Thermodynamics: Entropy and Free Energy

Spontaneity in Chemical Reactions

Chemical reactions are driven by two main factors: enthalpy (ΔH) and entropy (ΔS). Spontaneous reactions occur without external intervention and may proceed quickly or slowly, depending on their kinetics. The spontaneity of a reaction is determined by the interplay between enthalpy and entropy.

• Enthalpy (ΔH): Represents the heat content of a system. Exothermic reactions (ΔH < 0) are generally favored.

• Entropy (ΔS): Measures the disorder or randomness of a system. Increased disorder is favored by nature.

• Spontaneous reactions: Occur without outside intervention; can be fast (e.g., combustion) or slow (e.g., graphite to diamond).

Entropy: Definition and Laws

Entropy is a central concept in thermodynamics, describing the degree of disorder in a system. The second and third laws of thermodynamics provide foundational principles for understanding entropy.

• Second Law: The universe tends toward increasing disorder.

• Third Law: The entropy of a perfect crystal at 0 K is zero. Absolute entropy values can be determined for substances at temperatures above 0 K.

Predicting Entropy Changes

Entropy changes can be predicted based on physical evidence:

• The greater the disorder or randomness, the larger the entropy.

• Entropy increases as a substance changes from solid to liquid to gas.

• Dissolving a pure solid or liquid in a solvent increases entropy (exceptions: some carbonates).

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

• Entropy increases with molecular complexity.

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

Example: A disordered pile of playing cards visually represents increased entropy compared to an ordered deck.

Example: The number of possible arrangements of molecules in a two-bulbed flask illustrates the concept of entropy.

Calculating Entropy Changes

Entropy changes (ΔS) can be calculated using tables of standard values:

• ΔS is positive when disorder increases (favored).

• ΔS is negative when disorder decreases.

• Units: J/K·mol.

Formula:

Example: CO2(s) → CO2(g) has the largest increase in entropy due to the transition from a highly organized solid to a disorganized gas.

Entropy Changes for Reversible Phase Changes

For phase changes at constant temperature:

• q: Heat transferred (positive for endothermic, negative for exothermic).

• T: Temperature in Kelvin.

Favored conditions: For endothermic reactions, entropy increases; for exothermic, entropy of the surroundings increases.

Entropy of the Universe and Spontaneity

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

• If ΔSuniverse is positive, the reaction is spontaneous.

• If ΔSuniverse is negative, the reaction is nonspontaneous.

Even if the entropy of the system decreases, a sufficiently exothermic reaction can make the overall entropy change positive.

Free Energy and Spontaneity

Gibbs Free Energy (ΔG) determines whether a reaction is spontaneous. Negative ΔG values indicate spontaneity.

• ΔG can be calculated in several ways:

• From standard values:

• Grand Daddy Equation:

• Hess’s Law: Sum up equations as in enthalpy calculations.

• Non-standard conditions:

• Equilibrium:

• Electrochemistry:

Where:

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

• T = temperature in Kelvin

• Q = reaction quotient

• K = equilibrium constant

• n = number of moles of electrons transferred

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

Sample Calculations

• For the reaction 2SO2(g) + O2(g) → 2SO3(g): ΔH° = -198 kJ, ΔS° = -187 J/K, ΔG° = -142 kJ

• For Cdiamond(s) → Cgraphite(s): ΔG° = -3 kJ

• For CO(g) + 2H2(g) → CH3OH(l): ΔG = -38 kJ/mol rxn

Free Energy and Equilibrium

Gibbs free energy is also used to calculate equilibrium constants and phase change temperatures. At equilibrium, ΔG = 0.

Relationship between ΔG, K, and E:

Example: The thermodynamic boiling point of H2O(l) → H2O(g) can be calculated using:

Given: Hvap = +44 kJ, Svap = 118.8 J/K, T = 370 K

Free Energy Profiles and Maximum Work

The free energy profile of a reaction shows how the total free energy changes as the fraction of reactant converted to product increases. Equilibrium occurs at the minimum free energy.

Gibbs free energy is also useful for understanding the maximum amount of work a system can do at constant temperature and pressure:

When ΔG is negative (spontaneous), it represents the energy available to do work. When ΔG is positive (non-spontaneous), it is the work required to make the process occur.

Reversible and Irreversible Processes

A battery can do work by sending current to a starter motor and can be recharged by reversing the current. If the process is reversible, the work done in both directions is equal. In real processes, irreversibility means the universe is different after the cycle.

Summary Table: Conditions for Spontaneity

Key Takeaways:

• Spontaneity is determined by ΔG, which depends on ΔH and ΔS.

• Entropy measures disorder; nature favors increased entropy.

• Gibbs free energy links thermodynamics to equilibrium and maximum work.