Introduction to Aqueous Electrolyte Solutions

Margaret Robson Wright is the author of An Introduction to Aqueous Electrolyte Solutions, published by Wiley.

• Preface xixPreliminary Chapter Guidance to Student xxiiiList of symbols xxv1 Concepts and Ideas: Setting the Stage 11.1 Electrolyte solutions – what are they? 21.2 Ions – simple charged particles or not? 41.3 The solvent: structureless or not? 71.4 The medium: its structure and the effect of ions on this structure 81.5 How can these ideas help in understanding what might happen when an ion is put into a solvent? 91.6 Electrostriction 111.7 Ideal and non-ideal solutions – what are they? 111.8 The ideal electrolyte solution 141.9 The non-ideal electrolyte solution 141.10 Macroscopic manifestation of non-ideality 151.11 Species present in solution 171.12 Formation of ion pairs from free ions 171.13 Complexes from free ions 211.14 Complexes from ions and uncharged ligands 211.15 Chelates from free ions 221.16 Micelle formation from free ions 221.17 Measuring the equilibrium constant: general considerations 231.18 Base-lines for theoretical predictions about the behaviour expected for a solution consisting of free ions only, Debye-Hu¨ckel and Fuoss-Onsager theories and the use of Beer’s Law 241.19 Ultrasonics 261.20 Possibility that specific experimental methods could distinguish between the various types of associated species 291.21 Some examples of how chemists could go about inferring the nature of the species present 292 The Concept of Chemical Equilibrium: An Introduction 332.1 Irreversible and reversible reactions 342.2 Composition of equilibrium mixtures, and the approach to equilibrium 342.3 Meaning of the term ‘position of equilibrium’ and formulation of the equilibrium constant 352.4 Equilibrium and the direction of reaction 392.5 A searching problem 442.6 The position of equilibrium 452.7 Other generalisations about equilibrium 462.8 K and pK 462.9 Qualitative experimental observations on the effect of temperature on the equilibrium constant, K 472.10 Qualitative experimental observations on the effect of pressure on the equilibrium constant, K 492.11 Stoichiometric relations 492.12 A further relation essential to the description of electrolyte solutions – electrical neutrality 503 Acids and Bases: A First Approach 533.1 A qualitative description of acid–base equilibria 543.2 The self ionisation of water 563.3 Strong and weak acids and bases 563.4 A more detailed description of acid–base behaviour 573.5 Ampholytes 603.6 Other situations where acid/base behaviour appears 623.7 Formulation of equilibrium constants in acid–base equilibria 663.8 Magnitudes of equilibrium constants 673.9 The self ionisation of water 673.10 Relations between Ka and Kb: expressions for an acid and its conjugate base and for a base and its conjugate acid 683.11 Stoichiometric arguments in equilibria calculations 703.12 Procedure for calculations on equilibria 714 Equilibrium Calculations for Acids and Bases 734.1 Calculations on equilibria: weak acids 744.2 Some worked examples 804.3 Calculations on equilibria: weak bases 854.4 Some illustrative problems 904.5 Fraction ionised and fraction not ionised for a weak acid; fraction protonated and fraction not protonated for a weak base 974.6 Dependence of the fraction ionised on pKa and pH 984.7. The effect of dilution on the fraction ionised for weak acids lying roughly in the range: pKa ¼ 4.0 to 10.0 1014.8 Reassessment of the two approximations: a rigorous expression for a weak acid 1034.9 Conjugate acids of weak bases 1044.10 Weak bases 1054.11 Effect of non-ideality 1055 Equilibrium Calculations for Salts and Buffers 1075.1 Aqueous solutions of salts 1085.2 Salts of strong acids/strong bases 1085.3 Salts of weak acids/strong bases 1085.4 Salts of weak bases/strong acids 1095.5 Salts of weak acids/weak bases 1175.6 Buffer solutions 1196 Neutralisation and pH Titration Curves 1396.1 Neutralisation 1406.2 pH titration curves 1416.3 Interpretation of pH titration curves 1496.4 Polybasic acids 1536.5 pH titrations of dibasic acids: the calculations 1616.6 Tribasic acids 1666.7 Ampholytes 1687 Ion Pairing, Complex Formation and Solubilities 1777.1 Ion pair formation 1787.2 Complex formation 1847.3 Solubilities of sparingly soluble salts 1958 Practical Applications of Thermodynamics for Electrolyte Solutions 2158.1 The first law of thermodynamics 2168.2 The enthalpy, H 2178.3 The reversible process 2178.4 The second law of thermodynamics 2178.5 Relations between q, w and thermodynamic quantities 2188.6 Some other definitions of important thermodynamic functions 2188.7 A very important equation which can now be derived 2188.8 Relation of emfs to thermodynamic quantities 2198.9 The thermodynamic criterion of equilibrium 2208.10 Some further definitions: standard states and standard values 2218.11 The chemical potential of a substance 2218.12 Criterion of equilibrium in terms of chemical potentials 2228.13 Chemical potentials for solids, liquids, gases and solutes 2238.14 Use of the thermodynamic criterion of equilibrium in the derivation of the algebraic form of the equilibrium constant 2248.15 The temperature dependence of DHu 2308.16 The dependence of the equilibrium constant, K, on temperature 2318.17 The microscopic statistical interpretation of entropy 2368.18 Dependence of K on pressure 2378.19 Dependence of DGu on temperature 2428.20 Dependence of DSu on temperature 2428.21 The non-ideal case 2448.22 Chemical potentials and mean activity coefficients 2478.23 A generalisation 2518.24 Corrections for non-ideality for experimental equilibrium constants 2588.25 Some specific examples of the dependence of the equilibrium constant on ionic strength 2638.26 Graphical corrections for non-ideality 2708.27 Comparison of non-graphical and graphical methods of correcting for non-ideality 2708.28 Dependence of fraction ionised and fractiion protonated on ionic strength 2718.29 Thermodynamic quantities and the effect of non-ideality 2719 Electrochemical Cells and EMFs 2739.1 Chemical aspects of the passage of an electric current through a conducting medium 2749.2 Electrolysis 2759.3 Electrochemical cells 2809.4 Some examples of electrodes used in electrochemical cells 2859.5 Combination of electrodes to make an electrochemical cell 2929.6 Conventions for writing down the electrochemical cell 2939.7 One very important point: cells corresponding to a ‘net chemical reaction’ 2989.8 Liquid junctions in electrochemical cells 2989.9 Experimental determination of the direction of flow of the electrons, and measurement of the potential difference 3059.10 Electrode potentials 3059.11 Standard electrode potentials 3069.12 Potential difference, electrical work done and DG for the cell reaction 3089.13 DG for the cell process: the Nernst equation 3129.14 Methods of expressing concentration 3159.15 Calculation of standard emfs values for cells and DGu values for reactions 3179.16 Determination of pH 3209.17 Determination of equilibrium constants for reactions where K is either very large or very small 3229.18 Use of concentration cells 3249.19 ‘Concealed’ concentration cells and similar cells 3269.20 Determination of equilibrium constants and pK values for reactions which are not directly that for the cell reaction 3289.21 Use of concentration cells with and without liquid junctions in the determination of transport numbers 34310 Concepts and Theory of Non-ideality 34910.1 Evidence for non-ideality in electrolyte solutions 35010.2 The problem theoretically 35110.3 Features of the simple Debye-Hu¨ckel model 35110.4 Aspects of electrostatics which are necessary for an understanding of the procedures used in the Debye-Hückel theory and conductance theory 35310.5 The ionic atmosphere in more detail 36010.6 Derivation of the Debye-Hückel theory from the simple Debye-Hückel model 36310.7 The Debye-Hückel limiting law 38010.8 Shortcomings of the Debye-Hückel model 38210.9 Shortcomings in the mathematical derivation of the theory 38410.10 Modifications and further developments of the theory 38510.11 Evidence for ion association from Debye-Hückel plots 39110.12 The Bjerrum theory of ion association 39310.13 Extensions to higher concentrations 40110.14 Modern developments in electrolyte theory 40210.15 Computer simulations 40210.16 Further developments to the Debye-Hückel theory 40410.17 Statistical mechanics and distribution functions 40910.18 Application of distribution functions to the determination of activity coefficients due to Kirkwood; Yvon; Born and Green; and Bogolyubov 41410.19 A few examples of results from distribution functions 41710.20 ‘Born-Oppenheimer level’ models 41910.21 Lattice calculations for concentrated solutions 41911 Conductance: The Ideal Case 42111.1 Aspects of physics relevant to the experimental study of conductance in solution 42211.2 Experimental measurement of the conductivity of a solution 42511.3 Corrections to the observed conductivity to account for the self ionisation of water 42711.4 Conductivities and molar conductivities: the ideal case 42811.5 The physical significance of the molar conductivity, L 43111.6 Dependence of molar conductivity on concentration for a strong electrolyte: the ideal case 43211.7 Dependence of molar conductivity on concentration for a weak electrolyte: the ideal case 43311.8 Determination of L0 43611.9 Simultaneous determination of K and L0 43811.10 Problems when an acid or base is so weak that it is never 100% ionised, even in very, very dilute solution 44111.11 Contributions to the conductivity of an electrolyte solution from the cation and the anion of the electrolyte 44111.12 Contributions to the molar conductivity from the individual ions 44211.13 Kohlrausch’s law of independent ionic mobilities 44311.14 Analysis of the use of conductance measurements for determination of pKas for very weak acids and pKbs for very weak bases: the basic quantities involved 44711.15 Use of conductance measurements in determining solubility products for sparingly soluble salts 45111.16 Transport numbers 45311.17 Ionic mobilities 45711.18 Abnormal mobility and ionic molar conductivity of H3Oþ(aq) 46311.19 Measurement of transport numbers 46412 Theories of Conductance: The Non-ideal Case for Symmetrical Electrolytes 47512.1 The relaxation effect 47612.2 The electrophoretic effect 48012.3 Conductance equations for strong electrolytes taking non-ideality into consideration: early conductance theory 48012.4 A simple treatment of the derivation of the Debye-Hu¨ckel-Onsager equation 1927 for symmetrical electrolytes 48312.5 The Fuoss-Onsager equation 1932 48812.6 Use of the Debye-Hu¨ckel-Onsager equation for symmetrical strong electrolytes which are fully dissociated 48812.7 Electrolytes showing ion pairing and weak electrolytes which are not fully dissociated 49012.8 Empirical extensions to the Debye-Hu¨ckel-Onsager 1927 equation 49212.9 Modern conductance theories for symmetrical electrolytes – post 1950 49312.10 Fuoss-Onsager 1957: Conductance equation for symmetrical electrolytes 49312.11 A simple illustration of the effects of ion association on experimental conductance curves 50012.12 The Fuoss-Onsager equation for associated electrolytes 50012.13 Range of applicability of Fuoss-Onsager 1957 conductance equation for symmetrical electrolytes 50312.14 Limitations of the treatment given by the 1957 Fuoss-Onsager conductance equation for symmetrical electrolytes 50412.15 Manipulation of the 1957 Fuoss-Onsager equation, and later modifications by Fuoss and other workers 50512.16 Conductance studies over a range of relative permittivities 50612.17 Fuoss et al. 1978 and later 506Appendix 1 512Appendex 2 51513 Solvation 51713.1 Classification of solutes: a resume´ 51813.2 Classification of solvents 51813.3 Solvent structure 51913.4 The experimental study of the structure of water 52213.5 Diffraction studies 52213.6 The theoretical approach to the radial distribution function for a liquid 52613.7 Aqueous solutions of electrolytes 52613.8 Terms used in describing hydration 52813.9 Traditional methods for measuring solvation numbers 53013.10 Modern techniques for studying hydration: NMR 53313.11. Modern techniques of studying hydration: neutron and X-ray diffraction 53813.12 Modern techniques of studying solvation: AXD diffraction and EXAFS 54113.13 Modern techniques of studying solvation: computer simulations 54213.14 Cautionary remarks on the significance of the numerical values of solvation numbers 54313.15 Sizes of ions 54413.16 A first model of solvation – the three region model for aqueous electrolyte solutions 54413.17 Volume changes on solvation 55113.18 Viscosity data 55213.19 Concluding comment 55213.20 Determination of DGu hydration 55213 21 Determination of DHu hydration 55313.22 Compilation of entropies of hydration from DGu hydration and DHu hydration 55413.23 Thermodynamic transfer functions 55413.24 Solvation of non-polar and apolar molecules – hydrophobic effects 55413.25 Experimental techniques for studying hydrophobic hydration 55613.26 Hydrophobic hydration for large charged ions 55913.27 Hydrophobic interaction 56013.28 Computer simulations of the hydrophobic effect 560Subject Matter of Worked Problems 561Index 563

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