Chemical Sciences

Introduction: State functions, intensive and extensive, Independent variables, Phase, Thermodynamic state, Thermal equilibrium, Zero law, Temperature scales, Thermodynamic equilibrium, Reversible and irreversible processes, Work done by a volume variation, PV diagram, Work in reversible transformations, exact and non exact differentials, partial differential, exact and not exact differentials, simple systems First law: Heat, I Law Formulation, Internal Energy, Reversible Processes, Adiabatic Processes, Constant Pressure Transformations: Enthalpy, Constant Volume Transformations, Heat Capacity, Difference (Cp - Cv), Joule Experiment, Joule Experiment Kelvin, Application of the I Law to Ideal Gases, Difference (Cp - Cv) for ideal gas, Reversible adiabatic processes (ideal gas), Work: reversible adiabatic (ideal gas), Work: reversible isothermal (ideal gas), Work done by a van der Waals gas, V or P constant reaction heat, Hess law, Reaction heat measurement, Binding energy, Reaction heat vs temperature. II Law of Thermodynamics: Limits of the First Law, Work - Heat, Heat - Work, Refrigerator, Postulates of the II Law, Equivalence of the postulates of Kelvin & Planck and Clausius, Reversible and irreversible processes and II Law, Entropy - Classical treatment: Carnot cycle, Carnot theorem and corollaries, Thermodynamic temperature scale, Efficiency of a Carnot machine, Absolute temperature zero, Temperature on thermodynamic scale, Kelvin scale and ideal gas temperature scale, Replacement of a reversible process, Clausius theorem, Clausius inequality, Entropy, Entropy variation - irreversible process Entropy: Variations of entropy in isolated systems, The principle of energy dissipation, Combination of I and II Law, Entropy Variations, Entropy Variations for an Ideal Gas, Probability, Entropy and Probability, Probability and II Law, Isothermal Expansion of an Ideal Gas, Entropy and Disorder, The Meaning of Entropy Ideal gas mixtures: Gibbs-Dalton's law, Entropy of a mixture, Mixing entropy III Principle of Thermodynamics: Nernst's theorem, Determination of absolute entropy, Nernst's theorem and absolute zero, Entropy and degeneration, Mixtures, Helmholtz and Gibbs functions Helmholtz and Gibbs functions: Isothermal processes, Variations in Helmholtz and Gibbs functions, Gibbs-Helmholtz equation, Gibbs function for an ideal gas, Gibbs function of an ideal gas in a gaseous mixture, Standard state, Entropy and energy in chemical equilibrium, Gibbs and Helmholtz functions, Chemical equilibrium, van't Hoff isotherm General thermodynamic relations: Maxwell equations, TdS equations, Cp - Cv, Thermal capacity ratio, Joule-Kelvin coefficient Open systems: Chemical potential, Partial molar properties, Gibbs-Duhem equation, Mass transfer between phases, Relationship between partial molar properties, Chemical potential with intensive quantities P, T, x, Determination of partial molar quantities Phase equilibria: Surface P, V, T, PV Diagrams, PT Diagrams, Clapeyron Equation, Clausius-Clapeyron Equation, Trouton Rule, TS Diagrams, Q Calculation, Second Order Transitions, Phase Rule, Binary Solutions , Law of Raoult, Deviations from the law of Raoult, Equation of Duhem-Margules, Law of Henry, Diagrams x - P ex - T: complete miscibility, Completely miscible liquids not Raoultians, Diagrams P - T, Balance between two binary phases, Point eutectic, thermodynamic treatment of the eutectic point Solution thermodynamics: Chemical potential and perfect gas mixture, Real gas mixtures, Determination of fugacity, Condensed phase solutions, Definition of ideal solution, Ideal solutions - chemical potential, Non-ideal solutions, Standard states of solution components, Importance of standard states, use of the various standard states, properties of the solutions, lowering of the freezing point, boiling point rise, osmotic pressure, determination of molecular weight, meaning of the activity coefficient, determination of the activity coefficient Reaction equilibria: Van't Hoff's isotherm, Alternative reaction equilibrium, Equilibrium position, Homogeneous reaction of ideal gases, Homogeneous reaction of real gases, Homogeneous reaction in solution, Heterogeneous reactions, Constant equilibrium vs temperature, Constant of balance vs pressure, Le Chatelier's principle, Determination of Gibbs function, Free energy function, Thermodynamic tabulations, Chemical stability Electrolytes: Chemical potential, Activity, Solubility product, Deviations from ideal behavior, Dissociation constant, Electrochemical cells, Reversible cells, Thermodynamic functions from reversible cells, Liquid junction and salt bridge, Semi-cell elements, standard emf of reversible cells, Determination of standard and em emf, Standard electrode potential, Gibbs standard functions of ion formation, Concentration cells, Determination of solubility product. Laboratory Experiences • Combustion Calorimetry • Emf vs T – Weston Battery • Measurement of equivalent and limit equivalent conductivity (determination of constant of dissociation of benzoic acid) • Density measurement of aqueous solutions (partial molar volumes) • Determining the capacity of an accumulator • Construction of the Pb-Sn phase diagram from the acquisition of the cooling curves

Necessary prerequisites for understanding the topics proposed in the course of Physical Chemistry I with Laboratory are the most important topics of the course of General and Inorganic Chemistry (inorganic systematic, periodic table of elements, concept of mole, knowledge of different types of concentration , balance of reactions, electronic ion method of oxidation-reduction reactions, mass action law, colligative properties, pH, basic electrochemistry). Furthermore, the student must be familiar with the basic knowledge of mathematical analysis (derivatives and partial derivatives, differentials, integrals and simple differential equations, function studies).

- P.W. Atkins, J. De Paula - Chimica Fisica - Zanichelli Editore. - D. Gozzi – Termodinamica Chimica – Edizioni Nuova Cultura.

The course is developed in eighty hours distributed in fifty-six hours of lectures dedicated to the theoretical treatment of the topics proposed in the program (principles, theoretical models, demonstrations, applications and limits of equations obtained), twelve hours of numerical exercises, where the student are asked to use the theoretical information to solve problems, and another twelve hours of laboratory exercises in which the students have six practical experiences to perform in the lab, to elaborate and to report.

The exams will be oral. During the exam the student will be asked to solve problems and answer some questions related to basic principles of thermodynamics learned in class and deepened in the lab experiences (theoretical principles of experience, materials, methods, processing of experimental data and results). The student's ability to analyze, synthesize and clearly express the scientific concepts will be evaluated. Simple systems will be discussed to assess the student's ability to frame them in the right context and to choose the correct study methodologies.

The course is developed in eighty hours distributed in fifty-six hours of lectures dedicated to the theoretical treatment of the topics proposed in the program (principles, theoretical models, demonstrations, applications and limits of equations obtained), twelve hours of numerical exercises, where the student are asked to use the theoretical information to solve problems, and another twelve hours of laboratory exercises in which the students have six practical experiences to perform in the lab, to elaborate and to report.

First law of Thermodynamics Definitions, aims and limits of Thermodynamics. Thermodynamic systems. State variables and state functions. Thermodynamic state. Thermal, mechanical and chemical equilibrium. Reversible and irreversible processes. Mechanical work. First law of Thermodynamics. Heat, work and internal energy variations in thermodynamic transformations. Heat capacities. Internal energy and its dependence on temperature and volume. Ideal and real gases. Enthalpy and its variations in chemical reactions. Enthalpy changes determinations in chemical processes by calorimetric measurements. Second law of Thermodynamics Irreversibility of natural processes and the entropy function as a measure of the irreversibility of thermodynamic transformations; second law of Thermodynamics. Thermodynamic temperature and the Carnot cycle. Entropy changes in gases, liquids and solids physical transformations. Statistical interpretation of entropy, microstates and macrostates. Microstates number calculation. Boltzmann’s equation. Entropy and disorder. Entropy of mixing. Third law of Thermodynamics Nernst theorem and Planck’s statement. Brief introduction to experimental measurement of absolute entropies and to the calculation of the same. Thermodynamic equilibrium Thermodynamic potential. Gibbs free energy and Helmotz free energy. First order phase transitions and some very basic information about higher order transitions. Phase diagrams of one-component systems. Fugacities, activities and chemical potentials of pure gases, liquids and solids. Multi-component systems Partial molar quantities, Gibbs-Duhem law. Experimental methods for the determination of partial molar quantities. Ideal and regular solutions. Properties of solutions: colligative properties. Activity and activity coefficient. Phase rule for multi-component systems. Chemical equilibrium in homogeneous and heterogeneous systems Chemical equilibrium. Thermodynamic equilibrium constant and its variation with temperature. Electrochemical equilibrium. Electrochemical potential. Standard electrode potentials. Electromotive force: definition and measurement. Basics of electrochemical cells and electrodes. Ions and their activity in solution. Electrolytic solutions: basics of the Debye-Hückel theory. Basics of chemical kinetics Reaction mechanism. Molecularity. Reaction rate. Reaction order. Equilibrion constants and rate constants. Reaction rate and temperature. Photochemical reactions. Catalysts. Heterogeneous catalysis. Enzyme catalysis. Homogeneous catalysis.

In order to fully understand the topics presented in the course, it is advisable for the students to have already taken the curriculum's Maths courses and the first Physics course and passed the respective exams.

Daniele Gozzi, Termodinamica Chimica, IV Edizione, Edizioni Nuova Cultura Paolo Silvestroni, Fondamenti di Chimica, qualunque edizione. Daniele Gozzi, Problemi svolti di termodinamica chimica, Edizioni Nuova Cultura

Lectures attendance is not compulsory. The course is composed of classroom lectures and practical activities, i.e. numerical exercises and laboratory experiments. Weekly lectures take place and they are performed using the blackboard. Three midterms two hours each, are written. They take place in classrooms. This methodology aims at providing the students with the opportunity of verifying their knowledge and competencies. Furthermore, such method offers the opportunity of a more gradual evaluation of the preparation of the students.

not compulsory

The exam is aimed at verifying the knowledge and understanding level of the topics of the course, as well as the reasoning capabilities acquired by the student. The final grade is out of 30 (minimum 18/30, maximum 30/30 cum laude). The exam consists of an oral exam. The exam allows for the verification of the knowledge, skills and communication abilities of the students. The oral examination is aimed to check the degree of understanding of the course’s topics and the clarity of the presentation.

Classroom lessons, numerical problems solution, laboratory experiments with data analysis.

The first law of thermodynamics. Definition of a thermodynamic system. States and properties of the systems. State functions and thermodynamic state. Thermal, mechanical and chemical equilibrium. Reversible and irreversible processes. Reversible work. The first law of thermodynamics: the formulation, heat, work, internal energy and its changes in the thermodynamic processes. Heat capacity, enthalpy, its changes in the chemical reactions and dependence on the temperature. Thermochemistry. The second law of thermodynamics. Irreversibility of natural events and entropy as a measure of irreversibility of thermodynamic transformations. Clausius inequality. Thermodynamic temperature. Changes of entropy in different conditions. The statistical view of the entropy. Boltzmann equation. Entropy change in the phase transitions. Mixing entropy. Temperature and its measurement. The third law of thermodynamics. Nernst theorem and Planck statement. Absolute entropy and its evaluation. Thermodynamic equilibrium. Thermodynamic potentials; Gibbs and Helmholtz free energy. Phase transitions. Phase diagrams for pure materials. Fugacity and activity, and chemical potential of pure gases, liquids and solids. Multi-components systems. Chemical potential, partial molar quantities, Gibbs-Duhem equation: fugacity and activity, Solutions and their properties: osmotic pressure, freezing point lowering, boiling point raising. Ideal solutions and regular solutions. Experimental methods to determine the partial molar quantities. Phase rule. Chemical equilibrium. Chemical reactions. Chemical equilibrium, thermodynamic constant and its dependence on temperature. Equilibrium electrochemistry: electrochemical potential, ions, ion activity, electrodes, electrochemical cells, standard electrode potential, electromotive force. Work in chemical reactions. Thermodynamic functions from electromotive force measurements. Theories of ionic solutions: Debye-Hückel theory (outline). Chemical kinetics. The rate of chemical reactions. Order, molecularity and mechanism of a reaction. Kinetics of consecutive reactions, steady-state kinetics, kinetics of reversible and irreversible. The temperature dependence of the rate of chemical reactions. Experimental methods to measure the rate of a chemical reaction. Catalysis. Homogeneous catalysis. Enzymatic kinetics: kinetics of Michaelis-Menten. Heterogeneous catalysis (outline) Experimental activities 1. Measurement of the combustion heat of benzoic acid. 2. Measurement of heat capacity of metals. 3. Thermodynamic data of a chemical reaction by measurements of electromotive force as a function of temperature. 4. Determination of partial molar volumes by measurements of density of aqueous solutions.

For a better learning of the topics proposed in this course, basic skills of Chemistry (inorganic chemistry, the periodic table of the elements, the concept of mole, kinds of concentrations, balancing chemical equations, balancing redox reactions, law of mass action, colligative properties, pH, basic background of electrochemistry). In addition, the student should be familiar with the basic knowledge of mathematics (derivatives and partial derivatives, differentials, simple integrals and differential equations, study of functions).

There is no reference text. Some are suggested: 1. D. Gozzi Termodinamica Chimica, Edizioni Nuova Cultura 2. P. W. Atkins, J. de Paula - Chimica Fisica, Zanichelli 3. Notes on practical experiences written by Prof. Daniele Gozzi: https://www.chem.uniroma1.it/sites/default/files/allegati_insegnamento/dispense%20labChimFis.pdf 4. Notes on Chemical Kinetics written by Prof. Guido Gigli: https://www.chem.uniroma1.it/sites/default/files/allegati_insegnamento/cinetica_chimica.pdf

The course is composed of eighty hours, sixty-eight of which are devoted to the theoretical treatment of the topics proposed in the program (theoretical models, mathematical proofs, applications and limits of the obtained equations) and numerical exercises focused on thermodynamics and kinetics while the remaining twelve will be used to laboratory experiences where the student will carry practical experiences, the results of which have to be described and discussed in a report.

The student will be evaluated by a written and oral exam in which the student should discuss one of the laboratory experiences (theoretical principles, materials, methods, processing of experimental data and results), some thermodynamic and kinetic issues with the relative proofs, and solve some numerical exercises. The capability of analysis, making judgment and communication skills will be also evaluated. Simple systems will be discussed to evaluate the student skills to frame the chemical problem in the correct context and choose the most suitable methodologies of investigation.

To deepen some topics: 1. E. Fermi Termodinamica, Boringhieri (available at the library G. Illuminati of Chemistry Department) 2. G. N. Lewis, M. Randall Termodinamica, Leonardo Edizioni Scientifiche (per approfondimenti) (available at the library G. Illuminati of Chemistry Department)

The course is composed of eighty hours, sixty-eight of which are devoted to the theoretical treatment of the topics proposed in the program (theoretical models, mathematical proofs, applications and limits of the obtained equations) and numerical exercises focused on thermodynamics and kinetics while the remaining twelve will be used to laboratory experiences where the student will carry practical experiences, the results of which have to be described and discussed in a report.

Mandatory to participate in laboratory experiences