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Chapter

Cover From Molecules to Crystallizers

Introduction  

This introductory chapter provides an overview of crystallization, which is a purification technique, a separation process, and a branch of particle technology. It is a supramolecular process by which an ensemble of randomly organized molecules, ions, or atoms in a fluid come together to form an ordered three-dimensional molecular array which we call a crystal. Most commonly encountered solid materials are crystalline. The properties of crystals are often directionally dependent—they are anisotropic. They grow and dissolve at different rates in different directions, their refractive indices vary with direction, and their thermal expansion coefficients and electrical conductivity are directionally dependent, as are their mechanical properties. The chapter then explains the importance of knowing the crystalline phases and the underlying phase equilibrium.

Chapter

Cover Chemistry of the First-row Transition Metals

Metals in solution  

This chapter examines the occurrence of the dissociation of ligands, which may have a reaction between the ligands or the metal and the solvent and aggregation in order to give di- or oligo-nuclear species. It describes the thermodynamic stability of a complex that can be revealed by an equilibrium constant and relates its concentration to the concentration of all other related species when the system has reached equilibrium. It also analyses the kinetic stability of a species that refers to the speed at which transformation leads to the attainment of equilibrium. The chapter reviews the metal complexes of chelating ligands that have significantly higher stability than their analogues containing only mono- or uni-dentate ligands. It traces the origin of the chelate effect that lies in enthalpic and entropic factors.

Chapter

Cover Aqueous Acid-Base Equilibria and Titrations

Basic concepts  

This chapter discusses the basic concepts of acids, bases, and pH. The concept of acid and base can be generalized in several ways. The book uses the definition given by Brönsted, which emphasizes the complementary nature of acids and bases in aqueous solutions. It considers as an acid any substance that can donate a proton, and as a base any proton acceptor. In this nomenclature, an acid that loses its proton become a base, and vice versa, so that one can consider conjugate acid-base pairs. Meanwhile, the concept of pH was introduced by Sørensen as the negative logarithm of the hydrogen concentration. The chapter then looks at the mass action law, which is the fundamental law of chemical equilibrium. It also considers concentration fractions, logarithmic concentration diagrams, and the proton condition.

Chapter

Cover Aqueous Acid-Base Equilibria and Titrations

Activity effects  

This chapter addresses activity effects. The experimental evidence from almost a century of precise measurements of equilibrium constants shows that, in dilute solutions, they are essentially constant only when compared at constant ionic strength. By excluding the contributions from uncharged species, the ionic strength clearly reflects coulombic interactions. It is important to realize where activity corrections apply, and where they do not. Since interionic attractions can lower the energetics of ions, they can affect the numerical values of the equilibrium constants. However, activity effects have no direct influence on the mass and charge balance equations. Similarly, activity effects do not change the equivalence volume in a titration, but can change the shape of the titration curve. The chapter then looks at ionic interactions and non-ionic interactions.

Chapter

Cover Aqueous Acid-Base Equilibria and Titrations

Numerical solutions  

This chapter examines the numerical solutions of pH problems in order of their increasing complexity, and of the sophistication and numerical prowess of the tools needed for their solution. First, it uses the logarithmic concentration diagram to visualize the proton condition. It then considers methods that need no tools beyond a piece of paper and a pencil, before looking at those methods that require a simple calculator capable of computing square roots and taking logarithms. The chapter also describes general methods based on relatively simple iterative methods, such as a Newton-Raphson algorithm. Because iterations are repetitive, such calculations are most readily performed on a computer, using generally available software such as a spreadsheet or scientific calculators. Finally, the chapter explores some even more general approaches used in commercial programs that solve an arbitrary number of equilibrium expressions and the associated mass and charge balance equations.