H2 Chemistry (9476), JC1
Melting takes in heat, so why does ice melt by itself at room temperature?
2How can you tell, without doing the experiment, whether a reaction will happen by itself?
3Why does limestone decompose in a hot kiln, but never on a cold hillside?
4Diamond should slowly turn into graphite, as ΔG is negative. So why do diamonds last for ever?
1Define lattice energy.
2Why is hydration always exothermic?
3Which has the more exothermic LE, NaCl or MgCl₂? Why?
Spontaneous reaction: a reaction that is energetically feasible, i.e. ΔG⦵ < 0. Once started, it proceeds on its own without a continuous input of energy from the surroundings.
PredictIce melts on a warm day, and KCl dissolves in water, although both are endothermic. What drives them?
In both, particles gain freedom of motion: their energy becomes more dispersed.
ΔS = Sfinal − Sinitial units: J mol⁻¹ K⁻¹
AnalogyShuffle a sorted pack of cards: there are far more mixed-up orders than sorted ones, so it almost never comes back sorted.
ΔS > 0: particles have more average kinetic energy and there are more ways to distribute the larger number of quanta of energy.
S: solid < liquid ≪ gas.
Melting: particles no longer in fixed positions → more ways to arrange particles and distribute energy.
Boiling: particles move randomly, large ↑ in volume.
2NaN₃(s) → 2Na(s) + 3N₂(g): ΔS > 0, disorder increases as the number of moles of gas molecules increases. No change in moles of gas → ΔS ≈ 0.
| Predict ΔS | Sign | Reason |
|---|---|---|
| 2N₂O(g) + O₂(g) → 4NO(g) | + | moles of gas ↑ (3 → 4) → more ways to distribute particles and energy |
| 2H₂O₂(l) → 2H₂O(l) + O₂(g) | + | a gas forms from liquids |
| 3O₂(g) → 2O₃(g) | − | moles of gas ↓ (3 → 2) |
| 2SO₂(g) + O₂(g) → 2SO₃(g) | − | moles of gas ↓ (3 → 2) → fewer ways to distribute |
Quick checkWhich change has ΔS < 0?
DefinitionThe standard Gibbs free energy, ΔG⦵, is used to predict the feasibility of a reaction.
ΔGr = ΣΔGf(products) − ΣΔGf(reactants)
Worked example: RustingIron rusts in air: 2Fe(s) + 3/2O₂(g) → Fe₂O₃(s), ΔH = −825 kJ mol⁻¹, ΔS = −272 J mol⁻¹ K⁻¹. Is rusting spontaneous at 298 K?
ΔS = −0.272 kJ mol⁻¹ K⁻¹
ΔG = −825 − 298(−0.272) = −744 kJ mol⁻¹
ΔG < 0 → spontaneous at 298 K
Worked example: Melting iceIce melts at 273 K with ΔHfus = +6.0 kJ mol⁻¹. Find ΔS of melting.
At the m.p. ΔG = 0 → ΔH = TΔS
ΔS = 6000273 = +22.0 J mol⁻¹ K⁻¹
Your turnFor the Haber process, ΔH = −92 kJ mol⁻¹ and ΔS = −199 J mol⁻¹ K⁻¹. Is it spontaneous at 298 K?
| ΔH | ΔS | Spontaneity |
|---|---|---|
| − | + | Since ΔS > 0, −TΔS < 0 → ΔG negative at all temperatures: always spontaneous |
| + | − | Since ΔS < 0, −TΔS > 0 → ΔG positive at all temperatures: never spontaneous |
| − | − | Since ΔS < 0, −TΔS > 0. As T ↑, −TΔS becomes more positive → ΔG positive eventually: spontaneous only at low T |
| + | + | Since ΔS > 0, −TΔS < 0. As T ↑, −TΔS becomes more negative → ΔG negative eventually: spontaneous at high T |
| Case | Examples |
|---|---|
| ΔH −, ΔS + | combustion of octane, decomposition of nitroglycerine |
| ΔH +, ΔS − | photosynthesis: must be driven by a continuous energy input (sunlight) |
| ΔH −, ΔS − | precipitation of AgCl, condensation, freezing (enthalpy driven) |
| ΔH +, ΔS + | melting, boiling, decomposition of Group 2 carbonates (entropy driven) |
Worked example: Minimum temperatureIn a blast furnace, C(s) + CO₂(g) → 2CO(g), ΔH = +172.5 kJ mol⁻¹, ΔS = +176.2 J mol⁻¹ K⁻¹. Find the minimum temperature for the reaction to be spontaneous.
At 298 K, ΔG = 172.5 − 298(0.1762) = +120 > 0, not spontaneous
Spontaneous when ΔG < 0 → ΔH − TΔS < 0
T > 172.50.1762 = 979 K
Your turnBaking powder releases CO₂ on heating: 2NaHCO₃(s) → Na₂CO₃(s) + H₂O(g) + CO₂(g), ΔH = +130 kJ mol⁻¹, ΔS = +335 J mol⁻¹ K⁻¹. Above what temperature is this spontaneous?
Likewise MgCO₃ decomposes above 576 K but BaCO₃ only above 1566 K: ΔH(MgCO₃) is less positive, ΔS similar.
Quick checkA reaction has ΔH > 0 and ΔS > 0. When is it spontaneous?
ΔG⦵ applies only to standard conditions. Water boiling at 298 K: ΔG⦵ = 44.0 − 298(0.118) = +8.84 kJ mol⁻¹, yet water boils at 298 K if the pressure is reduced enough.
We assume ΔH and ΔS stay about constant with T. This fails if a reactant or product changes phase: H₂ + I₂ → 2HI has ΔG = +3.5 at 298 K (I₂ solid) but −20.0 at 500 K (I₂ gas).
Spontaneous does not mean fast. C(diamond) → C(graphite) has ΔG < 0 but a very high Ea: diamond is kinetically stable.
1Define entropy.
2Predict the sign of ΔS for CaCO₃(s) → CaO(s) + CO₂(g).
3Find ΔG at 298 K: ΔH = −50 kJ mol⁻¹, ΔS = −100 J mol⁻¹ K⁻¹.
4Why does diamond not turn into graphite, even though ΔG < 0?