Thermodynamics: Entropy, Free Energy, and Spontaneity

Spontaneity in Chemical Reactions

Chemical reactions are considered spontaneous if they occur without outside intervention. The spontaneity of a reaction is determined by two main factors: enthalpy (ΔH) and entropy (ΔS). Exothermic reactions (negative ΔH) and increased disorder (positive ΔS) are generally favored. However, spontaneity does not indicate the speed of a reaction, which is governed by kinetics.

• Enthalpy (ΔH): The heat content of a system. Exothermic reactions (ΔH < 0) are usually favored.

• Entropy (ΔS): The measure of disorder or randomness in a system. Nature tends toward greater disorder.

• Spontaneous reactions: Occur without external input; may be fast or slow.

Entropy (ΔS)

Entropy is a thermodynamic property that quantifies the degree of disorder or randomness in a system. The Second Law of Thermodynamics states that the entropy of the universe tends to increase. The Third Law of Thermodynamics establishes that the entropy of a perfect crystal at absolute zero (0 K) is zero, allowing the calculation of absolute entropy values for substances at higher temperatures.

• Greater disorder means higher entropy.

• Entropy increases as substances change from solid → liquid → gas.

• Dissolving a solid or liquid in a solvent usually increases entropy (with some exceptions, e.g., carbonates).

• When a gas escapes from a solvent, entropy increases.

• Increasing molecular complexity generally increases entropy.

• Reactions that increase the number of moles of particles often increase entropy.

Example: The image above shows a disordered pile of playing cards, which visually represents the concept of entropy as disorder.

Example: The image above demonstrates three possible arrangements (microstates) of four molecules in a two-bulbed flask. The greater the number of possible arrangements, the higher the entropy.

Predicting Entropy Changes

• Solid sugar dissolving in water: Entropy increases (ΔS > 0).

• Iodine vapor condensing to crystals: Entropy decreases (ΔS < 0).

Calculating Entropy Changes

Standard entropy changes can be calculated using tabulated values:

• ΔSrxn = Σ ΔS (products) - Σ ΔS (reactants)

Units: J/(K·mol)

Sample Problem

Which of the following has the largest increase in entropy?

• CO2(s) → CO2(g): Largest increase (solid to gas transition).

Entropy Changes for Reversible Phase Changes

For a phase change at constant temperature:

where q is the heat transferred and T is the temperature in Kelvin.

Entropy of the Universe and Spontaneity

The spontaneity of a reaction can be determined by the total entropy change of the universe:

• If ΔSuniverse > 0, the process is spontaneous.

• If ΔSuniverse < 0, the process is nonspontaneous.

For the surroundings:

Gibbs Free Energy (ΔG)

Gibbs free energy combines enthalpy and entropy to predict spontaneity at constant temperature and pressure. A negative ΔG indicates a spontaneous process.

• Standard free energy change:

• General equation:

• Non-standard conditions:

• At equilibrium:

• Electrochemistry:

Where:

• R = 8.3145 J/(mol·K) (universal gas constant)

• T = temperature in Kelvin

• Q = reaction quotient

• K = equilibrium constant

• n = moles of electrons transferred

• F = Faraday's constant (96,485 C/mol e-)

• E° = standard cell potential

Sample Problem

Calculate ΔG° for the reaction:

2SO2(g) + O2(g) → 2SO3(g)

• ΔH° = -198 kJ

• ΔS° = -187 J/K

• ΔG° = -142 kJ

Relationship Between ΔG, K, and Spontaneity

Temperature Dependence of Spontaneity

Free Energy and Maximum Work

Gibbs free energy also represents the maximum amount of work a system can perform at constant temperature and pressure:

When ΔG is negative, the system can do work; when positive, work must be done on the system to make the process occur.

Example: The image above shows a battery performing work in a reversible and irreversible process, illustrating the concept of maximum work and the difference between ideal and real processes.

Free Energy Profiles and Equilibrium

The free energy profile of a reaction shows how the Gibbs free energy changes as the reaction progresses. Equilibrium occurs at the minimum point of the free energy curve.

Example: The image above displays free energy curves for different reactions, with equilibrium points marked where the free energy is minimized.

Summary Table: Key Thermodynamic Quantities