This chapter loos at the thermodynamics of phase transitions. The Gibbs energy of a
system, particularly a single substance that might form the system, is defined as
G = H − TS, with H its
enthalpy, T its temperature, and S its entropy. It is at
centre stage in almost all the applications of thermodynamics to chemistry and in particular
of how physical and chemical processes depend on pressure and temperature. At equilibrium,
the molar Gibbs energies of the phases are equal. The molar Gibbs energy increases with
pressure and is most sensitive when the molar volume is large. Meanwhile, the molar Gibbs
energy decreases with temperature and is most sensitive when the molar entropy is large.
Although the temperature-dependence of the Gibbs energy is expressed in terms of the
entropy, it can also be expressed in terms of the enthalpy. The chapter then looks at the
Gibbs–Helmholtz equation.

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### Chapter

## The thermodynamics of transition

### Chapter

## Gibbs energy

This chapter addresses Gibbs energy, which is sometimes referred to as free energy, or as Gibbs free energy. Changes in Gibbs energy are more useful in chemistry because they determine whether reactions are energetically favourable. The second law of thermodynamics states that, in a spontaneous process, the change in entropy is equal to or greater than zero for the system and its surroundings. In the discussion of entropy, it was noted that it is important to distinguish in a chemical reaction that energy which is tied up in chemical bonds and that which is distributed amongst the translational, rotational, and vibrational degrees of freedom. For a spontaneous chemical process which leads to an enthalpy change, the corresponding change in the enthalpy of the surroundings is –∆H.

### Chapter

## Water in transition

This chapter examines water in transition. It explains that water (like any other substance) tends to make a transition to the phase with lowest molar Gibbs energy. As the chapter reveals, the freezing, melting, evaporating, and condensing of water are phase changes that have a profound effect on the environments in which life is found. The thermodynamic analysis of these phase changes opens up a route to understanding many other properties and some of the roles of water in cells. To that end, the chapter begins by examining the variation of Gibbs energy with pressure. Afterward, the variation of Gibbs energy with temperature is discussed.

### Chapter

## The origin of thermodynamic properties

This chapter shows how the molecular partition function is used to calculate and give
insight into important thermodynamic functions: internal energy, heat capacity, entropy, and
Gibbs energy. It talks about the final step into the calculations of chemically significant
expressions when the Gibbs energy is available that shows how equilibrium constants can be
calculated from structural and spectroscopic data. It also provides a molecular
interpretation of thermodynamic properties that acts as a bridge between spectroscopy and
thermodynamics. The chapter reviews how a partition function is used to calculate and
interpret thermodynamic properties of systems as small as atoms and as large as biopolymers.
It highlights the equilibrium constant, which is related to the distribution of molecules
over the available states of a system composed of reactants and products.

### Chapter

## The standard reaction Gibbs energy

This chapter focuses on standard reaction Gibbs energy. It explains how equilibrium constants and standard reaction Gibbs energies may be calculated from the standard Gibbs energies of formation of reactants and products. Additionally, the standard Gibbs energy of the formation of a compound is a measure of its thermodynamic stability. From there, the chapter relates the biochemical and thermodynamic standard states of solutes. Additionally, stability and instability are discussed. The chapter shows that standard Gibbs energies of formation of compounds are a measure of the ‘thermodynamic altitude’ of a compound above or below a ‘sea level’ of stability represented by the elements in their reference states.

### Chapter

## Concentrating on the system

This chapter highlights the Helmholtz and Gibbs energies to develop the Clausius
inequality. The Clausius inequality implies a number of criteria for spontaneous
change under a variety of conditions which may be expressed in terms of the
properties of the system alone. A spontaneous process at constant temperature and
volume is accompanied by a decrease in the Helmholtz energy. The change in the
Helmholtz energy is equal to the maximum work obtainable from a system at constant
temperature. Meanwhile, a spontaneous process at constant temperature and pressure
is accompanied by a decrease in the Gibbs energy. The change in the Gibbs energy is
equal to the maximum non-expansion work obtainable from a system at constant
temperature and pressure. The chapter then looks at the standard Gibbs energies of
formation and the Born equation.

### Chapter

## Energy: what makes reactions go?

This chapter explores the nature of energy, looking at how energy transfer drives the biochemical processes on which organisms depend for life. Energy is the capacity something has to do work, and is transferred between a system and its surroundings in the form of work and heat. The chapter introduces the concepts of enthalpy and entropy, and explains how the energy change associated with a chemical reaction is called the enthalpy change of reaction. Meanwhile, entropy is a measure of the energetic disorder of a system. The chapter also considers spontaneous reactions and what determines their spontaneity, and introduces the concept of Gibbs free energy.

### Chapter

## Thermodynamic functions: towards a statistical toolkit

This chapter explores thermodynamic functions as a statistical toolkit. It refers to state functions as major thermodynamic variables. The two thermodynamic functions most usually chosen as the basis for variables are the energy E—leading to the internal energy U—and entropy S. The chapter highlights that the Massieu bridge will form the basis of all of the other thermodynamic functions needed. It notes that the pressure is related to the Helmholtz free energy through the first derivative in relation to volume at a constant temperature. The chapter considers the relation between internal energy, heat capacity, entropy, enthalpy, and Gibbs free energy, which is linked with Helmholtz free energy. The chapter shares the full set of toolkit equations which can be used in the field of thermodynamics.

### Chapter

## The Gibbs energy

This chapter explores the procedure developed by American theoretician J. W. Gibbs, who laid the foundations of chemical thermodynamics towards the end of the nineteenth century. Gibbs discovered how to combine the two contributions needed in entropy calculations into one. Indeed, almost the whole of biochemical thermodynamics is now discussed in terms of the Gibbs energy. As this chapter shows, at constant temperature and pressure, the direction of spontaneous change is towards lower Gibbs energy. It also relates the Gibbs energy to work — particularly non-expansion work, which includes muscle contraction (for movement) and causing neurotransmitters to move across synapses to give rise to thought, or at least, neuronal response. Finally, the chapter examines the action of adenosine triphosphate in a case study.

### Chapter

## Entropy and Gibbs energy

This chapter details how thermodynamics can be used to predict different types of behaviour and determines whether or not reactions will occur and under what conditions their yields can be maximized. Spontaneous reactions are those that, once started, will continue without any outside intervention and spontaneous processes and move towards their equilibrium state without being driven by an external influence. The chapter describes and gives examples of spontaneous changes. It also talks about how the coupling of reactions allows nonspontaneous reactions to take place and how Gibbs energy changes with temperature, pressure, and concentration. It details the calculation of the temperature dependence of entropy using heat capacities and entropy changes of reaction from absolute entropies.

### Chapter

## Phase equilibrium and solutions

This chapter focuses on the concept of matter existing in either the solid, liquid, or gas phase and is dependent on temperature and pressure. It explains that this phase is part of a system that is homogeneous throughout and separated from other phases by a definite boundary. It also describes the factors that determine why compounds exist in a particular phase under a particular set of conditions and what influences the transitions between phases. The chapter talks about the Gibbs energy of the phases in order to derive quantitative information on phase transitions. It considers pressure and temperature as major experimental variables that affect phase behaviour, noting that matter exists in the solid phase at sufficiently low temperatures or high pressures.

### Chapter

## 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

## 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

## 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

## Thermodynamics

The aim of this tutorial is to introduce some key concepts about thermodynamics, which is the study of the energetics of a system.
Life depends on the redistribution of energy. The study of thermal energy (heat) has a fascinating history; the first and second...

### Chapter

## Electrochemical cells

This chapter examines electrochemical cells, which consist of two electrodes, or
metallic conductors, each in contact with an electrolyte, an ionic conductor.
Because many reactions involve the transfer of electrons, they can be studied (and
used) by allowing them to take place in a cell equipped with electrodes, with the
spontaneous reaction forcing electrons through an external circuit. The electric
potential of the cell is easily measured and is related to the reaction of Gibbs
energy, thus providing a convenient method for the determination of some
thermodynamic quantities. The chapter looks at galvanic cells, the liquid junction
potential, and the Nernst equation. It also considers how the standard cell
potential may be used to calculate the standard Gibbs energy of the cell reaction
and hence its equilibrium constant.

### Chapter

## Calculating equilibrium constants

This chapter explains the calculation of equilibrium constants. Deriving the relationship between partition functions and equilibrium constants provides a greater understanding of the true nature of chemical equilibrium. The chapter discusses molar Gibbs free energy to calculate perfect gases. It also looks at the equation, aspects, interpretation, and calculations for equilibrium constants. The chapter also tackles calculation problems of five different equilibria, including dissociation, isotopic exchange, and the water-gas shift reaction. Finally, the chapter highlights that statistical thermodynamics is not bounded by the limitations discussed in the book, which aims to foster understanding of key concepts through the discussion of ideal examples and does not consider the highly complex cases one would encounter in the real world.

### Chapter

## Introduction to electrochemistry

This chapter introduces the concept of electrochemistry. Electrochemistry is the movement of charge, ions in a liquid or solid solution, and electrons from a solid to a species in solution. Next, the chapter looks into oxidation, reduction, and polarization. It explores the basic concepts in electrical circuits such as alternating current, direct current, Ohm's law and resistivity, impedance, EMF, voltage, and capacitance. The chapter shows how current is carried in any of several ways around a circuit in electrochemistry. The chapter also highlights the significance of voltage, work, and Gibbs energy. It presents the symbols and equations needed to achieve desired electrochemical measurements.

### Chapter

## 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

## Spontaneous Change, Entropy, and Gibbs Energy

This chapter explores the concepts of spontaneous change, entropy, and Gibbs energy. Whilst spontaneous changes have a natural tendency to occur, the Gibbs energy equation cannot be used to predict the reaction rate. Entropy is a measure of the dispersal of energy. The criterion for spontaneous change is mostly based on the Second Law of thermodynamics. Gibbs energy, additionally, is the combination of enthalpy and entropy together to form a single physical quantity. An Ellingham diagram includes graphs showing the Gibbs energy change of formation for various metal oxides as a function of temperature. Finally, the chapter looks into the possibilities of negligible entropy changes or enthalpy changes in the systems.

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