calculate ΔG°:
ΔG° = (-187.78 kJ/mol) - (298 K)(ΔS°)
Convert ΔS° from J to kJ by dividing by 1000, then insert it into the formula to get ΔG°. The sign of ΔG° will indicate whether the reaction is spontaneous (-ΔG°) or nonspontaneous (+ΔG°) under standard conditions.