CHEMICAL STATISTICAL THERMODYNAMICS
Academic year and teacher
If you can't find the course description that you're looking for in the above list,
please see the following instructions >>
- Versione italiana
- Academic year
- 2015/2016
- Teacher
- CELESTINO ANGELI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- CHIM/02
Training objectives
- The course is the completion of the learning path concerning the properties of matter begun during Bachelor's Degree, where the description of the macroscopic behaviour of matter has been firstly treated (Physical Chemistry I with exercises) and the laws governing the the atomic and molecular behaviour have been described in the frame of quantum mechanics (Physical Chemistry II with exercises).
The aim of the course is to provide the conceptual tools allowing to understand how the microscopic properties of matter influence its macroscopic behaviour and therefore to build a connection between the concepts treated in the two preceding courses.
Yhanks to the concepts presented in this course the student acquires the ability to understant the microscopic factors controlling the macroscopic behavior of matter, in particular, for what concerns the most relevant quantities of classic thermodynamics (pressure, internal energy, entropy, etc.) and of the chemical reactions (equilibrium and kinetics constants). Prerequisites
- The complete knowledge of the subjects of classical thermodynamics (Physical Chemistry I with exercises) and atomic and molecular quantum mechanics (Physical Chemistry II with exercises) are required.
Moreover, the concepts acquired in the mathematical courses of the Bachelor's Degree are also required. Course programme
- The course is organized in 56 hours of lectures, subdivided in frontal lectures and exercises, where an educational path is developed, which, starting from the knowledge of the microscopic properties of mater, leads to the identification of the fundamental aspects of its macroscopic behaviour.
To this aim, the basis hypotheses (Gibbs' postulate, ergodic hypothesis, etc.) are defined together with the concepts of ensemble (micro-canonical, canonical, and grand-canonical), of configuration, and of statistical weight. The Boltzmann distribution is obtained and the canonical and molecular partition functions are defined.
These concepts are used to compute the partition function for the traslational motion, which is then linked to some macroscopic quantities, such as the internal energy and the entropy.
The course proceeds with a detailed treatment of the Einstein model of a solid. After the description of a gas of atoms and a short summary of the Born-Oppenheimer approximation, the gas of diatomic molecules is treated in details (traslation, rotation, and vibration) and the extension to the case of a gas of poliatomic molecules is sketched out.
These results are used to face the key concept of the chemical equilibrium from the statistical point of view, explicitly considering a few simple reactions in gas phase (dissociation, isomeric, ionization, isotopic exchange and diatomic reaction equilibrium), for which the equilibrium constant is computed and compared with the experimental value.
The description of the chemical kinetic processes is then considered, with a particular attention to the activated complex theory.
Once the distribution of the gran canonical ensemble is deduced in details and the chemical potential has been introduced, the quantum statistics are treated (Fermi-Dirac and Bose-Einstein) and explicitly derived.
In the last part of the course the fully classic approach is presented and used to obtain the Maxwell-Boltzmann distribution of speed in a gas and to derive the proof of the energy equipartition principle.
This approach is used to treat the problem of the real gasses and to compute the second virial coefficient.
The course ends with a few lectures dedicated to the approximated treatment of the dense fluids (liquids) introducing the concept of the radial correlation function. Didactic methods
- The course is based on theoretical frontal lectures with a periodic alternation of lectures with exercises carried out at the blackboard by the teacher and by the students.
Learning assessment procedures
- The learning check is based on an oral exam in which the subjects of the course are discussed and commented. In order to access the oral exam, it is required to have pass in advance a written exam (even in a different session) based on one or two open questions and on a few numerical exercises.
The written exam can be skipped if the student has passed the two partial written examinations which occur during the course (one at the middle and one at the end). Reference texts
- - P. Atkins, J. De Paula; "Chimica Fisica", Zanichelli.
- Terrell L. Hill; "An introduction to statistical thermodynamics", Courier Dover Publications
