4.4.3Additional lessons
Gibbs Free Energy (HL) — IB Chemistry HL Revision Notes & Topical Questions
5 min read 5 parts Lesson 87 of 172
Curriculum Equation Key Gibbs Free Energy FormulaFast Exam Solution
ΔG = ΔH - TΔS | (ΔG < 0: تلقائي Spontaneous, ΔG > 0: غير تلقائي, ΔG = 0: اتزان)
Part 1 of 5Defining Gibbs Energy
The Gibbs equation shows that the temperature changes the balance between energy and entropy.
Concept
- Gibbs free energy, G, combines the enthalpy and entropy effects to decide whether a process is energetically favourable.
Main equation
- ΔG⦵ = ΔH⦵ − TΔS⦵, where T is the temperature in kelvin.
Sign
- A negative ΔG⦵ means the reaction is spontaneous under standard conditions;
- a positive ΔG⦵ means it is non-spontaneous.
From formation data
- ΔG⦵ = ΣΔGf⦵(products) − ΣΔGf⦵(reactants), where elements in standard states have ΔGf⦵ of zero.
Part 2 of 5Calculation Method
The most common error is leaving ΔS⦵ in joules while ΔH⦵ is in kilojoules.
1
Obtain ΔH⦵ in kJ mol⁻¹ and ΔS⦵ in J K⁻¹ mol⁻¹ from the question or data.
2
Convert ΔS⦵ to kJ K⁻¹ mol⁻¹ by dividing by 1000 so the units match those of ΔH⦵.
3
Convert the temperature to kelvin by adding 273 to the Celsius value.
4
Substitute into ΔG⦵ = ΔH⦵ − TΔS⦵ and evaluate, taking care with the sign of the TΔS⦵ term.
5
Interpret the sign of the answer and state whether the reaction is spontaneous at that temperature.
Part 3 of 5Meaning of ΔG
Meaning of ΔG
Spontaneity
- ΔG⦵ < 0 indicates a reaction that can proceed without continuous input of energy.
Not rate
- A spontaneous reaction may still be extremely slow if its activation energy is high.
Maximum work
- The magnitude of ΔG represents the maximum useful work obtainable from a reaction at constant temperature and pressure.
Equilibrium
- At equilibrium ΔG = 0, so there is no further net tendency for change.
Part 4 of 5Worked Example
Question
- For N₂(g) + 3H₂(g) → 2NH₃(g), ΔH⦵ = −92 kJ mol⁻¹ and ΔS⦵ = −198.7 J K⁻¹ mol⁻¹.
- Calculate ΔG⦵ at 298 K.
- Convert ΔS⦵−198.7 J K⁻¹ mol⁻¹ = −0.1987 kJ K⁻¹ mol⁻¹.
- TΔS⦵ = 298 × (−0.1987) = −59.2 kJ mol⁻¹.
- ΔG⦵ = ΔH⦵ − TΔS⦵ = −92 − (−59.2) = −32.8 kJ mol⁻¹.
Answer ΔG⦵ = −32.8 kJ mol⁻¹, so spontaneous at 298 K
Part 5 of 5Exam Checklist & Tips
4.4.3 – Key Points for the Exam
- Gibbs free energy A quantity whose change predicts spontaneity at constant temperature and pressure.
- Spontaneous A change that occurs without continuous input of energy once started.
- ΔGf⦵ Standard Gibbs energy change for forming one mole of a compound from its elements.
- Kelvin The SI temperature scale required in all Gibbs energy calculations.
Common Mistakes
- Using a Celsius temperature in the equation instead of kelvin.
- Mixing kJ for ΔH⦵ with J for ΔS⦵ in the same calculation.
- Assuming a spontaneous reaction must be fast.
- Forgetting the minus sign in front of TΔS⦵ when ΔS⦵ itself is negative.
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