University of Limpopo
Faculty of Sciences & Agriculture
School of Physical and Mineral Sciences
Department of Chemistry
SCHA031
Physical Chemistry 3
Study Guide for SCHA031
16 Credits
First Semester
Prepared by Prof T Magadzu, University of Limpopo
Content evaluated by Dr LE Macevele, University of Limpopo
,TABLE OF CONTENT
Study Guide for SCHA031 ....................................................................................................................... 1
MODULE INFORMATION ......................................................................................................................... 6
Chemical kinetics .................................................................................................................................... 9
1. Introduction ........................................................................................................................................ 9
1.1 Application of the techniques ....................................................................................................... 9
1.1.1 Quenching methods ............................................................................................................... 9
1.2 The rates of chemical reaction...................................................................................................... 9
1.2.1 Rate laws and rate constants ............................................................................................... 10
1.2.2 Reaction order ..................................................................................................................... 10
1.2.3 The determination of the rate law....................................................................................... 11
1.3 Integrated rate laws .................................................................................................................... 13
1.3.1 First-order reactions ............................................................................................................ 13
1.3.2 Half-lives and time constants ............................................................................................... 14
1.3.3 Second-order reactions ........................................................................................................ 15
1.4 Reactions approaching equilibrium ............................................................................................ 18
1.4.1 First-order reactions close to equilibrium ........................................................................... 18
1.4.2 The temperature dependence of reaction rates ................................................................. 19
1.5 Exercise ....................................................................................................................................... 21
Catalysis ................................................................................................................................................ 22
2. Introduction ...................................................................................................................................... 22
2.1 Heterogeneous Catalysis............................................................................................................. 22
2.2 Molecular motion in gases .......................................................................................................... 23
2.2.1 The kinetic model of gases ................................................................................................... 23
2.2.2 The collision frequency ........................................................................................................ 24
2.2.3 The mean free path.............................................................................................................. 24
2.2.4 Collisions with walls and surfaces ........................................................................................ 26
2.3 The growth and structure of solid surfaces ................................................................................ 27
2.3.1 Flat surface of solid .............................................................................................................. 27
2.3.2 Kinds of defects .................................................................................................................... 28
2.3.3 Atoms on a surface (top layer)............................................................................................. 28
, 2.3.4 The extent of adsorption ..................................................................................................... 29
2.4 The importance of pore structure and surface area................................................................... 35
2.4.1 Pore Structure ...................................................................................................................... 36
2.4.2 Experimental Methods of Estimating Surface Areas. .......................................................... 36
2.5 Exercise ....................................................................................................................................... 40
Quantum Theory: Introduction and Principles ..................................................................................... 41
3.1 Classical mechanics ..................................................................................................................... 41
3.2 Quantum mechanics ................................................................................................................... 41
3.3 The origins of quantum mechanics ............................................................................................. 41
3.4 The failures of classical physics ................................................................................................... 43
3.4.1 Blackbody radiation ............................................................................................................. 43
3.4.2 Heat capacities ..................................................................................................................... 48
3.4.3 Atomic and molecular spectra ............................................................................................. 49
3.5 Wave-particle duality .................................................................................................................. 49
3.5.1 The particle character of electromagnetic radiation ........................................................... 50
3.5.2 The wave character of particles ........................................................................................... 52
3.6 The dynamics of microscopic systems ........................................................................................ 53
3.6.1 The Born interpretation of the wavefunction...................................................................... 54
3.6.2 Normalization....................................................................................................................... 55
3.6.3 Quantization......................................................................................................................... 56
3.6.4 Operators, eigenvalues, and eigenfunctions ....................................................................... 56
3.6.5 The uncertainty principle ..................................................................................................... 57
3.6.6 The postulates of quantum mechanics ................................................................................ 58
3.7 Exercise ....................................................................................................................................... 59
Quantum theory: Techniques and Applications ................................................................................... 61
4.1 Translational motion ................................................................................................................... 61
4.1.1 A particle in a box................................................................................................................. 61
4.2 Motion in two and more dimensions ......................................................................................... 66
4.2.1 Separation of variables ........................................................................................................ 66
4.2.2 Degeneracy .......................................................................................................................... 67
4.3 Tunnelling.................................................................................................................................... 67
4.4 Vibrational motion ...................................................................................................................... 69
, 4.4.1 The energy levels ................................................................................................................. 69
4.4.2 The wavefunctions ............................................................................................................... 71
4.5 Rotational motion ....................................................................................................................... 72
4.5.1 Rotation in two dimensions: a particle on a ring ................................................................. 72
4.5.2 Rotation in three dimensions: the particle on a sphere ...................................................... 73
4.6 Exercise ....................................................................................................................................... 76
Solids and X-ray diffraction ................................................................................................................... 77
5.1 Structures of Solids ..................................................................................................................... 77
5.1.1 Lattice and Unit cells ............................................................................................................ 77
5.2 X-ray diffraction .......................................................................................................................... 79
5.2.1 The Basics ............................................................................................................................. 79
5.2.2 The Interplanar Spacing, d(hkl)............................................................................................... 80
5.2.3 The investigation of Structure ............................................................................................. 81
5.2.4 Indexing the Reflections....................................................................................................... 83
5.2.5 Intensity of X-ray Diffraction patterns ................................................................................. 85
5.3 Exercise ....................................................................................................................................... 86
Atomic spectra and atomic structure ................................................................................................... 87
6.1 The structure and spectra of hydrogenic atoms ......................................................................... 87
6.1.1 Radial wave equation ........................................................................................................... 88
6.2 Atomic orbitals and their energies.............................................................................................. 90
6.2.1 The energy levels ................................................................................................................. 90
6.2.2 Ionization energies ............................................................................................................... 91
6.2.3 Shells and subshells.............................................................................................................. 93
6.2.4 Atomic orbitals ..................................................................................................................... 93
6.2.5 Boundary surface ................................................................................................................. 94
6.2.6 Radial distribution functions ................................................................................................ 94
6.2.7 Spectroscopic transition and selection rules ....................................................................... 97
6.3 Exercise ....................................................................................................................................... 99
Molecular spectroscopy: Rotational and Vibrational Spectra ............................................................ 100
7. Introduction .................................................................................................................................... 100
7.1 General features of spectroscopy ............................................................................................. 100
Faculty of Sciences & Agriculture
School of Physical and Mineral Sciences
Department of Chemistry
SCHA031
Physical Chemistry 3
Study Guide for SCHA031
16 Credits
First Semester
Prepared by Prof T Magadzu, University of Limpopo
Content evaluated by Dr LE Macevele, University of Limpopo
,TABLE OF CONTENT
Study Guide for SCHA031 ....................................................................................................................... 1
MODULE INFORMATION ......................................................................................................................... 6
Chemical kinetics .................................................................................................................................... 9
1. Introduction ........................................................................................................................................ 9
1.1 Application of the techniques ....................................................................................................... 9
1.1.1 Quenching methods ............................................................................................................... 9
1.2 The rates of chemical reaction...................................................................................................... 9
1.2.1 Rate laws and rate constants ............................................................................................... 10
1.2.2 Reaction order ..................................................................................................................... 10
1.2.3 The determination of the rate law....................................................................................... 11
1.3 Integrated rate laws .................................................................................................................... 13
1.3.1 First-order reactions ............................................................................................................ 13
1.3.2 Half-lives and time constants ............................................................................................... 14
1.3.3 Second-order reactions ........................................................................................................ 15
1.4 Reactions approaching equilibrium ............................................................................................ 18
1.4.1 First-order reactions close to equilibrium ........................................................................... 18
1.4.2 The temperature dependence of reaction rates ................................................................. 19
1.5 Exercise ....................................................................................................................................... 21
Catalysis ................................................................................................................................................ 22
2. Introduction ...................................................................................................................................... 22
2.1 Heterogeneous Catalysis............................................................................................................. 22
2.2 Molecular motion in gases .......................................................................................................... 23
2.2.1 The kinetic model of gases ................................................................................................... 23
2.2.2 The collision frequency ........................................................................................................ 24
2.2.3 The mean free path.............................................................................................................. 24
2.2.4 Collisions with walls and surfaces ........................................................................................ 26
2.3 The growth and structure of solid surfaces ................................................................................ 27
2.3.1 Flat surface of solid .............................................................................................................. 27
2.3.2 Kinds of defects .................................................................................................................... 28
2.3.3 Atoms on a surface (top layer)............................................................................................. 28
, 2.3.4 The extent of adsorption ..................................................................................................... 29
2.4 The importance of pore structure and surface area................................................................... 35
2.4.1 Pore Structure ...................................................................................................................... 36
2.4.2 Experimental Methods of Estimating Surface Areas. .......................................................... 36
2.5 Exercise ....................................................................................................................................... 40
Quantum Theory: Introduction and Principles ..................................................................................... 41
3.1 Classical mechanics ..................................................................................................................... 41
3.2 Quantum mechanics ................................................................................................................... 41
3.3 The origins of quantum mechanics ............................................................................................. 41
3.4 The failures of classical physics ................................................................................................... 43
3.4.1 Blackbody radiation ............................................................................................................. 43
3.4.2 Heat capacities ..................................................................................................................... 48
3.4.3 Atomic and molecular spectra ............................................................................................. 49
3.5 Wave-particle duality .................................................................................................................. 49
3.5.1 The particle character of electromagnetic radiation ........................................................... 50
3.5.2 The wave character of particles ........................................................................................... 52
3.6 The dynamics of microscopic systems ........................................................................................ 53
3.6.1 The Born interpretation of the wavefunction...................................................................... 54
3.6.2 Normalization....................................................................................................................... 55
3.6.3 Quantization......................................................................................................................... 56
3.6.4 Operators, eigenvalues, and eigenfunctions ....................................................................... 56
3.6.5 The uncertainty principle ..................................................................................................... 57
3.6.6 The postulates of quantum mechanics ................................................................................ 58
3.7 Exercise ....................................................................................................................................... 59
Quantum theory: Techniques and Applications ................................................................................... 61
4.1 Translational motion ................................................................................................................... 61
4.1.1 A particle in a box................................................................................................................. 61
4.2 Motion in two and more dimensions ......................................................................................... 66
4.2.1 Separation of variables ........................................................................................................ 66
4.2.2 Degeneracy .......................................................................................................................... 67
4.3 Tunnelling.................................................................................................................................... 67
4.4 Vibrational motion ...................................................................................................................... 69
, 4.4.1 The energy levels ................................................................................................................. 69
4.4.2 The wavefunctions ............................................................................................................... 71
4.5 Rotational motion ....................................................................................................................... 72
4.5.1 Rotation in two dimensions: a particle on a ring ................................................................. 72
4.5.2 Rotation in three dimensions: the particle on a sphere ...................................................... 73
4.6 Exercise ....................................................................................................................................... 76
Solids and X-ray diffraction ................................................................................................................... 77
5.1 Structures of Solids ..................................................................................................................... 77
5.1.1 Lattice and Unit cells ............................................................................................................ 77
5.2 X-ray diffraction .......................................................................................................................... 79
5.2.1 The Basics ............................................................................................................................. 79
5.2.2 The Interplanar Spacing, d(hkl)............................................................................................... 80
5.2.3 The investigation of Structure ............................................................................................. 81
5.2.4 Indexing the Reflections....................................................................................................... 83
5.2.5 Intensity of X-ray Diffraction patterns ................................................................................. 85
5.3 Exercise ....................................................................................................................................... 86
Atomic spectra and atomic structure ................................................................................................... 87
6.1 The structure and spectra of hydrogenic atoms ......................................................................... 87
6.1.1 Radial wave equation ........................................................................................................... 88
6.2 Atomic orbitals and their energies.............................................................................................. 90
6.2.1 The energy levels ................................................................................................................. 90
6.2.2 Ionization energies ............................................................................................................... 91
6.2.3 Shells and subshells.............................................................................................................. 93
6.2.4 Atomic orbitals ..................................................................................................................... 93
6.2.5 Boundary surface ................................................................................................................. 94
6.2.6 Radial distribution functions ................................................................................................ 94
6.2.7 Spectroscopic transition and selection rules ....................................................................... 97
6.3 Exercise ....................................................................................................................................... 99
Molecular spectroscopy: Rotational and Vibrational Spectra ............................................................ 100
7. Introduction .................................................................................................................................... 100
7.1 General features of spectroscopy ............................................................................................. 100
