Entropy (ΔS) - Chemistry

1. Fundamental Concepts

Definition: Entropy is a thermodynamic quantity that measures the degree of disorder, randomness, or energy dispersal in a system.
Units: Entropy is typically measured in joules per kelvin (J/K).
Second Law of Thermodynamics: The total entropy of the universe always increases for a spontaneous process.
ΔS (Entropy Change)：ΔS = S(products) − S(reactants)

2. Key Concepts

Qualitative Meaning of ΔS:
Positive ΔS → increase in entropy → disorder increases
Negative ΔS → decrease in entropy → disorder decreases

General Trends That Increase Entropy (ΔS > 0):
Phase change toward greater freedom of motion: solid → liquid → gas
Increase in moles of gas
Mixing or dissolving (pure substances → solution)
Higher temperature (more molecular motion, more microstates)
Larger / more complex molecules (more atoms, more vibrations)
Breaking down a structure (e.g., solid ionic compound dissolving)

3. Examples

Example 1 (Easy)

Problem: For the process below, predict if ΔS is positive or negative.
2H₂(g) + O₂(g) → 2H₂O(l)

Step-by-Step Solution:

Reactants: 3 moles of gas
Products: liquid, no gas
Large decrease in disorder
Therefore, ΔS < 0

Example 2 (Intermediate)

Problem: Calculate the entropy change for the vaporization of 1 mole of water at its boiling point (100°C or 373 K). The enthalpy of vaporization (\ $$ \Delta H_{vap} \ $$ ) for water is 40.7 kJ/mol.

Step-by-Step Solution:

Identify the given values: $$ \Delta H_{vap} = 40.7 \, \text{kJ/mol} $$ , $$ T = 373 \, \text{K} $$
Convert the enthalpy of vaporization to joules: $$ \Delta H_{vap} = 40.7 \times 10^3 \, \text{J/mol} $$
Use the entropy change formula for phase changes: $$ \Delta S = \frac{\Delta H_{vap}}{T} $$
Substitute the values: $$ \Delta S = \frac{40.7 \times 10^3 \, \text{J/mol}}{373 \, \text{K}} $$
Calculate: $$ \Delta S \approx 109.1 \, \text{J/(mol·K)} $$

Validation: The units are consistent (J/(mol·K)), and the calculation is correct.

4. Problem-Solving Techniques

First Check Gas Moles — this is often the dominant factor in predicting the sign of ΔS.
Complexity Rule: more atoms / larger molecules → higher S°.
Remember: The change in entropy (ΔS) depends only on the initial and final states of a system, regardless of the path taken between them.