Gibbs Free Energy (ΔG⦵) HL Only
Quick Notes:
- Gibbs free energy (ΔG) can be used to determine whether a reaction is spontaneous.
- Formula: ΔG⦵ = ΔH⦵ − TΔS⦵
- Units:
- ΔH⦵ = kJ mol⁻¹
- ΔS⦵ = J K⁻¹ mol⁻¹ (must be converted to kJ for ΔG calculation)
- T = temperature in Kelvin
- A reaction is:
- Spontaneous if ΔG < 0
- Non-spontaneous if ΔG > 0
- At equilibrium if ΔG = 0
Full Notes:
What Is Gibbs Free Energy (ΔG)?
Both the enthalpy change (ΔH) and entropy change (ΔS) of a reaction have an impact on whether the reaction can happen based on energy. These can be linked, along with temperature (T), by Gibbs Free Energy Change (ΔG).
Gibbs Free Energy Change can tell us whether a reaction can happen spontaneously (is feasible) under standard conditions.
A reaction is feasible if ΔG is negative (ΔG < 0).
Even if ΔG < 0, a reaction may not occur if activation energy is too high.
Gibbs Free Energy Change can be calculated using:
- ΔG = Gibbs Free Energy change (kJ mol⁻¹)
- ΔH = Enthalpy change (kJ mol⁻¹)
- T = Temperature (K)
- ΔS = Entropy change (J K⁻¹ mol⁻¹) (convert to kJ K⁻¹ mol⁻¹ by dividing by 1000)
Important Units and Conversions
Remember to check and convert units when using this equation! Entropy change (ΔS) is always given in J per K per mol, whereas Enthalpy change (ΔH) and Gibbs Free Energy Change (ΔG) are given in kJ per mol. Make sure to convert entropy to kJ per mol (divide by 1000).
How to Perform a ΔG Calculation
- Check units: ΔH in kJ mol⁻¹, ΔS in J mol⁻¹ K⁻¹ (convert to kJ).
- Insert values into the formula.
- Multiply T × ΔS, then subtract that from ΔH.
- Interpret the result: negative = feasible, positive = not feasible.
A reaction has ΔH = –150 kJ mol⁻¹, ΔS = –100 J mol⁻¹ K⁻¹, T = 298 K. Determine whether the reaction is feasible at 298 K.
- Convert ΔS: –100 J mol⁻¹ K⁻¹ = –0.100 kJ mol⁻¹ K⁻¹
- ΔG = –150 – (298 × –0.100)
- ΔG = –150 + 29.8 = –120.2 kJ mol⁻¹
The reaction is feasible under standard conditions.
What Does the Sign of ΔG Tell Us?
- ΔG < 0 → The reaction is feasible (spontaneous under standard conditions).
- ΔG = 0 → The system is in equilibrium; no net change occurs.
- ΔG > 0 → The reaction is not feasible unless conditions change.
This helps explain why some reactions only work when heated or cooled.
Summary
- Gibbs Free Energy links enthalpy, entropy, and temperature to determine spontaneity.
- A reaction is feasible if ΔG < 0, not feasible if ΔG > 0, and at equilibrium if ΔG = 0.
- Always convert ΔS from J to kJ before using in calculations.
- Temperature can determine feasibility depending on signs of ΔH and ΔS.