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Chapter

Cover Physical Chemistry

Chemical equilibrium  

This chapter analyses the reaction that ensues when reactants are mixed until equilibrium is established. It defines the term 'dynamic equilibrium', which refers to the fact that once equilibrium has been established, both forward and backward reactions continue at the same rate. It also talks about the presence of both reactants and products. Here, there is no further tendency for the mixture to undergo net change. The chapter cites the reaction between hydrogen and iodine to produce hydrogen iodide as an example. The chapter highlights how the equilibrium process may be investigated by setting up a reaction mixture of hydrogen and iodine in a sealed vessel, allowing it to come to equilibrium. It examines the ratio of reactants to products found at equilibrium. This is determined by the equilibrium constant for the reaction.

Chapter

Cover Chemistry3

Chemical equilibrium  

This chapter talks about a sign of the change in Gibbs energy for a reaction that can be used to predict whether or not the reaction is spontaneous. The size of the Gibbs energy changes allows quantitative predictions about the equilibrium composition of the reaction mixture to be made. The chapter defines and demonstrates how to use the three types of equilibrium constant: Kc, Kp, and the thermodynamic equilibrium constant, including the reaction quotient. It explains how the equilibrium constant and composition change when experimental conditions such as pressure, concentration, and temperature are varied. The application equilibrium thermodynamics to real chemical situations are also covered.

Chapter

Cover Elements of Physical Chemistry

The equilibrium constant  

This chapter assesses the equilibrium constant, which expresses the composition of an equilibrium mixture as a ratio of products of activities. It is a succinct summary of the equilibrium composition of a reaction mixture, but special techniques have to be applied in order to extract individual concentrations of the reactants and products. The chapter then explains how to set up and use an equilibrium table that does the task systematically. An equilibrium table is a table with columns headed by the species and, in successive rows, the changes in composition needed to reach equilibrium. Ultimately, the equilibrium constant of a gas-phase reaction may be expressed as a ratio of products of pressures or, after the appropriate conversion, concentrations.

Chapter

Cover Chemistry for the Biosciences

Equilibria: how far do reactions go?  

This chapter focuses on equilibrium reactions, which can proceed in both forward and reverse directions simultaneously. At equilibrium, the rates of the forward and back reactions are equal: they continue to proceed, but there is no overall change in the system—this is called dynamic equilibrium. The relative position of an equilibrium reaction when equilibrium has been reached is represented by an equilibrium constant. The chapter explains the reaction quotient, before looking at binding reactions and how they represent a type of equilibrium reaction. When an equilibrium is perturbed, the system acts to counteract the change so that a state of equilibrium is re-established. There are three key ways to perturb an equilibrium: by changing the concentration of species present, changing the temperature, or changing the pressure. Finally, the chapter considers the impact of free energy on chemical equilibria.

Book

Cover Physical Chemistry

Joanne Elliott and Elizabeth Page

Workbook in Physical Chemistry opens with a chapter on the fundamentals of this field. It then looks at thermodynamics before covering chemical equilibrium. After that, there follows a chapter on phase equilibrium. Towards the end there is a chapter which covers reaction kinetics. The final chapter looks at electrochemistry.

Chapter

Cover Elements of Physical Chemistry

The Boltzmann distribution  

This chapter highlights the Boltzmann distribution, which is used to predict the populations of states in systems at thermal equilibrium. It considers the Boltzmann distribution as one of the most important equations in chemistry as it summarizes the populations of states and provides insight into the nature of temperature. It also reviews how thermodynamic properties, the temperature dependence of equilibrium constants, and the rates of chemical reactions can be interpreted in their terms. The chapter recognizes temperature as the most probable distribution of molecules over the available energy levels subject to certain restraints. It looks at the concept of the Boltzmann distribution that underlie all the descriptions of the relation between the individual properties of molecules and the properties of bulk matter.

Chapter

Cover Why chemical reactions happen

Equilibrium  

This chapter covers equilibrium. It starts with the concept of the Second Law of Thermodynamics and Gibbs energy impacting entropy. It notes the general chemical equilibrium in terms of gas, solid, liquid, and solution. The chapter uses diagrams and equations to show how equilibrium is achieved in relation to Gibbs energy and equilibrium constants. It investigates how temperature, dimerization, extraction of metals, concentration, the Haber process, and coupling reactions influence the position of equilibrium. Additionally the chapter explores the rates of reaction in terms of equilibrium.

Chapter

Cover Thermodynamics of Chemical Processes

Equilibrium in chemical reactions  

This chapter applies the concept of Gibbs energy to describe the factors that govern chemical equilibrium. It determines how far a reaction will go before it comes to equilibrium and how to find the equilibrium yield and make predictions about the effect that changed the experimental conditions on equilibrium. It also discusses the Gibbs energy of the system which changes throughout a reaction, depending on the proportions of reactants and products. The chapter mentions an equilibrium reaction with straightforward stoichiometry, such as the reaction of dinitrogen tetroxide to form nitrogen dioxide. It points out how adding or removing one of the components of a reaction affects the activity of the other components in the equilibrium mixture, since it will change the mole fractions.

Chapter

Cover Making the Transition to University Chemistry

Chemical Equilibrium  

This chapter introduces equilibria and equilibrium constants. Equilibrium is recorded when the rate of the forward reaction equates to the rate of the backwards reaction. When equilibrium has been reached, the concentrations of all the substances remain constant. The thermodynamic equilibrium constant is devised when the standard Gibbs energy change is in line with the natural logarithm of the equilibrium constant. The chapter lists the equilibrium calculations mostly used in universities. Le Chatelier's principle refers to the small conditions changes subjected at a system in equilibrium as the equilibrium tends to shift to minimize the effect of the change.

Chapter

Cover Atkins’ Physical Chemistry

Derived functions  

This chapter discusses the derived functions of thermodynamics. It looks into how classical thermodynamics extensively uses various derived functions, referencing the power of chemical thermodynamics originating from its deployment of varying derived functions, particularly the enthalpy and Gibbs energy. The thermodynamic functions, such as the Helmholtz energy and Gibbs energy, can be calculated from the canonical partition function. Additionally, the equilibrium constant is defined in terms of the partial pressures of the reactants and products, such as instances of gas-phase reactions. Meanwhile, the physical basis of chemical equilibrium can be inferred under the terms of competition between energy separations and densities of states.

Chapter

Cover Atkins’ Physical Chemistry

The response of equilibria to the conditions  

This chapter studies how the thermodynamic formulation of the equilibrium constant is used to establish the quantitative effects of changes in the conditions. One very important aspect of equilibrium is the control that can be exercised by varying the conditions, such as the pressure or temperature. The thermodynamic equilibrium constant is independent of the presence of a catalyst and independent of pressure. The response of composition to changes in the conditions is summarized by Le Chatelier's principle. Meanwhile, the dependence of the equilibrium constant on the temperature is expressed by the van 't Hoff equation and can be explained in terms of the distribution of molecules over the available states.

Chapter

Cover Organic Chemistry

Equilibria, rates, and mechanisms  

This chapter studies a number of thermodynamic principles, looking at equilibria, rates, and mechanisms. At any one particular temperature, the equilibrium constant is just that: constant. This provides a means of forcing the equilibrium to favour the products (or reactants) since the ratio between them must remain constant. One way to make esters in the laboratory is to use a large excess of the alcohol and remove water continually from the system as it is formed, for example by distilling it out. This means that in the equilibrium mixture there is a tiny quantity of water, lots of the ester, lots of the alcohol, and very little of the carboxylic acid; in other words, we convert the carboxylic acid into the ester. The acid catalyst does not alter the position of the equilibrium; it simply speeds up the rate of the reaction, allowing equilibrium to be reached more quickly.

Chapter

Cover Elements of Physical Chemistry

The approach to equilibrium  

This chapter addresses how all forward reactions are accompanied by their reverse reactions. Close to the start of a reaction, when little or no product is present, the rate of the reverse reaction is negligible. However, as the concentration of products increases, the rate at which they decompose into reactants becomes greater. At equilibrium, the reverse rate matches the forward rate and the reactants and products are present in abundances given by the equilibrium constant for the reaction. The chapter then considers the term relaxation, which denotes the return of a system to equilibrium. It is used in chemical kinetics to indicate that an externally applied influence has shifted the equilibrium position of a reaction, normally abruptly, and that the reaction is adjusting to the equilibrium composition characteristic of the new conditions. Relaxation methods include the temperature jump technique.

Chapter

Cover Physical Chemistry for the Life Sciences

The thermodynamic background  

This chapter shows that reactions tend to proceed in the direction of decreasing Gibbs energy and towards a composition summarised by an equilibrium constant. It emphasises the importance of the thermodynamic criteria for spontaneous change and equilibration, as is central to an understanding of the molecular processes that occur in cells. The chapter begins by stating that, at constant temperature and pressure, a reaction mixture tends to adjust its composition until its Gibbs energy is a minimum. From there, the chapter discusses the variation of reaction Gibbs energy with composition. Reactions at equilibrium are then explored. The chapter ends with a case study involving the binding of oxygen to myoglobin and haemoglobin.

Chapter

Cover Molecular Spectroscopy

Vibrational spectroscopy  

This chapter defines vibrational motion, which is a periodic, concerted displacement of the nuclei in a molecule that leaves the centre of mass unaltered in laboratory space. It explains that the appropriate linear combination of the displacements of a nucleus from its equilibrium position is called the vibrational coordinate, which is used to describe a particular vibrational motion. It also mentions the polyatomic molecule. This has several distinct vibrational modes, while the diatomic molecule only has one. The chapter reviews two distinct contributions to energy: the kinetic part that arises from the motion of the nuclei and the potential part that comes from the compression or expansion of the bond from its equilibrium value. It highlights the form of the potential energy curve. This shows that molecular energy increases rapidly as the charged particles in the molecule experience strong repulsive forces.

Book

Cover Electrode Potentials

Richard G Compton and Giles H W Sanders

Electrode Potentials provides an introduction to the science of equilibrium electrochemistry, specifically addressing the topics of electrode potentials and their applications. It builds on a knowledge of elementary thermodynamics by giving the reader an appreciation of the origin of electrode potentials, and shows how these are used to deduce a wealth of chemically important information and data such as equilibrium constants; the free energy, enthalpy and entropy changes of chemical reactions; activity coefficients; and the selective sensing of ions. The emphasis throughout is on understanding the foundations of the subject and how it may be used to study problems of chemical interest.

Chapter

Cover Environmental Chemistry

Gases in water  

This chapter explores how gases distribute themselves between air and water and how the properties of water change accordingly. It cites Henry's law for simple gases, such as oxygen or nitrogen, that do not react with water and considers the specific case of carbon dioxide, which is a gas that reacts with water and creates a more complex equilibrium system. It also demonstrates how to define alkalinity and acid neutralization capacity and their relation to environmental issues. The chapter refers to gases and other volatile compounds whose vapours may be present at low concentration in the atmosphere. It provides a quantitative description of the distribution of gases between air and water, which depends on the substance's vapour pressure, solubility, and ability to react with water and other components in the hydrosphere.

Chapter

Cover Elements of Physical Chemistry

Standard potentials  

This chapter examines standard potentials. Although the contribution of a single electrode to the potential difference cannot be measured absolutely, a scheme can be devised for establishing the contributions relative to a standard. These standard potentials are of great importance for predicting equilibrium constants, for discussing the ability of one species to reduce another, for the determination of pH, and for the determination of thermodynamic data. The standard potential of a couple is the standard cell potential in which it forms the right-hand electrode and a hydrogen electrode is on the left. The chapter then looks at the electrochemical series, which is a table of relative reducing powers of couples.

Chapter

Cover Physical Chemistry for the Life Sciences

Ultracentrifugation  

This chapter considers ultracentrifugation, which provides methods for the characterisation of the sizes and shapes of macromolecules and macromolecular assemblies. Ultracentrifugation is used in three ways: velocity sedimentation, equilibrium sedimentation, and density-gradient sedimentation. Gravitational fields interact with mass, but the Earth's gravitational field is weak and so has little or no effect on the sedimentation of molecules in a solvent. The force of gravity can be emulated and greatly enhanced by using the rapid rotation of an ultracentrifuge. The rate of sedimentation of a macromolecule in the centrifugal field, or the equilibrium distribution of the sediment, can be interpreted in terms of its mass and in some cases its size.

Chapter

Cover Atkins’ Physical Chemistry

Reactions approaching equilibrium  

The chapter discusses how rate laws must take into account both the forward and reverse reactions and describe the approach to equilibrium in order to be complete. It notes that the results of the analysis are relations between the equilibrium constant of the overall process and the rate constants of the forward and reverse reactions. It also looks at how the analysis of the time dependence reveals the connection between rate constants and equilibrium constants. The chapter emphasizes that both forward and reverse reactions must be incorporated into a reaction scheme in order to account for the approach to equilibrium. It reviews kinetic studies that are made on reactions that are far from equilibrium and if the concentration of the products is low and the reverse reactions are unimportant.