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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 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.

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 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 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 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.

Chapter

Cover Atkins’ Physical Chemistry

The equilibrium constant  

This chapter explores equilibrium constants, which lie at the heart of chemistry and are a key point of contact between thermodynamics and laboratory chemistry. It develops the concept of chemical potential and shows how it is used to account for the equilibrium composition of a reaction mixture. The equilibrium composition corresponds to a minimum in the Gibbs energy. By locating this minimum, it is possible to establish the relation between the equilibrium constant and the standard Gibbs energy of reaction. The chapter differentiates between exergonic and endergonic reactions. The reaction Gibbs energy is the slope of the plot of Gibbs energy against extent of reaction. Meanwhile, the equilibrium constant is the value of the reaction quotient at equilibrium.

Chapter

Cover Atkins’ Physical Chemistry

Electrode potentials  

This chapter discusses electrode potentials. Each electrode can be considered to make a characteristic contribution to the overall cell potential. The standard potential of a couple is the potential of a cell in which the couple forms the right-hand electrode and the left-hand electrode is a standard hydrogen electrode, all species being present at unit activity. The electrochemical series lists the metallic elements in the order of their reducing power as measured by their standard potentials in aqueous solution: low reduces high. The chapter then explains how the difference of the cell potential from its standard value is used to measure the activity coefficient of ions in solution. Meanwhile, standard potentials are used to calculate the standard cell potential and then to calculate the equilibrium constant of the cell reaction.

Chapter

Cover Physical Chemistry

Phase equilibrium  

This chapter discusses phase, which is a form of gas, liquid, solid, or supercritical fluid which is uniform in its chemical composition and its physical state. The chapter emphasizes that 'vapour' is used to describe the gaseous phase of substances which are liquids or solids at room temperature. The chapter also looks at 'vapour pressure', which is the equilibrium partial pressure exerted by a liquid in a sealed container at a fixed temperature. The chapter also covers the phase behaviour and phase transitions of one-component systems. The chapter includes a mention of the phase behaviour of two-component mixtures, such as the phenomena of colligative properties. It explores the term 'ideal gas', which refers to a system where the gaseous molecules experience no intermolecular forces.

Chapter

Cover Physical Chemistry for the Life Sciences

The response of equilibria to the conditions  

This chapter examines the response of equilibria to various conditions. It introduces Le Chatelier's principle: ‘When a system at equilibrium is subjected to a disturbance, the composition of the system tends to adjust so as to minimize the effect of the disturbance’. The chapter shows that by exploring how the standard reaction Gibbs energy depends on the conditions, we can infer how the equilibrium constant responds. One influence that can be dismissed at the outset is the role of catalysts, which in a biochemical context means the role of enzymes. The chapter pays particular attention to the effects of pressure and temperature. It reveals that when a gas-phase reaction at equilibrium is compressed, the composition tends to adjust so as to reduce the number of molecules in the gas phase. Additionally, the chapter shows how changes in temperature, such as those brought about by certain infections, affect biological processes.

Chapter

Cover Physical Chemistry for the Life Sciences

The rate laws of multi-step reactions  

This chapter explores the consequences of an overall reaction taking place through a sequence of elementary steps, each with a characteristic rate law. The overall rate laws are in general too difficult to solve other than by numerical methods, but two simplifications, the ‘steady-state approximation’ and the existence of a ‘pre-equilibrium’, enable the general features of networks of reactions to be established. The steady-state approximation assumes that after the intermediates have started to form, and during the major part of the reaction, their concentrations remain nearly constant and close to zero. In a pre-equilibrium the reactants and products of an early step of a reaction mechanism are supposed to have reached equilibrium. The chapter also presents a case study on the kinetics of protein unfolding.

Chapter

Cover Atkins’ Physical Chemistry

Transition-state theory  

This chapter focuses on transition-state theory, in which it is assumed that the reactant molecules form a complex that can be discussed in terms of the population of its energy levels. The transition-state theory inspires an approach to reaction rates in which the rate constant is expressed in terms of thermodynamic parameters, which is useful for parametrizing the rates of reactions in solution. It shows how the transition-state theory provides a way to relate the rate constant of reactions to models of the cluster of atoms supposed to form when reactants come together. The chapter provides a link between information about the structures of reactants and the rate constant for their reaction. It makes use of two strands: one is the relation between equilibrium constants and partition functions; the other is the relation between equilibrium constants and thermodynamic functions.

Chapter

Cover Atkins’ Physical Chemistry

The Boltzmann distribution  

This chapter explains how the Boltzmann distribution has been used to predict the populations of states in systems at thermal equilibrium. It considers the calculation of the populations of the energy levels of a system consisting of a large number of non-interacting molecules. The relative populations of energy levels, as opposed to states, must take into account the degeneracies of the energy levels. The chapter mentions that energy levels can be associated with any mode of motion, such as vibration or rotation. Moreover, the principle of equal a priori probabilities assumes that all possibilities for the distribution of energy are equally probable in the sense that the distribution is blind to the type of motion involved.

Chapter

Cover Atkins’ Physical Chemistry

Reaction mechanisms  

This chapter reviews the study of reaction rates that leads to an understanding of the mechanisms of reactions and the analysis into a sequence of elementary steps. It demonstrates how to construct rate laws from a proposed mechanism. It also outlines the elementary steps for simple rate laws that can be combined into an overall rate law: invoking the concept of the rate-determining step of a reaction, making the steady-state approximation, and supposing the existence of a pre-equilibrium. The chapter discusses the process of constructing the rate law for a reaction that takes place by a sequence of steps provides insight into chemical reactions at the molecular level. It focuses on chemical reactions that occur as a sequence of simpler steps and corresponding rate laws that can be combined into an overall rate law by applying a variety of approximations.

Chapter

Cover Elements of Physical Chemistry

Response to conditions  

This chapter addresses a very important question in chemistry, which is how to influence the yield of a reaction by increasing the equilibrium constant by changing the conditions, especially the temperature, at which the reaction takes place. Le Chatelier's principle states that when a system at equilibrium is subjected to a disturbance, the composition of the system adjusts so as to tend to minimize the effect of the disturbance. The variation of an equilibrium constant with temperature is expressed by the van 't Hoff equation. The chapter then differentiates between an endothermic reaction and an exothermic reaction. When a system at equilibrium is compressed, the composition of a gas-phase equilibrium adjusts so as to reduce the number of molecules in the gas phase. Meanwhile, the equilibrium constant of a reaction is independent of the presence of a catalyst and is independent of the pressure.