PHYSICAL CHEMISTRY IN BRIEF Prof. Ing. Anatol Malijevsk´y, CSc., et al. (September 30, 2005) Institute of Chemical Technology, Prague Faculty of Chemical Engineering Annotation The Physical Chemistry In Brief offers a digest of all major formulas, terms and definitions needed for an understanding of the subject. They are illustrated by schematic figures, simple worked-out examples, and a short accompanying text. The concept of the book makes it different from common university or physical chemistry textbooks. In terms of contents, the Physical Chemistry In Brief embraces the fundamental course in physical chemistry as taught at the Institute of Chemical Technology, Prague, i.e. the state behaviour of gases, liquids, solid substances and their mixtures, the fundamentals of chemical thermodynamics, phase equilibrium, chemical equilibrium, the fundamentals of electrochemistry, chemical kinetics and the kinetics of transport processes, colloid chemistry, and partly also the structure of substances and spectra. The reader is assumed to have a reasonable knowledge of mathematics at the level of secondary school, and of the fundamentals of mathematics as taught at the university level. 3 Authors Prof. Ing. Josef P. Nov´ak, CSc. Prof. Ing. Stanislav Lab´ık,CSc. Ing. Ivona Malijevsk´a,CSc. 4 Introduction Dear students, Physical Chemistry is generally considered to be a difficult subject. We thought long and hard about ways to make its study easier, and this text is the result of our endeavors. The book provides accurate definitions of terms, definitions of major quantities, and a number of relations including specification of the conditions under which they are valid. It also contains a number of schematic figures and examples that clarify the accompanying text. The reader will not find any derivations in this book, although frequent references are made to the initial formulas from which the respective relations are obtained. In terms of contents, we followed the syllabi of “Physical Chemistry I” and “Physical Chem- istry II” as taught at the Institute of Chemical Technology (ICT), Prague up to 2005. However the extent of this work is a little broader as our objective was to cover all the major fields of Physical Chemistry. This publication is not intended to substitute for any textbooks or books of examples. Yet we believe that it will prove useful during revision lessons leading up to an exam in Physical Chemistry or prior to the final (state) examination, as well as during postgraduate studies. Even experts in Physical Chemistry and related fields may find this work to be useful as a reference. Physical Chemistry In Brief has two predecessors, “Breviary of Physical Chemistry I” and “Breviary of Physical Chemistry II”. Since the first issue in 1993, the texts have been revised and re-published many times, always selling out. Over the course of time we have thus striven to eliminate both factual and formal errors, as well as to review and rewrite the less accessible passages pointed out to us by both students and colleagues in the Department of Physical Chemistry. Finally, as the number of foreign students coming to study at our institute continues to grow, we decided to give them a proven tool written in the English language. This text is the result of these efforts. A number of changes have been made to the text and the contents have been partially extended. We will be grateful to any reader able to detect and inform us of any errors in our work. Finally, the authors would like to express their thanks to Mrs. Flemrov´a for her substantial investment in translating this text. CONTENTS [CONTENTS] 5 Contents 1 Basic terms 24 1.1 Thermodynamic system ............................... 24 1.1.1 Isolated system ................................ 24 1.1.2 Closed system ................................ 25 1.1.3 Open system ................................. 25 1.1.4 Phase, homogeneous and heterogeneous systems .............. 25 1.2 Energy ......................................... 27 1.2.1 Heat ...................................... 27 1.2.2 Work ...................................... 27 1.3 Thermodynamic quantities .............................. 28 1.3.1 Intensive and extensive thermodynamic quantities ............. 28 1.4 The state of a system and its changes ........................ 29 1.4.1 The state of thermodynamic equilibrium .................. 29 1.4.2 System’s transition to the state of equilibrium ............... 30 1.4.3 Thermodynamic process ........................... 30 1.4.4 Reversible and irreversible processes ..................... 31 1.4.5 Processes at a constant quantity ....................... 31 1.4.6 Cyclic process ................................. 32 1.5 Some basic and derived quantities .......................... 34 1.5.1 Mass m .................................... 34 1.5.2 Amount of substance n ............................ 34 1.5.3 Molar mass M ................................ 34 CONTENTS [CONTENTS] 6 1.5.4 Absolute temperature T ........................... 34 1.5.5 Pressure p ................................... 34 1.5.6 Volume V ................................... 35 1.6 Pure substance and mixture ............................. 36 th 1.6.1 Mole fraction of the i component xi .................... 36 1.6.2 Mass fraction wi ............................... 37 1.6.3 Volume fraction φi .............................. 38 1.6.4 Amount-of-substance concentration ci .................... 40 1.6.5 Molality mi .................................. 40 2 State behaviour 42 2.1 Major terms, quantities and symbols ........................ 43 2.1.1 Molar volume Vm and amount-of-substance (or amount) density c .... 43 2.1.2 Specific volume v and density ρ ....................... 43 2.1.3 Compressibility factor z ........................... 44 2.1.4 Critical point ................................. 44 2.1.5 Reduced quantities .............................. 45 2.1.6 Coefficient of thermal expansion αp ..................... 45 2.1.7 Coefficient of isothermal compressibility βT ................. 47 2.1.8 Partial pressure pi .............................. 47 2.2 Equations of state ................................... 48 2.2.1 Concept of the equation of state ....................... 48 2.2.2 Equation of state of an ideal gas ...................... 48 2.2.3 Virial expansion ................................ 49 2.2.4 Boyle temperature .............................. 49 2.2.5 Pressure virial expansion ........................... 50 2.2.6 Van der Waals equation of state ....................... 51 2.2.7 Redlich-Kwong equation of state ...................... 52 2.2.8 Benedict, Webb and Rubin equation of state ................ 53 2.2.9 Theorem of corresponding states ...................... 53 2.2.10 Application of equations of state ...................... 54 2.3 State behaviour of liquids and solids ........................ 56 CONTENTS [CONTENTS] 7 2.3.1 Description of state behaviour using the coefficients of thermal expansion αp and isothermal compressibility βT . .................... 56 2.3.2 Rackett equation of state ........................... 56 2.3.3 Solids ..................................... 57 2.4 State behaviour of mixtures ............................. 58 2.4.1 Dalton’s law .................................. 58 2.4.2 Amagat’s law ................................. 59 2.4.3 Ideal mixture ................................. 60 2.4.4 Pseudocritical quantities ........................... 60 2.4.5 Equations of state for mixtures ....................... 61 2.4.6 Liquid and solid mixtures .......................... 62 3 Fundamentals of thermodynamics 63 3.1 Basic postulates .................................... 63 3.1.1 The zeroth law of thermodynamics ..................... 63 3.1.2 The first law of thermodynamics ...................... 64 3.1.3 Second law of thermodynamics ....................... 65 3.1.4 The third law of thermodynamics ...................... 66 3.1.4.1 Impossibility to attain a temperature of 0 K ........... 67 3.2 Definition of fundamental thermodynamic quantities ............... 68 3.2.1 Enthalpy .................................... 68 3.2.2 Helmholtz energy ............................... 69 3.2.3 Gibbs energy ................................. 70 3.2.4 Heat capacities ................................ 72 3.2.5 Molar thermodynamic functions ....................... 74 3.2.6 Fugacity .................................... 74 3.2.7 Fugacity coefficient .............................. 75 3.2.8 Absolute and relative thermodynamic quantities ............. 75 3.3 Some properties of the total differential ....................... 77 3.3.1 Total differential ............................... 77 3.3.2 Total differential and state functions .................... 79 3.3.3 Total differential of the product and ratio of two functions ........ 81 3.3.4 Integration of the total differential ..................... 81 CONTENTS [CONTENTS] 8 3.4 Combined formulations of the first and second laws of thermodynamics ..... 83 3.4.1 Gibbs equations ................................ 83 3.4.2 Derivatives of U, H, F , and G with respect to natural variables ..... 83 3.4.3 Maxwell relations ............................... 84 3.4.4 Total differential of entropy as a function of T , V and T , p ........ 85 3.4.5 Conversion from natural variables to variables T , V or T , p ........ 85 3.4.6 Conditions of thermodynamic equilibrium ................. 87 3.5 Changes of thermodynamic quantities ........................ 90 3.5.1 Heat capacities ................................ 90 3.5.1.1 Temperature dependence