23.4 Gibb’s Free Energy
🎯 Learning Outcomes
Candidates should be able to:
- ✓ State and use the Gibbs equation ΔG⦵ = ΔH⦵ − TΔS⦵
- ✓ Perform calculations using the equation ΔG⦵ = ΔH⦵ − TΔS⦵
- ✓ State whether a reaction or process will be feasible, using the sign of ΔG
- ✓ Predict the effect of temperature change on the feasibility of a reaction, given standard enthalpy and entropy changes
- ✓ Describe and explain qualitatively the trend in the thermal stability of the nitrates and carbonates, including the effect of ionic radius on the polarisation of the large anion
1 🧭 Introduction to Gibbs Free Energy ▶
−ΔG represents the maximum useful energy a reaction can supply to do work — power a muscle, drive a motor, push electrons round a circuit. It’s the chemistry behind every battery, and every meal you eat.
The words spontaneous and feasible both mean “likely to happen.” Chemists use the word feasible specifically for chemical reactions; spontaneous is a broader term that also covers physical processes such as diffusion and dissolving.
To judge whether a chemical reaction is likely to be feasible, we use Gibbs’ free energy change, ΔG. It’s defined in terms of the total entropy change of the universe (system + surroundings):
🧮 Where Does This Equation Come From?
To work out whether a reaction is spontaneous, we need the entropy change of both the system (the reaction itself) and the surroundings (which absorb or release the heat).
The surroundings’ entropy change depends on the heat exchanged, q, at temperature T:
Substituting, then multiplying through by T and by −1:
Since G⦵ = −T·ΔS⦵(total), this gives the familiar form:
−ΔH⦵ measures the total heat energy lost from the system. −ΔG⦵ is the maximum amount of that energy which is actually available to do useful work — the rest is “lost” as the entropy change of the surroundings. The unit of ΔG⦵ is generally kJ mol⁻¹.
ΔH⦵ is usually given in kJ mol⁻¹, but ΔS⦵ is in J K⁻¹ mol⁻¹. Before combining them in ΔG⦵ = ΔH⦵ − TΔS⦵, convert ΔH⦵ to J mol⁻¹ (× 1000) — or convert ΔS⦵ to kJ K⁻¹ mol⁻¹ (÷ 1000). Forgetting this is one of the most common exam slips.
2 🚦 Predicting Feasibility ▶
Once ΔG has been calculated, it tells you everything about whether a reaction can go:
| Value of ΔG | What it means |
|---|---|
| ΔG negative 🟢 | The reaction is feasible |
| ΔG = 0 ⚖️ | The reaction is at equilibrium |
| ΔG positive 🔴 | The reaction will not go spontaneously to completion |
“Feasible” is a thermodynamic statement, not a kinetic one. A reaction with negative ΔG can still be immeasurably slow if the activation energy is high — feasibility says nothing about rate.
3 🌡️ Effect of Temperature on Feasibility ▶
Since ΔG = ΔH − TΔS, the signs of ΔH and ΔS between them decide when — if ever — a reaction becomes feasible.
| ΔH | ΔS | Feasible when… | Real examples |
|---|---|---|---|
| + | + | High T only (entropy-driven) | Melting, boiling, thermal decomposition, electrolysis |
| − | − | Low T only (enthalpy-driven) | Freezing, condensation, precipitation, addition reactions |
| − | + | All temperatures — always spontaneous | Combustion, explosions, ozone decomposition |
| + | − | Never spontaneous on its own | Photosynthesis (needs sunlight to drive it) |
🌟 Bringing the Table to Life
- Decomposition of CaCO₃ (ΔH > 0, ΔS > 0): ΔG = +131 kJ mol⁻¹ at 298 K (not spontaneous), but ΔG = −64 kJ mol⁻¹ at 1500 K (spontaneous) — exactly why lime kilns must be so hot.
- Hydrogenation of ethene (ΔH < 0, ΔS < 0): feasible at room temperature, but less so as temperature rises.
- Ozone decomposition (ΔH < 0, ΔS > 0): spontaneous at every temperature — this is precisely why ozone is so unstable.
- Photosynthesis (ΔH > 0, ΔS < 0): ΔG is always positive, so plants must constantly feed in sunlight energy to force the reaction to occur.
4 🔥 Thermal Stability: Carbonates & Nitrates ▶
Group 2 carbonates and nitrates need increasingly higher temperatures to decompose as you go down the group. Consider the general reactions:
Each carbonate releases one mole of gas, and each nitrate releases two-and-a-half moles of gas — so the entropy change of decomposition is similar across the whole group for each series. That means the enthalpy change is what really controls how easily each one decomposes.
| Mg | Ca | Sr | Ba | |
|---|---|---|---|---|
| ΔH / kJ mol⁻¹ | +100.3 | +178.3 | +234.6 | +269.3 |
| ΔG / kJ mol⁻¹ | +48.3 | +130.4 | +184.1 | +218.1 |
| ΔS / J K⁻¹ mol⁻¹ | +174 | +161 | +168 | +172 |
Decomposition of the Group 2 carbonates
| Mg | Ca | Sr | Ba | |
|---|---|---|---|---|
| ΔH / kJ mol⁻¹ | +255.4 | +369.7 | +452.6 | +505.0 |
| ΔG / kJ mol⁻¹ | +122.7 | +241.8 | +320.8 | +374.2 |
| ΔS / J K⁻¹ mol⁻¹ | +445 | +429 | +442 | +439 |
Decomposition of the anhydrous Group 2 nitrates (hydrated salts will differ slightly, but the trend holds)
At room temperature, ΔG is positive for all of these — none decompose spontaneously. As T rises, ΔG falls towards zero (since ΔG = ΔH − TΔS), and decomposition becomes feasible once TΔS ≈ ΔH. Because ΔH is smallest at the top of the group, that temperature is reached soonest there — exactly matching the observation that Mg compounds decompose at lower temperatures than Ba compounds.
⚛️ Why Does ΔH Increase Down the Group?
As the cation gets larger going down the group, its charge density falls — the same +2 charge spread over a bigger ion creates a weaker electrostatic field. A small, high charge-density cation like Mg²⁺ pulls harder on the electron clouds of the neighbouring carbonate or nitrate ion, distorting (polarising) it into a shape that already resembles the products. A large, low charge-density cation like Ba²⁺ barely distorts the anion at all.
More polarisation makes decomposition easier (lower ΔH, lower decomposition temperature); less polarisation makes the ion more stable (higher ΔH, higher decomposition temperature). That’s why thermal stability increases down Group 2 — bigger cation → lower charge density → less polarisation → more stable carbonate/nitrate → higher decomposition temperature.
Q: Describe the variation in the thermal stability of Group 2 carbonates. Explain your answer. [3]
Marking points: Stability increases down the group ✓ ionic radius of the cation increases down the group (charge density decreases) ✓ less polarisation/distortion of the carbonate ion ✓
Q: The carbonates and hydroxides of Group 2 elements show similar trends in thermal stability. Suggest and explain the variation in the trend for the Group 2 hydroxides. [3]
Marking points: Stability increases down the group ✓ radius/size of the cation (M²⁺) increases ✓ less polarisation/distortion of the hydroxide ion (OH⁻) ✓
Q: The lattice energy of the Group 2 carbonates, and of the Group 2 oxides, both become less exothermic down the group — but by different amounts. Suggest how the standard enthalpy change of decomposition for the Group 2 carbonates changes down the group, in terms of relative ionic sizes and lattice energy changes. [2]
Marking points: ΔH(decomposition) becomes more positive / less negative down the group ✓ the oxide ion is smaller than the carbonate ion, so ΔH(lattice) of the oxides changes faster (becomes less exothermic more quickly) than that of the carbonates ✓
5 🧪 Decomposition of Oxalates ▶
An oxalate (or ethanedioate) is a salt containing the C₂O₄²⁻ ion. On heating, the weak carbon–carbon (C–C) bond within this ion breaks, causing decomposition.
| Metal type | General equation | Solid product | Gaseous products |
|---|---|---|---|
| Group 2 metals (e.g. Ca, Ba, Mg) & alkali metals (Li, Na, K) | MeC₂O₄ → MeCO₃ + CO | Metal carbonate | Carbon monoxide (CO) |
| Transition metals (e.g. Zn, Cu, Fe, Ni) | MeC₂O₄ → MeO + CO + CO₂ | Metal oxide | Carbon monoxide & carbon dioxide |
- Key clue: barium ethanedioate decomposes to BaCO₃ and CO.
- Key clue: magnesium ethanedioate decomposes to MgO and a mixture of CO and CO₂ — the CO₂ turns limewater milky.
📈 The Trend in Thermal Stability
Stability increases down Group 2 — so the decomposition temperature increases down the group too. The reasoning is identical to the carbonates and nitrates:
- Going down Group 2, the metal cation (M²⁺) gets larger.
- A larger cation has a lower charge density.
- This causes less distortion (polarisation) of the oxalate anion (C₂O₄²⁻).
- Weaker distortion means a stronger ionic bond and a more stable compound — so more heat (a higher temperature) is needed to decompose it.
Carbonates, nitrates, hydroxides, and oxalates all follow the same story: smaller cation → higher charge density → more polarisation of the anion → easier decomposition → lower decomposition temperature. Going down any group, cations get bigger, charge density falls, and thermal stability rises.