Gibbs Free Energy Equations

Gibbs Free Energy equations help us understand the spontaneity of chemical processes and their relationship to energy changes. These concepts are essential in General Chemistry II and Physical Chemistry I, linking thermodynamics, equilibrium, and reaction dynamics in a cohesive way.

1. Gibbs free energy equation: ΔG = ΔH - TΔS

   • ΔG indicates the spontaneity of a process; negative ΔG means the process is spontaneous.
   • ΔH represents the change in enthalpy (heat content) of the system.
   • TΔS accounts for the change in entropy (disorder) of the system; higher entropy favors spontaneity.

2. Relationship between Gibbs free energy and equilibrium constant: ΔG° = -RT ln K

   • ΔG° is the standard Gibbs free energy change at standard conditions.
   • K is the equilibrium constant; a larger K indicates a more favorable reaction.
   • The equation shows that a negative ΔG° corresponds to a K greater than 1, indicating product-favored reactions.

3. Gibbs free energy change for non-standard conditions: ΔG = ΔG° + RT ln Q

   • Q is the reaction quotient, representing the ratio of products to reactants at any point.
   • This equation allows for the calculation of ΔG under non-standard conditions.
   • A positive Q can lead to a positive ΔG, indicating non-spontaneity under those conditions.

4. Gibbs-Helmholtz equation: (∂(ΔG/T)/∂T)p = -ΔH/T²

   • This equation relates the temperature dependence of Gibbs free energy to enthalpy changes.
   • It shows how ΔG changes with temperature, providing insight into thermodynamic stability.
   • Useful for understanding phase transitions and temperature effects on spontaneity.

5. Gibbs free energy of mixing for ideal solutions: ΔGmix = RT(x1 ln x1 + x2 ln x2)

   • ΔGmix quantifies the change in Gibbs free energy when mixing two ideal solutions.
   • x1 and x2 are the mole fractions of the components in the mixture.
   • Positive ΔGmix indicates that mixing is non-spontaneous, while negative indicates spontaneity.

6. Gibbs free energy and chemical potential: G = Σ(μi ni)

   • G represents the total Gibbs free energy of a system.
   • μi is the chemical potential of component i, and ni is its amount in moles.
   • This relationship emphasizes the contribution of each component to the overall energy of the system.

7. Gibbs free energy and work: ΔG = wmax (constant T and P)

   • ΔG represents the maximum reversible work obtainable from a process at constant temperature and pressure.
   • This highlights the practical application of Gibbs free energy in calculating work in thermodynamic systems.
   • It underscores the relationship between energy changes and work done by or on the system.

8. Gibbs free energy and electrochemistry: ΔG = -nFE

   • n is the number of moles of electrons transferred, and F is Faraday's constant.
   • E is the electromotive force (voltage) of the cell; a positive E results in a negative ΔG, indicating spontaneity.
   • This equation connects thermodynamics with electrochemical processes.

9. Gibbs free energy and phase transitions: ΔG = 0 at equilibrium

   • At equilibrium, the Gibbs free energy of the system is at a minimum, and no net change occurs.
   • This principle is crucial for understanding phase changes, such as melting and boiling.
   • It indicates that the forward and reverse processes occur at equal rates.

10. Gibbs-Duhem equation: Σ(xi dμi) = 0

    • This equation relates changes in chemical potential to changes in composition in a system.
    • It emphasizes the interdependence of the chemical potentials of components in a mixture.
    • Useful for understanding how the addition of one component affects the others in a thermodynamic system.