Gibbs Free Energy and Favorability
Quick Notes
- ΔG° is standard Gibbs free energy change.
- It can be used to predict if a reaction is thermodynamically favored.
- If ΔG° < 0, the process is thermodynamically favored (also called “spontaneous”).
- ΔG° can be calculated using:
- ΔG° = Σ ΔG°f(products) − Σ ΔG°f(reactants)
- ΔG° = ΔH° − TΔS°
- The signs of ΔH° and ΔS° determine how temperature affects favorability.
Full Notes
Note – Gibbs Free Energy has been covered in more detail here this page is just specifically for AP Chemistry.
What is Gibbs Free Energy (ΔG°)?
Gibbs free energy change (ΔG) combines enthalpy (ΔH), entropy (ΔS), and temperature (T) to predict whether a chemical or physical process is thermodynamically favored.
ΔG° represents the maximum amount of energy available to do work from a chemical or physical process at constant temperature and pressure.
A negative ΔG° means the reaction is thermodynamically favored – it can proceed without an external input of energy.
A positive ΔG° means the reaction is not favored under standard conditions.
Key note - Standard Conditions
Gibbs Free Energy values measured under standard conditions are referred to as standard Gibbs Free Energy values, shown with a ° symbol. Standard conditions refer to:
- Pure substances being in their most stable form (standard states)
- Solutes at 1.0 M concentration
- Gases at 1.0 atm (or 1.0 bar)
- A common reference temperature is 25°C (298 K)
There Are Two Main Ways to Calculate ΔG°
Equation 1: Gibbs Free Energy from Formation Values
Use standard tables for ΔG°f values (free energy of formation) and multiply each ΔG°f by its stoichiometric coefficient (molar ratios in balanced equation).
For Example
Calculate ΔG° for the following reaction, using the provided ΔG°f values.
Reaction: C(graphite) + O2(g) → CO2(g)
ΔG°f(C) = 0, ΔG°f(O2) = 0, ΔG°f(CO2) = −394 kJ·mol−1
- Products: [1 × (−394)] = −394 kJ·mol−1
- Reactants: [1 × 0] + [1 × 0] = 0 kJ·mol−1
- ΔG° = (−394) − 0 = −394 kJ·mol−1
Conclusion: Reaction is thermodynamically favored (ΔG° < 0).
Equation 2: Gibbs Free Energy from Enthalpy and Entropy
Given: ΔH° = +5.0 kJ·mol−1, ΔS° = +100 J·mol−1·K−1 = 0.100 kJ·mol−1·K−1, T = 298 K
- ΔG° = ΔH° − TΔS°
- ΔG° = 5.0 − (298 × 0.100) = 5.0 − 29.8
- ΔG° = −24.8 kJ·mol−1
Conclusion: Even though ΔH° is positive, the large positive ΔS° makes the reaction thermodynamically favored at this temperature.
Remember to check and convert units when using this equation! Entropy change (ΔS) is given in J·K−1·mol−1, whereas enthalpy change (ΔH) and Gibbs free energy change (ΔG) are in kJ·mol−1. Convert ΔS to kJ·mol−1·K−1 by dividing by 1000.
Interpreting the Signs of ΔH° and ΔS°
| ΔH° | ΔS° | ΔG° Prediction | Thermodynamic Favorability |
|---|---|---|---|
| − | + | ΔG° < 0 at all T | Always favored |
| − | − | ΔG° < 0 at low T | Favored only at low temperature |
| + | + | ΔG° < 0 at high T | Favored only at high temperature |
| + | − | ΔG° > 0 at all T | Never favored |
Why is Gibbs Free Energy Important?
Some processes cannot be predicted by enthalpy change (ΔH) alone — both enthalpy and entropy (ΔS) must be considered to determine if the process is thermodynamically favorable. This is where Gibbs free energy (ΔG) becomes important. A process is spontaneous when ΔG is negative (ΔG < 0).
ExampleFreezing of water: This is exothermic (ΔH < 0), but entropy decreases (ΔS < 0). The process is spontaneous only at low temperatures where the enthalpy term dominates.
ExampleDissolution of sodium nitrate (NaNO3): This is endothermic (ΔH > 0), but it increases entropy (ΔS > 0) as the solid dissolves into ions. The process can still be spontaneous at higher temperatures when the positive ΔS outweighs the positive ΔH.
Key Terms
- Thermodynamically favored = reaction can proceed under given conditions (ΔG° < 0).
- Not thermodynamically favored = reaction requires input of energy (ΔG° > 0).
- ΔG° values can be used to predict favorability, not the rate of the reaction (see Topic 9.4).
Summary
- ΔG° predicts whether a process is thermodynamically favored.
- It can be calculated from formation values or ΔH° and ΔS°.
- The signs of ΔH° and ΔS° reveal how temperature affects favorability.
- Always convert entropy to kJ when using the ΔG° = ΔH° − TΔS° equation.