Physical Chemistry: Concepts, Calculations, and Applications

Analyze chemical reactions, molecular motion, and energy transformations using probability, quantum mechanics, and thermodynamics.

Interpret phase diagrams, equilibrium constants, and spectroscopic data.

Build a strong foundation for advanced studies, research, or careers in chemistry, engineering, and related fields.

Explore entropy from both classical and probabilistic perspectives, and learn to distinguish between extensive and intensive properties.

Develop skills in mathematical optimization, including single and multivariate functions, constrained optimization, and the use of Lagrange multipliers.

Analyze the Boltzmann distribution, energy constraints, and the meaning of thermodynamic parameters such as beta, with practical examples like air pressure at altitude.

Gain a solid introduction to quantum mechanics, including quantization of light and matter, wavefunctions, Schrödinger’s equation, operators, eigenvalue problems, and the particle-in-a-box model.

Apply the postulates of quantum mechanics to wavefunctions, operators, eigenvalues, expectation values, and time dependence.

Learn about the partition function, degeneracy, and how to connect statistical mechanics to thermodynamic quantities like energy, entropy, and pressure.

Solve and interpret the three-dimensional particle-in-a-box problem, including normalization, degeneracy, and applications to molecules and dye systems.

Understand the properties of ideal gases, including partition functions, Gaussian integrals, and kinetic theory concepts such as molecular velocity distributions, mean free path, and collision frequency.

Compare ideal and real gases, study the van der Waals model, equations of state, compressibility factor, and Boyle temperature.

Delve into thermodynamic states, exact and inexact differentials, integrating factors, heat and work, the first law of thermodynamics, enthalpy, heat capacity, entropy changes, adiabatic processes, Carnot cycle, heat engines, calorimetry, and thermochemistry.

Study the rigid rotor and harmonic oscillator models, including their quantum mechanical solutions, rotational and vibrational spectroscopy, selection rules, and thermodynamic properties.

Analyze diatomic molecules, equipartition theorem, rovibrational states, anharmonicity, and rotational-vibrational coupling.

Explore spectroscopy techniques for polyatomic molecules, including infrared, electronic, fluorescence, and phosphorescence, and understand the Franck-Condon principle and types of luminescence.

Investigate the properties of solids, including the law of Dulong and Petit, Einstein solid model, and electronic degrees of freedom.

Learn about molecular symmetry, symmetry operators and elements, group theory, point groups, and their determination.

Understand spontaneity, the second law of thermodynamics, entropy and internal energy relationships, fundamental thermodynamic equations, and entropy of mixing.

Master free energy concepts, including Helmholtz and Gibbs free energies, their fundamental equations, thermodynamic connections, and the Gibbs-Helmholtz equation.

Apply thermodynamic relationships, including Maxwell relations, chain rule, reciprocal rule, cyclic rule, and change of constraint rule.

Study phase equilibria, phase transitions, phase diagrams, triple and critical points, Clapeyron and Clausius-Clapeyron equations, and van der Waals phase behavior.

Learn about solutions, measures of concentration, partial molar quantities, chemical potential, Gibbs phase rule, Raoult’s law, distillation, non-ideal solutions, activity coefficients, Henry’s law, azeotropes, eutectics, colligative properties, and osmotic pressure.

Explore electrolytic solutions, mean ionic activity, ionic strength, and the Debye-Hückel limiting law.

Solve the hydrogen atom using quantum mechanics, including separation of variables, radial and angular components, Laguerre polynomials, and energy levels.

Study many-electron atoms, variational methods, Hartree product, electron spin, antisymmetry, and Slater determinants.

Learn about nuclei, nuclear spin, magnetic resonance, NMR shielding, chemical shift, isotope effects, and bond dissociation energy.

Analyze chemical equilibrium, equilibrium constants, reaction quotients, van’t Hoff equation, and temperature dependence of equilibrium.

Investigate surface phenomena, adsorption models (Langmuir and BET), isotherms, thermodynamics, kinetics, and limitations.

Understand the basics of lasers, including three-state and He-Ne lasers, and their physical chemistry principles.