Physical Chemistry I A - L

The course has as its primary objective to learn the meaning of thermodynamic quantities of chemical interest, the relationships between them, and their use for the purpose of predicting the spontaneity or otherwise of chemical and physical transformations.

More specifically, the course's aim is the development of the following skills:

• knowledge and understanding: the goal is to learn and understand the fundamental thermodynamic laws and the thermodynamic quantities that describe a system and the transformations of a system
• applying knowledge and understanding: the goal is the application of the laws and thermodynamic quantities to predict the course of chemical and physical transformations
• making judgments: the goal is to make the student able to evaluate, through participatory lessons and numerical exercises, the conditions within which a transformation occurs spontaneously
• communication skills: the goal is to make the student, through participatory lessons, able to communicate scientific topics with accuracy and rigor 
• learning skills: the goal is to make the student, through examples and participatory lessons, able to apply the concepts learned during the course to the understanding of phenomena and processes of specific interest

The course will consist of 5 credits provided through lectures also in participatory mode. There are also 3 credits of numerical exercises aimed at better understanding the practical application of thermodynamic laws and quantities.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Chemistry prerequisites:

Stoichiometry calculations, ionic and redox equilibria, and basic knowledge of the various aggregation states of the matter

Physics prerequisites:

Knowledge of the fundamental physical quantities and their units, fundamental laws of the mechanics and dynamics, understanding of the concept of work and energy

Prerequisiti di matematica:

Knowledge of the study of a function, knowledge of differential calculus and of the derivatives of the elementary functions

Aggregation states of matter.

Macroscopic world, microscopic world and property-structure correlations. Solid state, liquid, gaseous. Driving forces in the assembly of condensed phases. Morse curve, potentials of interaction.

Properties of gases.

State variables of gas, The zero law of Thermodynamics, Equation of state of ideal gases; the kinetic model of gases, ideal gas mixtures, deviations from ideality and equations of state for real gases. The compressibility factor; the principle of corresponding states 

The first law of Thermodynamics.

Heat, work and energy conservation. Expansion and compression work. Concept of reversibility and spontaneous phenomena. Path functions. State and differential functions.Heat, work and energy conservation. Expansion and compression work. Concept of reversibility and spontaneous phenomena. Path functions. State and differential functions.

Thermology.

Thermal capacity and specific heats. Internal energy and temperature; enthalpy and temperature: relations between the specific heats. Isothermal and adiabatic processes - reversible or irreversible. 

Thermochemistry.

Enthalpy of reaction and Hess's law; Standard enthalpy, relations between ΔH and ΔU; ΔH as a function of temperature. Born-Haber cycle. Examples of reaction enthalpies. Kirchoff's law

The second principle of thermodynamics.

Il secondo principio. Efficienza delle macchine termiche e ciclo di Carnot. Il refrigerante di Carnot. Definizione dell'entropia. Entropia ed integrale ciclico. Prova generale per l'integrale ciclico dell'entropia. La diseguaglianza di Clausius. Proprietà dei differenziali esatti. Entropia in funzione di T,V e T,P. Variazioni di stato ed entropia.

Entropy and probability.

Entropy, probability of the state and spontaneity. Probability, thermodynamic probability and entropy. General form for the thermodynamic probability. The distribution of energy.

The third law.

Entropy variations for the ideal gas. The standard state for ideal gas. The third law and standard entropy. Entropy variations for a chemical reaction and temperature dependence. Third principle, entropy of mixing. 

Spontaneity and balance.

Entropy of the system, entropy of the environment and conditions of spontaneity and balance. The function of Helmotz and the Gibbs function. The fundamental equation of thermodynamics. Gibbs function e variations of T, P and composition. The chemical potential. Chemical potential in an ideal gas and in real gases. The fugacity

Status changes.

Chemical potential and principle of phase stability. First-order phase transitions. Transitions of second order stage. State diagram of water. The surface, the surface tension and the capillarity.

The blends and the activity.

Molar volume in mixtures. The Gibbs-Duhem law. Processes of mixing and spontaneity. Solutions of non-volatile solutes; colligative properties: ebullioscopy, cryoscopy and osmosis. Mixtures of volatile liquids: the concept of activity. The limit laws of Raoult and Henry. The limit equations of chemistry.

The chemical equilibrium.

The criterion of spontaneity and equilibrium for a chemical reaction. Equilibrium, the equilibrium constant e the influence of catalysts, inert substances, temperature and pressure.

Electrochemistry.

Activity of ions in solution and Debye-Huckel law. The concept of ionic strength . Form of the limiting laws of chemistry in dilute solution. Electrochemical potential. Electrodes e most common electrochemical cells. Standard electrochemical potentials and electrochemical series. The equation of Nernst.

The phase equilibria.

Free energy of mixing and phase diagrams. Phase rule, lever rule and diagrams of phase. One component systems. Two-component systems. Two-component systems with one or more products. Three component systems. Influence of ionic strength.

Recommended texts for studying:

•  P. Atkins, J. De Paula, J. Keeler : Physical Chemistry (Oxford)
•  G.W. Castellan: Physical Chemistry (Addison-Wesley Pu. Co.)
•  L.K. Nash: Elements of Chemical Thermodynamics (Dover)

Recommended texts for excercises:

• Physical Chemistry from a Different Angle Workbook (Springer)

The written examination will be evaluated according to:

• the correctness of numerical results
• the explicitness of the applied mathematical procedures and approximations
• the accuracy of the use of the proper units of measurement of the different quantities and constants

The oral examination will be evaluated according to:

• the accuracy of the definitions and demonstrations
• the in-depth study of the subjects
• the ability to link different phenomena and to generalize their physico-chemical interpretation

The exam can also be performed online, should the conditions require it.

Sample questions:

1) Description of the water state diagram and the corresponding water behaviour

2)How do intermolecular interactions affect the behaviour of a gas?

3) Discussion and comparison between the thermodynamic and statistical definition of entropy. 

Sample exercises:

1) At 373,15 K and 101325 Pa pure water requires 2259,0 kJ/kg  to evolve from the liquid to the vapour state. Calculate the universe entropy variation when:

a) A mole of water evaporates very slowly in contact with a body whose temperature is infinitesimally higher than 373,15 K;

b) A mole of water evaporates quicklyin contact with a body whose temperature is 400 K.

In both cases consider that the vapour temperature is 373,15 K, its pressure is 101325 Pa and that the value of latent heat of vaporization is the same. 

2) 0,5 moles of nitrogen expand at a constant temperature of  1000 K from 1.981,89 cm3 to 10,00 L.

In the assumption of ideal gas behaviour, calculate:

a) the work on the system, the heat exchanged with the environment and the internal energy variation of the system in the case of a reversible expansion.;

b) the work on the system, the heat exchanged with the environment and the internal energy variation of the system in the case of a irreversible expansion against an external pressure equal to the gas pressure at the end of the expansion

Comment any differences between results in a) and b).

3) Considering the equilibrium:

H2(g) + CO2(g)  CO(g) +H2O(g)

it is known that

DrG° (cal/gmol)  =  10100  -  0,541T - 1,81TlnT + 4,4510-3T2 - 6,810-7T3  .

In the assumption of ideal gas behaviour, calculate the molar equilibrium composition at 986°C and 1 atm for a mixture having  10,1 %  vol of CO2 e 89,9 % vol of  H2.