Understanding Spontaneity in Chemical Reactions
🌡️ What is a Spontaneous Process?
A spontaneous process occurs naturally without external help and proceeds in one direction only. Examples include gas expanding to fill a container or carbon burning in oxygen. Key points:
- 🔥 Irreversible: Can only be reversed by external intervention.
- ⏳ Rate-independent: Spontaneity doesn’t mean “fast” (e.g., hydrogen + oxygen mix slowly at room temperature but are still spontaneous!).
❌ Why Enthalpy Alone Can’t Predict Spontaneity
Many spontaneous reactions release heat (exothermic), like:
- \( \frac{1}{2}N_2(g) + \frac{3}{2}H_2(g) \rightarrow NH_3(g) \quad \Delta_r H^\circ = -46.1 \text{kJ mol}^{-1} \)
- \( H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l) \quad \Delta_r H^\circ = -285.8 \text{kJ mol}^{-1} \)
But some endothermic reactions are also spontaneous:
- \( \frac{1}{2}N_2(g) + O_2(g) \rightarrow NO_2(g) \quad \Delta_r H^\circ = +33.2 \text{kJ mol}^{-1} \)
- \( C(\text{graphite}) + 2S(l) \rightarrow CS_2(l) \quad \Delta_r H^\circ = +128.5 \text{kJ mol}^{-1} \)
Conclusion: Decreased enthalpy helps, but isn’t the only factor!
🎲 Entropy: The Real Game-Changer
Entropy (\( S \)) measures disorder/randomness in a system. Spontaneous processes increase total entropy (system + surroundings).
- ⚖️ For isolated systems: More chaos = more spontaneity.
- 🧊 → 💨 Entropy order: Solid < Liquid < Gas (gases are most disordered!).
Entropy change (\(\Delta S\)) is calculated as:
\[ \Delta S = \frac{q_{\text{rev}}}{T} \]
For spontaneous processes:
\[ \Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} > 0 \]
📝 Predicting Entropy Changes (Examples)
- ✅ Increases:
- Solid heated from 0K → 115K (particles move more).
- \( 2NaHCO_3(s) \rightarrow Na_2CO_3(s) + CO_2(g) + H_2O(g) \) (solid → gas).
- \( H_2(g) \rightarrow 2H(g) \) (1 molecule → 2 atoms).
- ❌ Decreases: Liquid freezing into solid (more ordered).
✨ Gibbs Free Energy: The Ultimate Spontaneity Test
Gibbs energy (\( G \)) combines enthalpy and entropy:
\[ \Delta G = \Delta H – T \Delta S \]
This tells us if a reaction is spontaneous:
- ✅ Spontaneous: \(\Delta G < 0\)
- 🚫 Non-spontaneous: \(\Delta G > 0\)
Example: Iron oxidation (\(4Fe + 3O_2 \rightarrow 2Fe_2O_3\)) has \(\Delta S = -549.4 \text{JK}^{-1}\text{mol}^{-1}\) (negative!), but \(\Delta H = -1648 \times 10^3 \text{J mol}^{-1}\) is large & negative. Result: \(\Delta G < 0\) → spontaneous! 🧲🔥
🌡️ Temperature’s Role (Table Summary)
| \(\Delta H\) | \(\Delta S\) | Spontaneity |
|---|---|---|
| – | + | Spontaneous at all T |
| – | – | Spontaneous at low T |
| + | + | Spontaneous at high T |
| + | – | Non-spontaneous at all T |
*”High” and “low” temperatures depend on the reaction!
⚖️ Equilibrium & Gibbs Energy
At equilibrium:
- ⚖️ \(\Delta_r G = 0\) (no net change).
- 🔗 Linked to equilibrium constant (\(K\)): \[ \Delta_r G^\circ = -RT \ln K \]
Exothermic (\(\Delta H < 0\)) → large \(K\) → reaction goes to completion. Endothermic reactions need entropy help!
📜 Laws of Thermodynamics & Entropy
- 🔑 Second Law: Total entropy of the universe increases in spontaneous processes.
- ❄️ Third Law: Entropy of a perfect crystal is 0 at 0 K (absolute zero).
🚀 High-Yield NEET Concepts
- Gibbs Free Energy (\(\Delta G\)): Master \(\Delta G = \Delta H – T\Delta S\) and its sign for spontaneity.
- Entropy Change Predictions: Know how physical states (solid→gas) or particle count (1 molecule → 2 atoms) affect \(\Delta S\).
- Endothermic Spontaneity: Reactions with \(\Delta H > 0\) can be spontaneous if \(\Delta S > 0\) and \(T\) is high.
- Equilibrium & \(\Delta G\): At equilibrium, \(\Delta_r G = 0\) and \(\Delta_r G^\circ = -RT \ln K\).
- Entropy Laws: Second Law (total entropy ↑) and Third Law (\(S \rightarrow 0\) at 0 K for crystals).
