Thermodynamics: Entropy, Spontaneity, and Gibbs Free Energy

Introduction to Thermodynamics and Spontaneity

Thermodynamics is the study of energy changes and the direction of chemical processes. While enthalpy changes (ΔH) indicate whether a reaction is endothermic or exothermic, they alone do not determine if a reaction is spontaneous. Spontaneity also depends on entropy changes and temperature. For example, the melting of ice is endothermic but spontaneous above 0°C, while freezing is spontaneous below 0°C.

• Spontaneous process: Occurs naturally without external intervention and only in one direction under given conditions.

• Nonspontaneous process: Requires continuous external energy to proceed.

Entropy and the Second Law of Thermodynamics

Entropy (S) is a measure of the disorder or randomness of a system. It quantifies the tendency for energy to disperse and for systems to move toward greater disorder. Entropy is a state function, meaning its change depends only on the initial and final states, not the path taken.

• Change in entropy:

• Isothermal process: , where is the reversible heat transfer and is the absolute temperature.

The Second Law of Thermodynamics states that the entropy of the universe increases for any spontaneous process:

This law explains why certain processes are spontaneous and why their reverse is not.

Standard Molar Entropies

Standard molar entropy () is the entropy content of one mole of a substance in its standard state (pure substance at 1 atm and 298 K). These values are used to calculate entropy changes in reactions.

Calculating Entropy Changes in Reactions

The standard entropy change for a reaction () is calculated as the difference between the sum of the standard molar entropies of the products and the reactants, each multiplied by their stoichiometric coefficients:

Example: For the synthesis of ammonia:

• Using standard molar entropies,

Gibbs Free Energy and Spontaneity

Gibbs free energy (G) is a thermodynamic function that combines enthalpy and entropy to predict the spontaneity of a process at constant temperature and pressure. It is defined as:

• Change in free energy:

• Under standard conditions:

The sign of determines spontaneity:

• : Reaction is spontaneous in the forward direction.

• : Reaction is at equilibrium.

• : Reaction is nonspontaneous in the forward direction.

Example: For the formation of NO2 from N2 and O2:

• Given and , calculate using

Summary Table: Criteria for Spontaneity

Additional info: The examples and sample exercises provided illustrate the calculation of entropy and free energy changes, reinforcing the connection between thermodynamic quantities and the prediction of reaction spontaneity.