Thermodynamics: Spontaneous Processes & Entropy

• Thermodynamics is the study of energy and its transformations, determining the spontaneity and equilibrium of physical and chemical processes

Spontaneous Processes

• A spontaneous process happens without external intervention.
• Spontaneity shows reaction direction, not its rate.
• Many spontaneous processes release heat (ΔH < 0), but some absorb heat and are still spontaneous.
• Melting ice above 0°C exemplifies a spontaneous, endothermic reaction.
• Spontaneity relies on temperature.

Entropy

• Entropy (S) measures a system's disorder or randomness.
• Entropy serves as a state function, depending only on the system's current state, not its history.
• Entropy relates to microstates (W), showing system arrangement possibilities.
• Formula: S = k ln W, with k as Boltzmann constant (1.38 x 10⁻²³ J/K).
• Entropy escalates with rising temperature, volume, and independent particle count.
• Entropy change (ΔS) is defined as: ΔS = qrev/T, where qrev is reversible process heat.
• Entropy is measured in J/K.
• Reversible processes see zero total entropy change (ΔStotal = 0).
• Irreversible, spontaneous processes have positive total entropy change (ΔStotal > 0).

The Second Law of Thermodynamics

• The second law dictates that an isolated system's total entropy rises in spontaneous processes.
• ΔS(universe) = ΔS(system) + ΔS(surroundings)
• Spontaneous processes: ΔS(universe) > 0.
• Reversible processes: ΔS(universe) = 0.

Entropy Changes in Chemical Reactions

• Standard entropy change (ΔS°) calculation involves standard molar entropies (S°) of reactants and products.
• ΔS° = ΣnS°(products) - ΣnS°(reactants), where n is the stoichiometric coefficient.
• Standard molar entropy (S°) indicates one mole's entropy under standard conditions (298 K, 1 atm).
• Elements' standard entropy isn't zero, unlike standard formation enthalpy.
• Entropy typically increases when reactions yield more gas molecules than consumed, solids convert to liquids or gases, liquids turn into gases, and the mole count rises

The Third Law of Thermodynamics

• At absolute zero (0 K), a perfect crystal's entropy equals zero.
• This provides a baseline for determining a substance's absolute entropy at different temperatures.

Gibbs Free Energy

• Gibbs free energy (G) combines enthalpy (H) and entropy (S) to determine process spontaneity at constant temperature and pressure.
• G = H - TS
• ΔG = ΔH - TΔS
• ΔG acts as a state function.
• Spontaneous processes: ΔG < 0 (constant temperature, pressure).
• Non-spontaneous processes: ΔG > 0 (constant temperature, pressure).
• Equilibrium systems: ΔG = 0 (constant temperature, pressure).
• ΔG's sign hinges on ΔH, ΔS magnitudes, and temperature (T).

Standard Free-Energy Change

• Standard free-energy change (ΔG°) occurs when reactions proceed under standard conditions.
• Standard conditions entail 298 K (25°C) and 1 atm pressure.
• ΔG° = ΣnΔGf°(products) - ΣnΔGf°(reactants), with ΔGf° as standard formation free energy.
• Standard formation free energy (ΔGf°) reflects the free energy change when forming one mole of a compound from elements in their standard states.
• Any element's standard formation free energy in its standard state is zero.

Free Energy and Equilibrium

• Gibbs Free Energy change is linked to the equilibrium constant K: ΔG = -RT lnK, where R is the gas constant (8.314 J/mol·K).
• Under standard conditions: ΔG° = -RT lnK
• ΔG < 0 indicates K > 1, favoring products at equilibrium.
• ΔG > 0 indicates K < 1, favoring reactants at equilibrium.
• ΔG = 0 means K = 1, indicating equilibrium.
• The van't Hoff equation describes the temperature dependence of the equilibrium constant.

Temperature Dependence of Spontaneity

• Reaction spontaneity relies on temperature, especially when ΔH and ΔS aren't zero.
• If ΔH < 0 and ΔS > 0, ΔG is always negative, ensuring spontaneity at any temperature.
• If ΔH > 0 and ΔS < 0, ΔG remains positive, making the reaction non-spontaneous across all temperatures.
• When ΔH < 0 and ΔS < 0, reactions are spontaneous at lower temperatures (|ΔH| > |TΔS|).
• Reactions with ΔH > 0 and ΔS > 0 become spontaneous at elevated temperatures (|TΔS| > |ΔH|).
• The temperature at which spontaneity shifts can be found by setting ΔG = 0 and solving for T, yielding T = ΔH / ΔS.

Applications of Thermodynamics

• Predicting reaction feasibility and extent.
• Designing efficient chemical processes.
• Understanding phase transitions (e.g., melting, boiling).
• Studying electrochemical cells and biological systems.