Chemical energetics II: entropy, Gibbs free energy, feasibility of reactions

Chemical Energetics II: Entropy, Gibbs Free Energy & Feasibility of Reactions

1️⃣ Entropy (S)

Entropy is a measure of how spread out the energy of a system is. Think of it like a messy room: the more disordered the room, the higher the entropy.

• 🔹 Disorder: More ways to arrange the same energy → higher entropy.
• 🔹 Temperature dependence: At higher temperatures, molecules move faster → entropy increases.
• 🔹 Units: J mol⁻¹ K⁻¹.

Key formula:

2️⃣ Gibbs Free Energy (G)

Gibbs free energy tells us whether a reaction will happen spontaneously at constant temperature and pressure.

Formula:

$$G = H - TS$$

• 🔹 $H$ = enthalpy (heat content)
• 🔹 $T$ = absolute temperature (K)
• 🔹 $S$ = entropy

Spontaneity rule:

1. 🔹 If $ΔG < 0$, the reaction is spontaneous.
2. 🔹 If $ΔG > 0$, the reaction is non‑spontaneous.
3. 🔹 If $ΔG = 0$, the system is at equilibrium.

3️⃣ Feasibility of Reactions

To decide if a reaction will occur, calculate $ΔG$ using:

$$ΔG = ΔH - TΔS$$

• 🔹 Exothermic reactions ($ΔH < 0$) often have $ΔG < 0$ at lower temperatures.
• 🔹 Endothermic reactions ($ΔH > 0$) can become spontaneous if $ΔS$ is large and positive.
• 🔹 Temperature can tip the balance: higher $T$ favours reactions with $ΔS > 0$.

🔬 Example: Combustion of Methane

$$\ce{CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)}$$

Given:

• $ΔH° = -890$ kJ mol⁻¹
• $ΔS° = -200$ J mol⁻¹ K⁻¹
• $T = 298$ K

Calculate $ΔG°$:

$$ΔG° = (-890\,000) - 298(-200) = -890\,000 + 59\,600 = -830\,400\ \text{J mol}^{-1}$$

Since $ΔG° < 0$, combustion is spontaneous at room temperature. 🔥

4️⃣ Quick Reference Table