Thermodynamics and Spontaneity

Definition of Spontaneity:
- Spontaneous process: occurs without ongoing external intervention.
  - Examples include:
    - Objects falling under gravity.
    - Combustion reactions.
    - Gas escaping from a pressurized can.
    - Ice melting at 1 atm and > 0°C.
    - Water freezing at 1 atm and < 0°C.
Nonspontaneous Process:
- Requires ongoing external intervention to occur.
  - Reverse process of spontaneous reactions often is nonspontaneous.
  - Examples include:
    - Lifting objects to higher gravitational potential.
    - Reforming fuel from CO2 and H2O (reverse combustion).
    - Gas returning to a pressurized container.
Spontaneity is not synonymous with speed:
- Some spontaneous processes are slow, e.g.,
  - Rust formation.
  - Graphite converting to diamond under certain conditions.
  - The reverse process (diamond reverting to graphite) is spontaneous at room temperature and pressure.
Importance of Predicting Spontaneity:
- Spontaneous processes can drive nonspontaneous ones.
  - E.g., falling water powering a mill or spontaneous reactions in batteries producing electricity.
  - Combustion reactivity helps in vehicle acceleration.
  - Photosynthesis integrates spontaneous reactions to facilitate nonspontaneous products.
Quantities that do not predict spontaneity:
- First Law of Thermodynamics:
  - Energy cannot be created or destroyed; only transformed or transferred.
  - This law does not dictate the direction of spontaneous energy transfer.
- Enthalpy Changes (ΔH):
  - Spontaneous processes can either be exothermic (ΔH < 0) or endothermic.
  - Not all exothermic processes are spontaneous, illustrated by varying spontaneity at different temperatures.
Entropy (S) and Spontaneity:
- Second Law of Thermodynamics:
  - Entropy of the universe increases in a spontaneous process (∆_{universe} > 0).
  - Entropy is a measure of disorder or the number of ways energy can be distributed.
Boltzmann Definition of Entropy:
- S = k_B imes ext{ln}(W)
  - Where:
    - k_B = Boltzmann constant (1.38 x 10^-23 J/K)
    - W = Number of microstates for a macrostate.
Microstates vs. Macrostates:
- Microstate: Specific arrangements of particles among energy states.
- Macrostate: Overall observed state, typically with higher probabilities of associated arrangements for disorder.
Entropy and Disorder:
- Systems tend towards states with higher entropy.
  - More microstates correspond to higher configurations of disorder.
  - Examples illustrating higher disorder include gases compared to solids.
Entropy Trends:
- State of Matter: Solids < Liquids < Gases in increasing entropy.
- Solution Formation: A mixture has higher entropy than separate components.
- Temperature: Higher average kinetic energy correlates to higher entropy states.
- Molecule Size & Complexity: Larger and more complex molecules exhibit higher entropy.
Calculating Entropy:
- At the microscopic level: S = k_B imes ext{ln}(W)
- At macroscopic level: ∆S = q_{rev}/T
  - q_{rev}: Amount of heat during reversible processes, where T is in Kelvin.
  - Reversible processes assume equilibrium throughout.
  - Examples include phase changes such as melting and freezing which can be treated reversibly.
Example Calculation:
- Melting of Ice:
  - For 6.80 g of ice at 25.0°C with ΔH_{fus} = 6.0 kJ/mol:
  - Calculate ∆S:
    - ∆S = q_{rev}/T; converting units as necessary yields ∆S = 7.6 ext{ J/K}, indicating an increase in disorder.
Final Notes:
- Spontaneity is fundamentally linked to entropy increase as reiterated by the Second Law of Thermodynamics.
- The overall change in entropy of the universe must be positive for any spontaneous process: ∆S{universe} = ∆S{system} + ∆S_{surroundings} providing insight into energy interactions.