Thermodynamics and Spontaneity Notes

Why Can Liquids Be Reversibly Frozen and Melted?

  • Liquids can freeze and melt around a specific temperature due to the balance between kinetic energy and intermolecular forces at different phases.

Laws of Thermodynamics

  • First Law: Energy is conserved; the total amount of energy in the universe is constant.
    • Energy can be transformed between forms such as chemical, electrical, thermal, and mechanical.
  • Second Law: In any spontaneous process, the total entropy of the universe increases.
    • Entropy is a measure of disorder or randomness.

Understanding Spontaneous Processes

  • A spontaneous process occurs without external intervention and typically leads to equilibrium.
    • Examples: Ice melts at temperatures greater than 0 ºC, and water freezes at temperatures below 0 ºC.
  • Spontaneity is determined by thermodynamics; however, it does not imply speed—kinetics plays a role in the rate of the process.

Gibbs Free Energy

  • The Gibbs free energy change, denoted as ΔG, determines whether a reaction is spontaneous.
  • Thermodynamics focuses on energy changes (ΔG) whereas kinetics focuses on how those changes occur.

Entropy (S)

  • Definition: $S = k ext{ln}(W)$, where W is the number of microstates and k is the Boltzmann constant.
    • Entropy increases with disorder; for example, gases expand to fill available volume, increasing disorder.
  • Units: Entropy is measured in J K⁻¹ and is always positive.

Entropy Changes (ΔS)

  • For a system change:
    • $ΔS = S{final} - S{initial}$
  • Positive ΔS indicates disorder (e.g., ice melting). Negative ΔS indicates order (e.g., freezing water).

System and Surroundings

  • The total entropy change of the universe (ΔSuniv) is the sum of system and surroundings:
    • $ΔSuniv = ΔS{sys} + ΔS{surr}$
  • Heat exchanged affects the surroundings:
    • For exothermic processes, $ΔSsurr$ is positive while for endothermic, it is negative.

Third Law of Thermodynamics

  • At absolute zero (0 K), a perfectly ordered crystalline solid has zero entropy (S = 0).
  • As the temperature rises, the entropy increases due to lattice vibrations and disorder.

Standard State and Standard Molar Entropy

  • The standard state of substances is defined under specific conditions (1 atm, 25°C).
  • Standard molar entropy (Sº) is the entropy of 1 mole of a substance under standard conditions.

Calculating ΔS° for Reactions

  • For a general reaction:
    • $ΔS° = Σnp S°(products) - Σnr S°(reactants)$
  • ΔS° indicates the change in positional entropy due to reaction changes.

Gibbs Free Energy and Reaction Quotient

  • For reactions, Gibbs free energy is related to temperature and entropy:
    • $ΔG = ΔH - TΔS$.
  • The relationship between the reaction quotient (Q) and Gibbs free energy at equilibrium is $-ΔG° = RT ext{ln}(K)$.

Effect of Enthalpy (ΔH) and Entropy (ΔS) on Spontaneity

  • Various combinations of ΔH and ΔS determine reaction spontaneity:
    • +ΔS, -ΔH: Spontaneous at all temperatures
    • +ΔS, +ΔH: Spontaneous at high temperatures
    • -ΔS, -ΔH: Spontaneous at low temperatures
    • -ΔS, +ΔH: Not spontaneous at any temperature.

Conclusion

  • The maximum possible work obtainable from a process at constant temperature and pressure is equal to ΔG.
  • All real processes are irreversible, causing an increase in the universe's entropy over time.

Applications

  • Understanding these principles allows predicting the feasibility of reactions, their spontaneity, and the constraints imposed by the environment.