General Rules for Predicting ΔS:

Phase changes:

• S(gas) >> S(liquid) > S(solid)

• Melting, vaporization, sublimation: ΔS > 0

• Freezing, condensation, deposition: ΔS < 0

Dissolving:

• Solid → aqueous: usually ΔS > 0 (increased disorder)

• Liquid → aqueous: usually ΔS > 0 (increased dispersion)

• Gas → aqueous: ΔS < 0 (decreased freedom)

Mixing substances (e.g., dissolving salt in water) increases entropy because the components are more dispersed.

Number of particles:

• More moles of gas → higher entropy

• Increase in moles of gas: ΔS > 0

• Decrease in moles of gas: ΔS < 0

Molecular complexity:

• More complex molecules → higher entropy

• More atoms → more ways to distribute energy

Larger, more complex molecules have higher entropy because they can vibrate, rotate, and arrange themselves in more ways.

Temperature:

• Entropy increases as temperature increases because molecules move more rapidly and occupy more possible energy levels.

Entropy in Chemical Reactions

Standard Molar Entropy ($S^\circ$)

• Definition: The entropy of 1 mole of a substance at a standard state (298 K, 1 atm).

• Units: $\text{J/K}\cdot\text{mol}$ (Joules per Kelvin per mole).

Change in Entropy ($\Delta S^\circ$)

The change in entropy for a chemical reaction can be calculated using the standard molar entropies of the products and reactants:

$$\Delta S^\circ = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}}$$

Spontaneity and Entropy (Second Law of Thermodynamics)

• A process is spontaneous (thermodynamically favored) if the change in entropy of the universe ($\Delta S_{\text{universe}}$) is greater than zero.

• Condition for Spontaneity: $\Delta S_{\text{universe}} > 0$