Gibbs free energy predicts whether a chemical reaction will happen on its own. It combines heat changes and disorder changes to tell us if a process is spontaneous. This helps chemists understand which reactions will occur naturally and which need a push.

Temperature plays a big role in spontaneity. Some reactions only happen when it's hot, while others prefer the cold. Understanding these relationships helps us control chemical processes in labs and industries.

Gibbs Free Energy and Spontaneity

Gibbs free energy and spontaneity

• Gibbs free energy ($G$) thermodynamic quantity predicts spontaneity of process at constant temperature and pressure
  • Spontaneous processes occur without external intervention release free energy (rusting of iron)
  • Non-spontaneous processes require external energy input to proceed (electrolysis of water)
• Change in Gibbs free energy ($\Delta G$) determines spontaneity of reaction
  • $\Delta G < 0$: Reaction is spontaneous proceeds in forward direction (combustion of fuel)
  • $\Delta G > 0$: Reaction is non-spontaneous proceeds in reverse direction (photosynthesis)
  • $\Delta G = 0$: Reaction is at equilibrium no net change occurs (saturated solution)

Free energy calculations from formation data

• Standard Gibbs free energy of formation ($\Delta G_f^\circ$) change in free energy when one mole of compound formed from constituent elements in standard states at standard conditions (25℃ and 1 atm)
• Calculate standard change in Gibbs free energy ($\Delta G^\circ$) using equation:
  • $\Delta G^\circ = \sum \Delta G_f^\circ(\text{products}) - \sum \Delta G_f^\circ(\text{reactants})$
    • $\sum \Delta G_f^\circ(\text{products})$: Sum of standard Gibbs free energies of formation for products multiplied by stoichiometric coefficients (2 moles of H2O)
    • $\sum \Delta G_f^\circ(\text{reactants})$: Sum of standard Gibbs free energies of formation for reactants multiplied by stoichiometric coefficients (1 mole of CH4 and 2 moles of O2)

Free energy from enthalpy and entropy

• Gibbs free energy change ($\Delta G$) related to change in enthalpy ($\Delta H$) and change in entropy ($\Delta S$) by equation:
  • $\Delta G = \Delta H - T\Delta S$
    • $\Delta H$: Change in enthalpy (heat released or absorbed)
    • $T$: Absolute temperature in Kelvin (0℃ = 273.15 K)
    • $\Delta S$: Change in entropy (measure of disorder)
• To calculate $\Delta G$ using enthalpy and entropy values:
  1. Determine $\Delta H$ and $\Delta S$ for reaction
  2. Multiply absolute temperature ($T$) by change in entropy ($\Delta S$)
  3. Subtract product $T\Delta S$ from change in enthalpy ($\Delta H$)

Temperature effects on spontaneity

• Temperature affects spontaneity of reaction by influencing relative contributions of enthalpy and entropy to Gibbs free energy change
• For exothermic reactions ($\Delta H < 0$):
  • Low temperatures favor spontaneity $\Delta H$ term dominates (formation of ice)
  • High temperatures may cause reaction to become non-spontaneous if $T\Delta S$ term becomes larger than $\Delta H$ term (melting of ice)
• For endothermic reactions ($\Delta H > 0$):
  • High temperatures favor spontaneity $T\Delta S$ term can overcome positive $\Delta H$ term (evaporation of water)
  • Low temperatures typically result in non-spontaneous reactions $\Delta H$ term dominates (condensation of water vapor)

Free energy changes vs equilibrium constants

• Standard Gibbs free energy change ($\Delta G^\circ$) related to equilibrium constant ($K$) by equation:
  • $\Delta G^\circ = -RT \ln K$
    • $R$: Gas constant (8.314 J/mol·K)
    • $T$: Absolute temperature in Kelvin
    • $\ln K$: Natural logarithm of equilibrium constant
• Rearranging equation to solve for $K$:
  • $K = e^{-\Delta G^\circ / RT}$
• Relationship between $\Delta G^\circ$ and $K$:
  • $\Delta G^\circ < 0$ corresponds to $K > 1$ indicating spontaneous forward reaction (product-favored)
  • $\Delta G^\circ > 0$ corresponds to $K < 1$ indicating non-spontaneous forward reaction (reactant-favored)
  • $\Delta G^\circ = 0$ corresponds to $K = 1$ indicating system at equilibrium (no net change)

Thermodynamics and Free Energy

• Thermodynamics is the study of energy transformations in physical and chemical processes
• Gibbs free energy is a fundamental concept in thermodynamics, developed by Josiah Willard Gibbs
• Chemical potential is the change in Gibbs free energy when the amount of a substance in a system changes
• Reversibility in thermodynamics refers to processes that can be reversed without any net change in the system or surroundings