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: 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).

\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}

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 npS^\circ(products) - \sum nrS^\circ(reactants)

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.

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)