Part II: Thermodynamics & Equations of State
Thermodynamics provides the macroscopic framework for understanding energy, equilibrium, and spontaneity in chemical systems. This part develops the key equations of state that describe gas behavior — from the ideal gas law through sophisticated models for real gases — and then extends these ideas to phase equilibria, chemical potential, and the thermodynamics of mixtures.
Part Overview
How do gases behave under different conditions of temperature and pressure? Why do phase transitions occur at specific temperatures? What governs the mixing of chemical species? This part answers these fundamental questions by building from kinetic molecular theory and ideal gas behavior to the thermodynamic description of real gases, phase diagrams, and multicomponent systems. We develop the concept of chemical potential as the central quantity governing equilibrium in heterogeneous and multicomponent systems.
Key Topics
- • Kinetic molecular theory and Maxwell-Boltzmann distribution
- • Ideal gas law and the equipartition theorem
- • Van der Waals equation and virial expansions
- • Critical phenomena and the law of corresponding states
- • Clausius-Clapeyron equation and phase diagrams
- • Gibbs phase rule and degrees of freedom
- • Chemical potential and partial molar quantities
- • Gibbs-Duhem equation and activity coefficients
- • Raoult's law and colligative properties
- • Regular solution theory and excess functions
5 chapters | Thermodynamics & Equations of State | Phase Equilibria & Mixtures
Key Equations
Ideal Gas Law
$$PV = nRT$$
Van der Waals Equation
$$\left(P + \frac{a}{V_m^2}\right)(V_m - b) = RT$$
Clausius-Clapeyron Equation
$$\frac{dP}{dT} = \frac{\Delta H}{T\,\Delta V}$$
Chemical Potential
$$\mu_i = \mu_i^\circ + RT \ln a_i$$
Chapters
Chapter 1: Ideal Gas Laws
Kinetic molecular theory, the Maxwell-Boltzmann speed distribution, the equipartition theorem, and the derivation of the ideal gas law from first principles.
Chapter 2: Real Gases & Equations of State
Deviations from ideality, the van der Waals equation, virial expansion, compressibility factor, critical phenomena, and the law of corresponding states.
Chapter 3: Phase Equilibria
The Clausius-Clapeyron equation, one-component and multicomponent phase diagrams, the Gibbs phase rule, and the thermodynamic criteria for phase coexistence.
Chapter 4: Chemical Potential
Partial molar quantities, the chemical potential as the key equilibrium criterion, the Gibbs-Duhem equation, and the concept of thermodynamic activity.
Chapter 5: Mixtures & Solutions
Raoult's law, Henry's law, colligative properties (boiling point elevation, freezing point depression, osmotic pressure), and regular solution theory.