entropy gibbs free energy
Overview
# Entropy and Gibbs Free Energy - A-Level Chemistry Summary This lesson examines spontaneity in chemical reactions through thermodynamic principles. Students learn that entropy (S) measures disorder in a system, with spontaneous processes favoring increased total entropy (ΔS_total > 0), while Gibbs free energy (ΔG = ΔH - TΔS) provides a single criterion for spontaneity at constant temperature and pressure, where ΔG < 0 indicates a feasible reaction. These concepts are essential for predicting reaction feasibility, explaining temperature-dependent equilibria, and form regular examination questions requiring calculation of entropy changes, free energy values, and determination of reaction spontaneity under varying conditions.
Core Concepts & Theory
Entropy (S) is a measure of the disorder or randomness of a system, measured in J K⁻¹ mol⁻¹. Systems naturally tend toward greater entropy. The Second Law of Thermodynamics states that the total entropy of the universe increases for any spontaneous process.
Key Principles:
- Gases have higher entropy than liquids, which have higher entropy than solids (S_gas > S_liquid > S_solid)
- Entropy increases with: temperature rise, dissolution, increasing number of particles, and phase changes to more disordered states
- Standard entropy (S°) is measured at 298 K and 100 kPa
Gibbs Free Energy (G) determines reaction spontaneity, combining enthalpy and entropy:
ΔG = ΔH - TΔS
Where:
- ΔG = Gibbs free energy change (kJ mol⁻¹)
- ΔH = enthalpy change (kJ mol⁻¹)
- T = temperature (K)
- ΔS = entropy change (kJ K⁻¹ mol⁻¹)
Spontaneity Rules:
- ΔG < 0: Reaction is spontaneous (feasible)
- ΔG = 0: System at equilibrium
- ΔG > 0: Reaction is non-spontaneous
Standard Gibbs Free Energy: ΔG° = ΔH° - TΔS°
Also: ΔG° = -RT ln K
Memory Aid (SHEEP): Spontaneous reactions have Heat loss (negative ΔH) Encouraging Entropy increase with Positive ΔS values being most favorable.
Calculating ΔS°: ΔS°_system = ΣS°(products) - ΣS°(reactants)
Detailed Explanation with Real-World Examples
Understanding Entropy Through Everyday Life:
Think of your bedroom: left alone, it naturally becomes messier (higher entropy). Tidying it requires energy input (non-spontaneous process). Similarly, ice melting is spontaneous at room temperature because liquid water has higher entropy than solid ice—molecules move more freely.
Real-World Applications:
1. Instant Cold Packs: Ammonium nitrate dissolution is endothermic (ΔH > 0) yet spontaneous because ΔS is highly positive—solid dissolves into freely moving ions. The large TΔS term makes ΔG negative despite positive ΔH.
2. Combustion Reactions: Burning methane (CH₄ + 2O₂ → CO₂ + 2H₂O) is spontaneous because it's both exothermic (ΔH < 0) and increases entropy (3 moles gas → 3 moles gas, releasing heat that increases surroundings' entropy).
3. Protein Folding: Proteins fold into specific 3D shapes (decreased entropy) because numerous hydrogen bonds form (highly exothermic), making ΔG negative. This explains why denaturation (unfolding) occurs at high temperatures—TΔS becomes dominant.
4. Refrigeration: Refrigerators create local order (low entropy) by removing heat, but they increase the universe's total entropy by releasing more heat to the surroundings.
Temperature's Role:
At low temperatures, ΔH dominates ΔG. At high temperatures, TΔS dominates. This explains why some reactions become spontaneous only above certain temperatures. For example, calcium carbonate decomposition (CaCO₃ → CaO + CO₂) requires heating because ΔS > 0 but ΔH > 0—high temperature makes TΔS larger than ΔH.
Worked Examples & Step-by-Step Solutions
**Example 1: Calculating ΔG and Predicting Spontaneity** For the reaction: N₂(g) + 3H₂(g) → 2NH₃(g) ΔH° = -92 kJ mol⁻¹, ΔS° = -199 J K⁻¹ mol⁻¹ Is the reaction spontaneous at 298 K and 500 K? **Solution:** *Step 1:* Convert ΔS to kJ: -199 J K⁻¹ mol⁻¹ = -0.199 kJ K⁻¹ mol⁻¹ *Step 2:* At 298 K: ΔG° =...
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Key Concepts
- Entropy (S): A measure of the disorder or randomness of a system. Higher entropy means more disorder.
- Gibbs Free Energy (G): A thermodynamic potential that measures the 'useful' or process-initiating work obtainable from an isothermal, isobaric thermodynamic system.
- Spontaneity: The tendency of a process to occur without continuous external input of energy.
- Enthalpy (H): A measure of the total energy of a thermodynamic system, including its internal energy and the product of its pressure and volume.
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Exam Tips
- →Always ensure consistent units when using the ΔG = ΔH - TΔS equation. Convert ΔS from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ if ΔH is in kJ mol⁻¹.
- →Clearly state the conditions (e.g., 'spontaneous at high temperatures') when discussing spontaneity based on the signs of ΔH and ΔS.
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