Entropy Calculations to Know for General Chemistry II

Understanding entropy is key in General Chemistry II, as it helps explain the disorder in systems and the spontaneity of reactions. These notes cover standard molar entropy, changes during reactions, phase transitions, and the relationship between entropy and Gibbs free energy.

1. Standard molar entropy (S°)

   • Defined as the entropy of one mole of a substance at standard conditions (1 bar, 25°C).
   • Values are tabulated for various substances and can be used to predict spontaneity.
   • Higher S° values indicate greater disorder and more possible microstates.

2. Entropy change in chemical reactions (ΔS°rxn)

   • Calculated as the difference between the total standard molar entropies of products and reactants.
   • Positive ΔS°rxn indicates an increase in disorder, while negative ΔS°rxn indicates a decrease.
   • Important for determining the spontaneity of reactions alongside ΔH and temperature.

3. Third law of thermodynamics and absolute entropy

   • States that the entropy of a perfect crystal at absolute zero (0 K) is zero.
   • Provides a reference point for calculating absolute entropies of substances.
   • As temperature increases, the entropy of a substance also increases due to increased molecular motion.

4. Entropy changes in phase transitions

   • Entropy increases when a substance transitions from solid to liquid (melting) or liquid to gas (vaporization).
   • Entropy decreases when a substance transitions from gas to liquid (condensation) or liquid to solid (freezing).
   • The magnitude of ΔS during phase changes can be calculated using the heat of transition divided by the temperature.

5. Entropy changes in temperature changes

   • Entropy change can be calculated using the formula ΔS = nC ln(T2/T1) for temperature changes.
   • C represents the heat capacity, and T1 and T2 are the initial and final temperatures.
   • Entropy increases with temperature due to increased molecular motion and disorder.

6. Entropy of mixing and dissolution

   • Mixing two or more substances generally leads to an increase in entropy due to increased randomness.
   • The dissolution of solids in liquids often results in a positive ΔS due to the dispersal of solute particles.
   • The extent of entropy change depends on the nature of the solute and solvent.

7. Entropy in spontaneous processes

   • Spontaneous processes tend to increase the total entropy of the universe (system + surroundings).
   • A process is spontaneous if ΔS_universe = ΔS_system + ΔS_surroundings > 0.
   • Entropy is a key factor in determining the direction of chemical reactions and physical changes.

8. Relationship between entropy and disorder

   • Entropy is often described as a measure of disorder or randomness in a system.
   • Higher entropy corresponds to a greater number of microstates and more disorder.
   • Systems naturally progress towards states of higher entropy, reflecting the second law of thermodynamics.

9. Calculating entropy changes using Hess's Law

   • Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.
   • Similarly, entropy changes can be calculated by summing the ΔS° for each step in a reaction pathway.
   • Useful for complex reactions where direct measurement of ΔS° is difficult.

10. Gibbs free energy and its relation to entropy (ΔG = ΔH - TΔS)

    • Gibbs free energy (ΔG) combines enthalpy (ΔH) and entropy (ΔS) to predict spontaneity.
    • A negative ΔG indicates a spontaneous process, while a positive ΔG indicates non-spontaneity.
    • The temperature (T) plays a crucial role in determining the impact of entropy on the free energy of a system.