67035 - Physical Chemistry

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

Prerequisites

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).

Physics:

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

Chemistry:

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 ).

Topics:

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).

The course provides the conceptual and methodological foundations of physical chemistry, with particular emphasis on the thermodynamic and kinetic analysis of chemical processes, as well as on the quantum principles underlying molecular structure and properties. The content is organized into three main modules, in line with the learning objectives of the degree program, and is complemented by practical and numerical exercises aimed at developing applied skills.

 

I Thermodynamics

Gases: Ideal and Real

• Ideal gas equation of state
• Mixtures of ideal gases and Dalton’s law of partial pressures
• Validity limits of the ideal gas equation
• Real gases: introduction to intermolecular forces
• Real behavior of CO₂ as a function of pressure, temperature, and molar volume
• Critical point and its physical meaning
• Compressibility factor Z and its use to evaluate deviations from ideality
• Virial equation: series expansion for real gases
• Van der Waals equation

Thermodynamic Systems and the First Law

• Thermodynamic systems: open, closed, isolated, adiabatic
• Work and heat as forms of energy transfer
• First law of thermodynamics
• Mechanical work: free expansion, expansion against constant pressure, reversible work
• Heat at constant volume. State functions and exact differentials
• Partial derivatives of internal energy. Heat capacities at constant volume and pressure
• Internal energy and heat capacity of an ideal gas
• Definition and meaning of enthalpy
• Relation between enthalpy, internal energy, and heat at constant pressure
• Isothermal and adiabatic expansions of an ideal gas

Thermochemistry

• Standard enthalpy changes
• Enthalpy of reaction, combustion, and formation
• Temperature dependence of enthalpy: Kirchhoff’s law

Second Law and Entropy; Third Law

• Spontaneous transformations and the second law of thermodynamics
• Entropy: definition and changes in characteristic processes (expansion, heating, phase transitions)
• Third law: absolute entropies
• Reaction entropy and its relation to spontaneity
• Gibbs and Helmholtz free energies and their relation to spontaneity
• Chemical potentials

Gibbs Energy

• Gibbs energy of reaction
• Combination of the first and second laws
• Gibbs–Helmholtz equation
• Dependence of ΔG on temperature and pressure

Thermodynamic Stability and Phase Diagrams

• Criteria for thermodynamic stability
• ΔG dependence and phase transitions
• P–T diagrams of pure substances, triple point and critical point
• Clapeyron and Clausius–Clapeyron equations for phase boundaries

Phases and Solutions

• Gibbs phase rule
• Partial molar quantities: volume and Gibbs energy
• Entropy of mixing. Ideal mixtures and Raoult’s law
• Chemical potential in ideal and real solutions

Colligative Properties

• Vapor pressure lowering. Boiling point elevation and freezing point depression
• Osmotic pressure
• Dilute solutions: Henry’s law

Two-Component Systems

• Liquid–vapor diagrams: P–X and T–X
• Phase localization and the lever rule
• Simple and fractional distillation
• Azeotropes, deviations from Raoult’s law
• T–X diagrams for liquid–liquid and solid–liquid systems
• Eutectic points and compound formation (brief mention)

Chemical Equilibrium

• Extent of reaction, Gibbs energy, and reaction quotient
• Equilibrium constant (Kp, Kc, Kx)
• Activities and standard states
• Effects of temperature and pressure on equilibrium
• Van’t Hoff equation

Electrochemistry

• Galvanic and electrolytic cells. Electrodes, anode and cathode
• Half-reactions and cell potential
• Relationship between ΔG and cell potential
• Nernst equation
• Equilibrium constant and standard potential
• Electrochemical series and temperature dependence
• Ionic activity coefficients. Debye–Hückel limiting law

 

 

II Chemical kinetics
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.

III Quantum mechanics

 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.

Readings/Bibliography

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

Assessment for Course 67037

After each lab practical, the students in each group must draft a summary report, using the template provided, in which only the experimental data must be reported and commented on. The summary reports must be submitted by the next laboratory session, or— for the final practical—within 8 days of its conclusion.

At least 24 hours before the final exam, a single detailed individual report on one of the lab experiments (freely chosen by the student) must be submitted by email in digital format (Word or PDF). This report must be written according to the instructions provided during the laboratory course lectures.

The mark for course 67037 comprises:

• the overall evaluation of the group summary reports (maximum 5/30), and

• the individual detailed report (maximum 5/30),

for a total maximum of 10/30, to be added to the mark obtained in course 67035.

Please note: the individual report must be submitted before the final exam. If the deadline is missed, the evaluation for course 67037 will be based only on the summary reports.

 

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

 

Office hours

See the website of Elisabetta Venuti

See the website of Riccardo Tarroni