Warszawa, 28 May 2012
Questions for the examination after the second year of the International Ph.D. in Chemistry
Studies at the Institute of Physical Chemistry of the Polish Academy of Sciences
The questions, with minor exceptions, are based on the book by P.W. Atkins: “Physical Chemistry"
Canon: Thermodynamics and termochemistry
1. Basic concepts of thermodynamics.
System, state of thermodynamic equilibrium, process, state function, extensive and
intensive parameters.
2. First law of thermodynamics and its implications.
State function, internal energy, work, heat, enthalpy, heat capacity at constant volume and
at constant pressure.
3. Second law of thermodynamics and the direction of spontaneous processes.
Thermodynamic definition of entropy, Carnot cycle, Carnot efficiency of a heat engine.
4. Free energy and free enthalpy.
Relation to the second law of thermodynamics, maximum work, chemical potential of a
pure substance.
5. Free enthalpy of a mixture and the fundamental equation of chemical thermodynamics.
Chemical potential of a substance in a mixture, Gibbs-Duhem equation.
6. Model of a perfect gas.
Microscopic justification, state equation, thermodynamic temperature scale, Dalton’s
law, internal energy.
7. Deviations of real gases from the perfect gas model.
Compression factor, virial equation of state, Boyle temperature, van der Waals equation
of state.
8. Classification of phase transitions.
Condition of phase equilibrium, Ehrenfest first- and second-order phase transitions,
-transitions, slope of the phase boundary for the first-order transitions.
9. The phase rule and examples of a phase diagram for pure substances (e.g., water or carbon
dioxide).
Boundaries of phase equilibrium, boiling, melting, sublimation, critical point, triple point.
10. Clausius-Clapeyron equation.
11. Canonical ensemble and its relation to thermodynamics.
Concept of statistical ensemble, canonical distribution, canonical partition function and
its relation to the free energy, canonical partition function for a system of non-interacting
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molecules.
12. Third law of thermodynamics.
Nernst heat theorem, statistical definition of entropy, residual entropy.
13. Boltzmann distribution and the statistical definition of entropy.
Thermodynamic probability, molecular partition function
14. The equipartition theorem, its validity range and examples of applications
Degree of freedom, modes of atomic and molecular motions, internal energy of a perfect
gas, Dulong and Petit’s law.
15. Laws of thermochemistry and their applications.
standard reaction enthalpy, standard enthalpy of formation, Hess’s and Kirchhoff’s laws.
16. Joule – Thomson effect.
Joule-Thomson coefficient, inversion temperature, gas liquefaction.
17. Surface tension.
Laplace equation, capillary phenomena, contact angle.
18. Ideal and ideal-dilute solutions.
Chemical potential of a component of ideal solution, free enthalpy and entropy of mixing,
Raoult’s law, Henry's law.
19. Colligative properties of diluted solutions.
Elevation of boiling point, depression of freezing point, osmotic pressure.
20. Liquid-vapour equilibrium in two-component mixtures.
Ideal and azeotropic mixtures, liquid and vapour phase composition, the lever rule
distillation of mixtures.
21. Phase diagrams for mixtures of two partially miscible liquids.
Equilibrium between two liquid phases, critical solubility temperatures, azeotropeforming mixtures.
22. Liquid-solid equilibrium in two-component mixtures.
Eutectics, freezing of a mixture of eutectic composition, zone refining.
23. The condition for chemical equilibrium.
Free reaction enthalpy, endergonic and exergonic reactions, reaction quotient,
equilibrium constant of a reaction.
24. Influence of external conditions upon chemical equilibrium.
Le Chatelier’s principle, van't Hoff equation.
25. Average molecular energies and heat capacities for a system of non-interacting particles.
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Contributions of translational, rotational and vibrational motions, active and inactive
degrees of freedom, comparison with the equipartition theorem.
Canon: Quantum chemistry and spectroscopy
26. Experimental foundations of quantum mechanics.
27. Dual character of radiation. De Broglie hypothesis.
28. Schrödinger equation. Wave function: definition and interpretation.
29. The particle in a box. Potential barrier. Tunnel effect.
30. Classical and quantum harmonic oscillator.
31. Quantum rigid rotator.
32. Heisenberg uncertainty principle.
33. Description of the state of the electron in the hydrogen atom.
34. Spin of the electron. Stern-Gerlach experiment.
35. Variational principle and perturbation method in quantum chemistry.
36. Basic properties of the wave function of a multielectron system and the interpretation of
the wave function.
37. Atomic and molecular orbitals. Pauli principle.
38. Hund rules.
39. Angular momentum and the magnetic moment of an electron. Zeeman effect.
40. Chemical bond in diatomic molecules.
41. Basic concepts of group theory and its applications in physics and chemistry.
42. Molecular symmetry and chirality.
43. Einstein equation. Absorption, spontaneous and stimulated emission. Working principle
of a laser. Examples of applications of lasers.
44. Selection rules in spectroscopy. Transition moment.
45. Vibrational and rotational energy levels. Intensities of the corresponding spectroscopic
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transitions.
46. Scattering of radiation. Raman spectra.
47. Comparison of IR and Raman spectra.
48. Electronically excited states. Jabłoński diagram. Radiative and radiationless transitions.
49. Franck-Condon principle.
50. Nuclear magnetic resonance, electron paramagnetic resonance, and their applications in
chemistry.
51. Comparison of classical and Fourier spectroscopic techniques.
Canon: Electrochemistry
52. Models of electrical double layer at the electrode/electrolyte interface.
53. Basic electrodes in electrochemistry (properties, laboratory and practical applications).
54. Nernst equation (equilibrium potential, standard potential, examples of applications).
55. Rates of electrode processes (controlling factors, electrode overpotential and its types,
limiting current density).
56. Butler-Volmer equation – charge transfer rate (exchange current density, cases of low and
high overpotential (Tafel equation)).
57. Galvanic versus electrolytic cells. Examples and applications in research and practice.
58. Electrolysis of water and classical hydrogen fuel cell.
59. Basics of electrochemical corrosion of metals (conditions for the occurrence, mechanism,
thermodynamic and kinetic aspects, prevention).
60. Ion mobility in strong electrolyte solutions. Debye-Hückel-Onsager theory.
61. Mean activity coefficient for ions in solution and its determination using Debye-Hückel
limiting law.
62. What are concentration cells and which systems occurring in nature can be considered
their counterparts?
63. Electrochemical versus chemical reactions. Physico-chemical sources of the generation of
electrode potentials.
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64. Concept of pH and methods of its measurement.
Canon: Structure of matter
65. Describe anomalous properties of water.
66. Electrical conductivity of metals, semiconductors and superconductors.
Band structure in metals, semiconductors and insulators. Fermi level.
67. Determination of crystal and molecular structure using X-ray and neutron diffraction.
68. Classification of crystal systems. Miller indices.
69. Close-packed structures of atoms in space lattice.
70. Dipole moment of a molecule. How can it be measured?
71. Hydrogen bonding.
72. Structure of proteins and methods of its determination. Electrophoresis.
73. Electric properties of molecules. Debye and Clausius-Mossotti equations.
74. Types of intermolecular interactions.
75. Magnetic properties of molecules. Diamagnetism, paramagnetism, and ferromagnetism.
76. Allotropic forms of carbon. Properties and structure.
77. Colloids. Zeta-potential.
78. Surfactants and their structures.
Canon: Chemical reaction kinetics
79. Basic concepts and relations in chemical kinetics. Define: extent of conversion, rate and
order of a chemical reaction. Determination of the rate law.
80. The temperature dependence of reaction rate. Activation energy.
81. The phenomenon of catalysis and the role of the transition state in homogeneous and
heterogeneous catalysis.
82. Autocatalytic reactions. Definition, reaction rate law, examples.
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83. Chain reactions. Mechanism of reaction and examples.
84. Basic ideas of the collision theory in chemical kinetics.
85. Reaction rate in terms of the transition state theory.
86. Diffusion- and activation-controlled reactions.
87. Examples of catalytic reactions used in industry.
88. Comparison of STM and AFM microscopy.
89. Physical and chemical adsorption. Adsorption isotherms.
90. Which physicochemical processes make the basis for chromatographic separation?
91. Relation between chemisorption and the rate of reaction catalyzed by a solid surface.
92. Heterogeneous catalysis. Basic reaction mechanisms.
93. Steady-state approximation in chemical kinetics (example of application).
94. Describe the kinetics of enzymatic reactions (Michaelis-Menten mechanism).
95. Mass transport phenomena. Laws of diffusion.
96. Heat conductivity.
97. Viscosity.
98. Growth and structure of solid surfaces.
99. Kinetics of polymerization reactions.
100. Photochemical reactions.
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