Spontaneity, Entropy, and Free Energy - Summary

Spontaneous Processes and Entropy

• Thermodynamics:
  • First law: Universe's energy is constant (conservation).
  • Spontaneous process: Occurs without intervention, can be fast or slow.
• Kinetics vs. Thermodynamics:
  • Kinetics: Reaction rate depends on the pathway.
  • Thermodynamics: Determines spontaneity based on reactant/product properties.
• Entropy (S):
  • Describes arrangements available to a system.
  • Measure of molecular randomness or disorder.
• Ideal Gas Expansion:
  • Nature favors states with highest probabilities.
• Microstate:
  • Each configuration of a particular arrangement.
  • State probability depends on the number of microstates.
• Positional Probability:
  • Depends on configurations yielding a state.
  • Gas expands to uniform distribution, highest positional probability.
• State Changes:
  • Positional entropy increases from solid to gas.
• Solutions:
  • Mixing increases positional entropy (more microstates).
  • Increased volume for particles after mixing.
  • Solution formation favored by increased positional entropy.

Second Law of Thermodynamics

• Second Law: In spontaneous processes, the entropy of the universe increases.
• $\Delta S_{univ}$:
  • Positive: Spontaneous process.
  • Negative: Spontaneous in opposite direction.
  • Zero: No tendency to occur (equilibrium).

Effect of Temperature on Spontaneity

• $\Delta S_{surr}$
  • Determined by heat flow.
  • Exothermic: Increases $\Delta S_{surr}$, favors spontaneity.
  • Endothermic: Decreases $\Delta S_{surr}$.
  • Impact greater at lower temperatures.
• $\Delta S_{surr}$ and $\Delta H$
  • $\Delta S_{surr} = -\frac{\Delta H}{T}$

Free Energy (G)

• Formula: $G = H - TS$
• At constant temperature:
  • $\Delta G = \Delta H - T\Delta S$
• Spontaneity:
  • Spontaneous: Negative $\Delta G$ (positive $\Delta S_{univ}$).

Entropy Changes in Reactions

• Positional probability determines changes; fewer molecules, fewer configurations.
• Gaseous Molecules:
  • Dominated by relative numbers of gaseous reactants/products.
  • More product molecules: Positional entropy increases, $\Delta S$ is positive.
• Third Law of Thermodynamics:
  • Entropy of a perfect crystal at 0 K is zero.
  • Entropy increases with temperature.
• Standard Entropy Values ($S^\circ$):
  • Entropy increase when heated from 0 K to 298 K at 1 atm.
  • More complex molecules have higher $S^\circ$ values.
  • $\Delta S^\circ = \sum n<em>pS^\circ(products) - \sum n</em>rS^\circ(reactants)$

Standard Free Energy Change

• Change in G when reactants in standard states convert to products in standard states.
• The more negative $\Delta G^\circ$ the further the reaction shifts right to reach equilibrium.
• $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$
• Standard Free Energy of Formation ($\Delta G_f^\circ$):
  • Free energy change for forming 1 mole from constituent elements in standard states.
  • $\Delta G_f^\circ$ of an element in its standard state = 0.

Free Energy and Pressure

• System at constant P and T proceeds spontaneously by lowering free energy.
• Free energy depends on gas pressure or solution concentrations.
• Equilibrium: lowest free energy.
• For ideal gases:
  • Enthalpy is not pressure-dependent.
  • Entropy depends on pressure.
  • $G = G^\circ + RT\ln(P)$
  • $\Delta G = \Delta G^\circ + RT\ln(Q)$

Free Energy and Equilibrium

• Equilibrium occurs at the lowest free energy.
• $\Delta G = 0$
• $\Delta G^\circ = -RT\ln(K)$

Free Energy and Work

• Maximum useful work = change in free energy (at constant T and P).
• Reversible process: Universe is the same after a cyclic process.
• Irreversible process: Universe is different after a cyclic process.
• All real processes are irreversible.