There are essentially two theories of solutions that can be considered exact: the McMillan-Mayer theory and Fluctuation Solution Theory (FST). The first is mostly limited to solutes at low concentrations, while FST has no such issue. It is an exact theory that can be applied to any stable solution regardless of the number of components and their co

Expertise in electrolyte systems has become increasingly important in traditional CPI operations, as well as in oil/gas exploration and production. This book is the source for predicting electrolyte systems behavior, an indispensable "do-it-yourself" guide, with a blueprint for formulating predictive mathematical electrolyte models, recommended tabular values to use in these models, and annotated bibliographies. The final chapter is a general recipe for formulating complete predictive models for electrolytes, along with a series of worked illustrative examples. It can serve as a useful research and application tool for the practicing process engineer, and as a textbook for the chemical engineering student.

This book was first published in 1991. It considers the concepts and theories relating to mostly aqueous systems of activity coefficients.

Electrolytes and salt solutions are ubiquitous in chemical industry, biology and nature. This unique compendium introduces the elements of the solution properties of ionic mixtures. In addition, it also serves as a bridge to the modern researches into the molecular aspects of uniform and non-uniform charged systems. Notable subjects include the Debye-Hückel limit, Pitzer's formulation, Setchenov salting-out, and McMillan-Mayer scale. Two new chapters on industrial applications — natural gas treating, and absorption refrigeration, are added to make the book current and relevant.This textbook is eminently suitable for undergraduate and graduate students. For practicing engineers without a background in salt solutions, this introductory volume can also be used as a self-study.

An advanced-level textbook of physical chemistry for the graduate (B.Sc) and postgraduate (M.Sc) students of Indian and foreign universities. This book is a part of four volume series, entitled "A Textbook of Physical Chemistry – Volume I, II, III, IV". CONTENTS: Chapter 1. Quantum Mechanics – I: Postulates of quantum mechanics; Derivation of Schrodinger wave equation; Max-Born interpretation of wave functions; The Heisenberg’s uncertainty principle; Quantum mechanical operators and their commutation relations; Hermitian operators (elementary ideas, quantum mechanical operator for linear momentum, angular momentum and energy as Hermition operator); The average value of the square of Hermitian operators; Commuting operators and uncertainty principle(x & p; E & t); Schrodinger wave equation for a particle in one dimensional box; Evaluation of average position, average momentum and determination of uncertainty in position and momentum and hence Heisenberg’s uncertainty principle; Pictorial representation of the wave equation of a particle in one dimensional box and its influence on the kinetic energy of the particle in each successive quantum level; Lowest energy of the particle. Chapter 2. Thermodynamics – I: Brief resume of first and second Law of thermodynamics; Entropy changes in reversible and irreversible processes; Variation of entropy with temperature, pressure and volume; Entropy concept as a measure of unavailable energy and criteria for the spontaneity of reaction; Free energy, enthalpy functions and their significance, criteria for spontaneity of a process; Partial molar quantities (free energy, volume, heat concept); Gibb’s-Duhem equation. Chapter 3. Chemical Dynamics – I: Effect of temperature on reaction rates; Rate law for opposing reactions of Ist order and IInd order; Rate law for consecutive & parallel reactions of Ist order reactions; Collision theory of reaction rates and its limitations; Steric factor; Activated complex theory; Ionic reactions: single and double sphere models; Influence of solvent and ionic strength; The comparison of collision and activated complex theory. Chapter 4. Electrochemistry – I: Ion-Ion Interactions: The Debye-Huckel theory of ion- ion interactions; Potential and excess charge density as a function of distance from the central ion; Debye Huckel reciprocal length; Ionic cloud and its contribution to the total potential; Debye - Huckel limiting law of activity coefficients and its limitations; Ion-size effect on potential; Ion-size parameter and the theoretical mean-activity coefficient in the case of ionic clouds with finite-sized ions; Debye - Huckel-Onsager treatment for aqueous solutions and its limitations; Debye-Huckel-Onsager theory for non-aqueous solutions; The solvent effect on the mobality at infinite dilution; Equivalent conductivity (Λ) vs. concentration c 1/2 as a function of the solvent; Effect of ion association upon conductivity (Debye- Huckel - Bjerrum equation). Chapter 5. Quantum Mechanics – II: Schrodinger wave equation for a particle in a three dimensional box; The concept of degeneracy among energy levels for a particle in three dimensional box; Schrodinger wave equation for a linear harmonic oscillator & its solution by polynomial method; Zero point energy of a particle possessing harmonic motion and its consequence; Schrodinger wave equation for three dimensional Rigid rotator; Energy of rigid rotator; Space quantization; Schrodinger wave equation for hydrogen atom, separation of variable in polar spherical coordinates and its solution; Principle, azimuthal and magnetic quantum numbers and the magnitude of their values; Probability distribution function; Radial distribution function; Shape of atomic orbitals (s,p & d). Chapter 6. Thermodynamics – II: Classius-Clayperon equation; Law of mass action and its thermodynamic derivation; Third law of thermodynamics (Nernest heat theorem, determination of absolute entropy, unattainability of absolute zero) and its limitation; Phase diagram for two completely miscible components systems; Eutectic systems, Calculation of eutectic point; Systems forming solid compounds Ax By with congruent and incongruent melting points; Phase diagram and thermodynamic treatment of solid solutions. Chapter 7. Chemical Dynamics – II: Chain reactions: hydrogen-bromine reaction, pyrolysis of acetaldehyde, decomposition of ethane; Photochemical reactions (hydrogen - bromine & hydrogen -chlorine reactions); General treatment of chain reactions (ortho-para hydrogen conversion and hydrogen - bromine reactions); Apparent activation energy of chain reactions, Chain length; Rice-Herzfeld mechanism of organic molecules decomposition(acetaldehyde); Branching chain reactions and explosions ( H2-O2 reaction); Kinetics of (one intermediate) enzymatic reaction : Michaelis-Menton treatment; Evaluation of Michaelis 's constant for enzyme-substrate binding by Lineweaver-Burk plot and Eadie-Hofstae methods; Competitive and non-competitive inhibition. Chapter 8. Electrochemistry – II: Ion Transport in Solutions: Ionic movement under the influence of an electric field; Mobility of ions; Ionic drift velocity and its relation with current density; Einstein relation between the absolute mobility and diffusion coefficient; The Stokes- Einstein relation; The Nernst -Einstein equation; Walden’s rule; The Rate-process approach to ionic migration; The Rate process equation for equivalent conductivity; Total driving force for ionic transport, Nernst - Planck Flux equation; Ionic drift and diffusion potential; the Onsager phenomenological equations; The basic equation for the diffusion; Planck-Henderson equation for the diffusion potential.

This book deals with density, temperature, velocity and concentration fluctuations in fluids and fluid mixtures. The book first reviews thermal fluctuations in equilibrium fluids on the basis of fluctuating hydrodynamics. It then shows how the method of fluctuating hydrodynamics can be extended to deal with hydrodynamic fluctuations when the system is in a stationary nonequilibrium state. In contrast to equilibrium fluids where the fluctuations are generally short ranged unless the system is close to a critical point, fluctuations in nonequilibrium fluids are always long-ranged encompassing the entire system. The book provides the first comprehensive treatment of fluctuations in fluids and fluid mixtures brought out of equilibrium by the imposition of a temperature and concentration gradient but that are still in a macroscopically quiescent state. By incorporating appropriate boundary conditions in the case of fluid layers, it is shown how fluctuating hydrodynamics affects the fluctuations close to the onset of convection. Experimental techniques of light scattering and shadowgraphy for measuring nonequilibrium fluctuations are elucidated and the experimental results thus far reported in the literature are reviewed.· Systematic exposition of fluctuating hydrodynamics and its applications· First book on nonequilibrium fluctuations in fluids· Fluctuating Boussinesq equations and nonequilibrium fluids· Fluid layers and onset of convection· Rayleigh scattering and Brillouin scattering in fluids· Shadowgraph technique for measuring fluctuations· Fluctuations near hydrodynamic instabilities

An Introduction to Aqueous Electrolyte Solutions is a comprehensive coverage of the subject including the development of key concepts and theory that focus on the physical rather than the mathematical aspects. Important links are made between the study of electrolyte solutions and other branches of chemistry, biology, and biochemistry, making it a useful cross-reference tool for students studying this important area of electrochemistry. Carefully developed throughout, each chapter includes intended learning outcomes and worked problems and examples to encourage student understanding of this multidisciplinary subject. * a comprehensive introduction to aqueous electrolyte solutions including the development of key concepts and theories * emphasises the connection between observable macroscopic experimental properties and interpretations made at the molecular level * key developments in concepts and theory explained in a descriptive manner to encourage student understanding * includes worked problems and examples throughout An invaluable text for students taking courses in chemistry and chemical engineering, this book will also be useful for biology, biochemistry and biophysics students required to study electrochemistry.