Gibbs Free Energy

Gibbs Free Energy ( $ G $ ) is a thermodynamic potential that measures the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It’s a crucial concept for predicting the spontaneity of a reaction.

Defining Gibbs Free Energy

Gibbs Free Energy is defined by the equation:

$ G = H - TS $

where:

• $ G $ is the Gibbs Free Energy (in Joules or Kilojoules)
• $ H $ is the enthalpy of the system (in Joules or Kilojoules) Enthalpy
• $ T $ is the absolute temperature (in Kelvin)
• $ S $ is the entropy of the system (in Joules/Kelvin) Entropy

Spontaneity and Gibbs Free Energy

The change in Gibbs Free Energy ( $ \Delta G $ ) for a process determines its spontaneity under conditions of constant temperature and pressure:

• $ \Delta G < 0 $ : The process is spontaneous (occurs without external intervention).
• $ \Delta G > 0 $ : The process is non-spontaneous (requires external work to occur). The reverse process is spontaneous.
• $ \Delta G = 0 $ : The process is at equilibrium; there is no net change in the system.

Relationship to Equilibrium Constant ( $ K $ )

For a reaction at equilibrium, the change in Gibbs Free Energy is zero ( $ \Delta G = 0 $ ). The standard Gibbs Free Energy change ( $ \Delta G° $ ) is related to the equilibrium constant ( $ K $ ) by the following equation:

$ \Delta G° = -RT \ln K $

where:

• $ R $ is the ideal gas constant (8.314 J/mol·K)
• $ T $ is the absolute temperature (in Kelvin)
• $ K $ is the equilibrium constant

This equation allows us to calculate the equilibrium constant from the standard Gibbs Free Energy change, and vice versa. A large positive $ \Delta G° $ indicates a small $ K $ (reaction favors reactants), while a large negative $ \Delta G° $ indicates a large $ K $ (reaction favors products).

Standard Gibbs Free Energy Change ( $ \Delta G° $ )

The standard Gibbs Free Energy change ( $ \Delta G° $ ) refers to the change in Gibbs Free Energy when reactants in their standard states are converted to products in their standard states at a specified temperature (usually 298 K). Standard states are defined as: 1 atm pressure for gases, 1 M concentration for solutions, and the pure substance for solids and liquids.

$ \Delta G° $ can be calculated from standard enthalpy changes ( $ \Delta H° $ ) and standard entropy changes ( $ \Delta S° $ ):

$ \Delta G° = \Delta H° - T\Delta S° $

It can also be calculated from the standard Gibbs Free Energies of formation ( $ \Delta G°_f $ ) of the reactants and products:

$ \Delta G°{rxn} = \sum \Delta G°{f,products} - \sum \Delta G°_{f,reactants} $

Gibbs Free Energy and Non-Standard Conditions

The equation relating $ \Delta G $ to $ \Delta G° $ and the reaction quotient ( $ Q $ ) is:

$ \Delta G = \Delta G° + RT \ln Q $

This equation is crucial for calculating the Gibbs Free Energy change under non-standard conditions. The reaction quotient ( $ Q $ ) has the same form as the equilibrium constant ( $ K $ ), but uses the actual concentrations or partial pressures of reactants and products at any given time, not just at equilibrium.

Enthalpy

Enthalpy ( $ H $ ) is a measure of the total heat content of a system. A positive change in enthalpy ( $ \Delta H > 0 $ ) indicates an endothermic process (heat is absorbed), while a negative change in enthalpy ( $ \Delta H < 0 $ ) indicates an exothermic process (heat is released).

Entropy

Entropy ( $ S $ ) is a measure of the disorder or randomness of a system. A positive change in entropy ( $ \Delta S > 0 $ ) indicates an increase in disorder, while a negative change in entropy ( $ \Delta S < 0 $ ) indicates a decrease in disorder.

This rundown provides a comprehensive overview of Gibbs Free Energy for AP Chemistry. Remember to practice applying these concepts through various problem-solving exercises.