Chapter 18 (April 16)

Second Law of Thermodynamics

  • The second law states that for a process to be spontaneous, the entropy of the universe must increase.
  • Entropy is a measure of disorder; it tends to increase over time.

Understanding Entropy

  • Entropy of a Perfect Crystal: According to the third law of thermodynamics, a perfect crystal at absolute zero (0°C, or 273.15 K) has zero entropy (only one microstate available).
  • This concept allows us to calculate changes in entropy as the temperature changes and as the number of microstates increases.

Calculating Standard Molar Entropy

  • Units: Standard molar entropy values are measured in extJextmol−1extK−1ext{J} ext{mol}^{-1} ext{K}^{-1}.
  • Standard Conditions: Standard thermodynamic conditions are:
    • Temperature: 298 K (25°C)
    • Pressure: 1 atm for gases
    • Concentration: 1 M for solutions

Entropy Change in Reactions

  • Calculating Entropy Change: The change in entropy (ΔS) for a chemical reaction can be computed using:
    • extΔSextreaction=extΣextstandardentropiesofproducts−extΣextstandardentropiesofreactantsext{ΔS}_{ ext{reaction}} = ext{Σ} ext{standard entropies of products} - ext{Σ} ext{standard entropies of reactants}
  • This method is similar to enthalpy calculations from the previous semester.

Example: Combustion of Propane

  • Reaction: Combustion of propane at 25°C yields expected results about entropy.
  • Reaction Direction: The progression from reactants to products shows a decrease in the number of moles from reactants to products, indicating lower entropy for the system.
  • The summary of steps includes:
    1. Write out reactants and products using standard entropy values.
    2. Calculate ΔS using the formula mentioned above.

Understanding Spontaneity in Reactions

  • For a reaction to be spontaneous, ΔS of the universe must be positive.
  • The reaction can be spontaneous if:
    1. Both ΔS for the system and surroundings are positive.
    2. ΔS for the system is negative, but ΔS for the surroundings exceeds that value.
  • The overall result can show a decrease in entropy in the system, but an increase in the surroundings can still support spontaneity.

Entropy of Surroundings

  • Entropic Changes in Surroundings: Unlike enthalpy, when the system gains entropy, the surroundings may not necessarily lose it. Understanding heat exchange ( Q) is critical in these scenarios.
    • Exothermic processes: Increase the entropy of surroundings since heat is released into them.
    • Endothermic processes: Decrease the entropy of surroundings as they absorb energy.

Entropy Calculation in Surroundings

  • The entropy of the surroundings can be calculated from the heat exchanged:
    • extΔSextsurr=−QText{ΔS}_{ ext{surr}} = -\frac{Q}{T}
  • This relationship indicates the inverse relationship between the temperature and the impact entropy changes.

Gibbs Free Energy (ΔG)

  • Gibbs Free Energy combines system entropy and enthalpy for predicting spontaneity under varying conditions:
    • extΔG=extΔH−TimesextΔSext{ΔG} = ext{ΔH} - T imes ext{ΔS}
  • A negative ΔG indicates a spontaneous reaction, while a positive ΔG indicates a non-spontaneous reaction. A ΔG of zero indicates that the reaction is at equilibrium.

Practical Applications of ΔG

  • Maximum efficient work available at any time during spontaneity relates to ΔG values, which can help in understanding energy use during chemical reactions, including battery operations.

Summary Points

  • The entropy of a system may decrease while the entropy of the universe increases, allowing for spontaneous reactions.
  • Calculating ΔS values is crucial for understanding the direction of reactions and their spontaneity at given temperatures.
  • Gibbs Free Energy is a vital tool to assess the spontaneous nature of chemical processes and their operational limits.