67035 - Physical Chemistry

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2022/2023

Learning outcomes

After completing the course, the student will have acquired the physical and mathematical bases to understand structure and properties of matter and the physical and chemical transformations concerning atoms and molecules in their aggregation states.

The laws of thermodynamics, dealing with energy transformations, and the fundamentals of kinetics , investigating the speed of chemical reactions and the factors influencing them, will be presented.

Finally, the course will deal with the principles of quantum mechanics and their applications consistently explaining the properties of atoms and molecules, the nature of the chemical bond, and the spectroscopic properties. Theoretical topics will be supplemented by examples, numerical exercises and practical laboratory tests.

Course contents


Needed Mathematics Core:

Algebraic, trigonometric, exponential, logarithmic functions. Fundamentals of calculus. Linear differential equations. Principles of Linear Algebra: Matrices, vector spaces, linear transformations.(Attività formativa: Matematica con esercitazioni).


Physical quantities and relationships that bind them, main units of measure (Attività formativa: Fisica con esercitazioni).


Basic chemical principles concerning structure and main properties of the elements, the chemical bond, the molecules and their geometry. Chemical reactions and their balance. (Attività formativa: General and Inorganic Chemistry ).


Understanding of the most important physical concepts in mechanics and electromagnetism.(Attività formativa: Fisica con esercitazioni)

Atomic and molecular theory, chemical equations, stiochiometry, problem-solving techniques. (Attività formativa: Chimica Generale e Inorganica con Laboratorio).

States of matter. Description of the states of matter in terms of state variables. Definition of volume, pressure, temperature, amount of matter and of their respective measurement units. Definition of the equation of state. Definition of standard temperature and pressure (SATP) Equation of state of an ideal gas. Combined equation of the ideal gas. Mixtures of ideal gas and Dalton's law. Limits of applicability of the ideal gas equation. Real gases and intermolecular forces. CO2 behavior at different pressures, molar volume and temperature. Definition of critical point of a real gas. Compressibility factor of a real gas. Virial equation of state. Equation of state of Van der Waals. Relationship between critical variables and parameters of the VdW equation

Definition of thermodynamic system (open, closed, isolated, adiabatic). Work and heat as modalities of energy transfer. First law of thermodynamics. Expansion work and extra work. Mechanical work in a free expansion, in an expansion against a constant external pressure and in a reversible expansion. Exchanges heat at constant volume. State functions and exact differentials. Partial derivatives of internal energy and of other state functions. Definition of heat capacity at constant volume and internal pressure.

Internal energy of an ideal gas. Heat capacity at constant volume and internal pressure of a perfect gas. Definition of enthalpy. Relationship between enthalpy and internal energy. Relationship between enthalpy and heat exchanged at constant pressure. Definition of heat capacity at constant pressure. Heat capacity at constant pressure of a perfect gas. Isothermal expansion of an ideal gas. Adiabatic expansion of an ideal gas. Thermochemical. Changes in enthalpy at standard conditions. Definition of reaction enthalpy, enthalpy of combustion, and enthalpy of formation. Dependence of the reaction enthalpies of the temperature. Kirchhoff's law

Spontaneous transformations. Second law of thermodynamics. Definition of entropy. Entropy changes for some typical processes: expansion of a gas at constant temperature, adiabatic expansion reversible, temperature variation in volume and constant pressure, phase transitions. Absolute entropies and third law of thermodynamics. Entropy of reaction. Relationship between entropy and the spontaneity of chemical reactions. Definition of Gibbs's and Helmholtz's energies

Gibbs energy of reaction. Combination of the first and second law of TD. Gibbs energy properties. Gibbs energy dependence with the temperature. Gibbs-Helmholtz equation. Gibbs energy dependence with the pressure for gas and condensed phases. Definition of fugacity of a real gas.

Criterion for thermodynamic stability of phases. Dependence of Gibbs energy on temperature and phase transitions. State diagrams of a pure substance. Pressure-Temperature diagrams and location of the phases in the different areas of the graph. Characteristic points (triple point, critical point). Derivation of Clapeyron. Limit of solid-liquid phase. Limit of liquid-vapor phase. Clausius-Clapeyron. Limit phase solid-vapor.

Gibbs phase rule. Partial molar quantities. Partial molar volume. Partial molar Gibbs energy and chemical potential. Spontaneous mixing of two ideal gases. Entropy of mixing. Raoult law and ideal solutions. Chemical potential of an ideal and a real solution.

Colligative properties. Lowering the the vapor pressure. Th elevation of boiling point. The depression of freezing point. Ideal solubility of a substance. Osmotic pressure. Very dilute solutions and Henry's law.

Two-component systems. Liquid-vapor phase.diagrams Pressure - composition and temperature-composition diagrams. Localization of the phases in the different areas of the phase diagrams. The lever rule. Simple and fractional distillation. Calculation of P-X and T-X diagrams for an ideal mixture. Real mixtures. Positive and negative deviations from Raoult's law. Minimum and maximum azeotropes. T-X liquid-liquid phase diagrams . Localization of the phases in the different areas of the graph. Definition of upper and lower critical temperature. T-X solid-liquid phase diagrams .Localization of the phases in the different areas of the graph. Definition of eutectic point. Solid-liquid diagrms for reacting systems.

Chemical balance. Definition of the degree of progress of a reaction. Relationship between the reaction Gibbs energy and the reaction quotient. Definition of the equilibrium constant. Relationship between Kp, Kc and Kx. Equilibrium constant expressed in terms of activity. Definition of the states standards for gases, for pure liquids, for solutions and for solids. Effect of pressure on the equilibrium composition. Dependence of the equilibrium constant on temperature. Van't Hoff equation.

Introduction to electrochemistry. Galvanic cells and electrolytic cells. Types of electrode. Half-reactions of reduction. Definition of the anode and cathode. The cell reaction. Cell potential and relationship with the change in Gibbs energy of reaction. Nernst equation. Relation between equilibrium constant and standard potential of the cell. Standard potential of electrode. Electrochemical series. Dependence of the standard potential of electrode temperature. Ionic activity coefficients. Debye-Huckel limit law.

Introduction to chemical kinetics. Experimental techniques to study the speed of the reactions. Definition of istantaneous and initial reaction rate. Kinetic laws and order of reaction. Determination of kinetic laws. Method of isolation and method of initial rates. Integrated kinetic law for first order reactions. Half-life for first order reactions. Integrated kinetic laws for second order reactions. Half-life for reactions of second order.

Introduction to quantum mechanics. Experimental evidence that led to quantum mechanics. De Broglie wavelength. Complex numbers. Operators. Derivation of time-dependent Schrödinger equation for a free particle. Eigenvalues and eigenvectors. Schroedinger equation independent of time. Postulates of quantum mechanics. Particle in a potential well of infinite size. Heisenberg uncertainty principle. Quantum harmonic oscillator. Molecular vibrations. Rigid rotor. Molecular energy levels. Vibro-rotational spectra.


P. W. Atkins, J. De Paula, Physical Chemistry, or any english edition of the same author. 


Lecture notes (slides, exercises with solutions etc) will be available on the institutional website

Assessment methods

Written exams will typically consist in the solution of six numerical problems (very  similar to assigned homework in class problems), often involving interpreting graphs or sketching answers. 

The written test is passed with a score of 60% (18/30) and is followed by an oral exam consisting in at least two questions of theory.  





Office hours

See the website of Elisabetta Venuti

See the website of Riccardo Tarroni