Chemistry
Free Energy and Equilibrium
Free energy is a measure of a system's ability to do work. In a system at equilibrium, the free energy is at a minimum, indicating a stable state. Changes in free energy can be used to predict whether a reaction will occur spontaneously, with a decrease in free energy indicating a reaction that will proceed without added energy.
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11 Key excerpts on "Free Energy and Equilibrium"
- Wallace Brey(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Spontaneous chemical processes are those that take the sys-tem in the direction of a free energy minimum; the situation at the min-imum corresponds to an equilibrium condition. Reactions tending away from equilibrium, reactions that therefore lead to an increase in the free energy of the system, must have some external driving force if they are to take place. F R E E E N E R G Y C H A N G E S F O R P H Y S I C A L P R O C E S S E S A T C O N S T A N T T E M P E R A T U R E For processes in which the temperature does not change, the free en-ergy change can be calculated from Equation (4-20). For a physical change, such as a phase change, at constant temperature and pressure, AH is equal to T AS, so that AG is equal to zero. It is therefore possible to make the very important statement that the free energy per mole of any material in one phase is the same as the free energy per mole in any other phase with which the first phase is in equilibrium. Processes such as the melting of a pure solid or the vaporization of a pure liquid, 1 3 0 FOUR THERMODYNAMICS: SECOND LAW AND EQUILIBRIUM if conducted at a fixed pressure such as atmospheric pressure, neces-sarily fall into the category of constant-temperature processes. If the phases concerned in an equilibrium are mixed phases, the same principle of equal free energy applies for each component. If two phases in which the free energy of some component differs are in contact, then there will be a spontaneous transfer of that component from the phase in which its free energy is greater to the phase in which its free energy is less. For an ideal gas, the value of the enthalpy change for any alteration in pressure and volume at constant temperature is equal to zero.
eBook - PDF- Young, William Vining, Roberta Day, Beatrice Botch(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
Because it can be confusing to know when to use the different energies and to what situa-tions they apply, their definitions are summarized here. 1. Internal energy, E , is the sum of all the submicroscopic kinetic and potential energies of all the particles that make up a system. The change in internal energy, uni2206 E , is calcu-lated from the first law of thermodynamics, uni2206 E 5 q 1 w . 2. Enthalpy, H , is a defined energy that is based on the internal energy, H 5 E 1 PV . It is convenient to use enthalpy in the constant-pressure processes that are common in chemistry because uni2206 H 5 q , the heat absorbed at constant pressure. You can think about enthalpy as the internal energy measured at constant pressure. 3. Gibbs free energy, G , like enthalpy is a defined energy ( G 5 H 2 TS ) . Free energy is related to reaction spontaneity by the second law, uni2206 S universe 7 0 . At constant temperature and pressure, the change in the entropy of the universe is equal to 2 uni2206 G > T , and under these conditions, uni2206 G points the direction of chemical change. Internal energy, E , and enthalpy, H , are first law energies. They are associated with the amount of energy exchanged. Gibbs free energy is a second law energy. It has to do with the direction of change and the quality of the energy, the maximum amount of energy that is available to do work. Interactive Table 20.3.1 Relationship between uni2206 G and Reaction Spontaneity uni2206 G 6 0 Spontaneous in the forward direction uni2206 G 5 0 At equilibrium; no net change will occur uni2206 G 7 0 Nonspontaneous in the forward direction; spontaneous in the reverse direction Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300
eBook - PDFBasic Physical Chemistry
The Route to Understanding
- E Brian Smith(Author)
- 2012(Publication Date)
- ICP(Publisher)
8 Chemical Equilibrium The position of equilibrium can be expressed for an isolated system, or for a system and its surroundings, in terms of entropy (Section 7.6). Under these circumstances, the entropy will be a maximum at equilibrium and for any small change d S = 0. However, it is usually more convenient to express the criteria for equilibrium in terms of the properties of the system alone without reference to its surroundings, and the systems we deal with in chemistry are often not isolated and may transfer energy to and from their surroundings. 8.1 Free energy To identify conditions that define the position of equilibrium for systems that are not isolated, we need to return to the concept of maximum possible work. For a reversible change, since d S = d q rev /T , we obtain d U = d q rev + d w rev = T dS + d w rev . The reversible work is d w rev = d U − TdS. We define a new thermodynamic state function, the Helmholtz free energy , A (now often referred to simply as Helmholtz energy), by A = U − TS and, at constant temperature and volume, d w rev = d U − T d S = d A . Since this equality is defined for a reversible process, d w = d A is a condition for the system to be at equilibrium. If, during a reversible change, the system does work, both d w and d A will be negative. The Helmholtz free energy is equivalent, in a system at constant temperature and volume, to the energy in a mechanical system. It is a measure of the maximum amount of work that can be done by the system 175 176 | Basic Physical Chemistry on its surroundings. For a spontaneous change, the system will do less work and d w > d A . Both d w and d A will be negative, but d w will be less negative than d A . Most chemical systems (other than electrochemical cells) do only PV work which, for a system at constant volume, is zero. For such a system, d w = 0 and d A < 0 and the change in A will again be negative.
eBook - PDFBiosimulation
Simulation of Living Systems
- Daniel A. Beard(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
5 Chemical reaction systems: thermodynamics and chemical equilibrium Overview This and the following two chapters are focused on analyzing and simulating chem- ical systems. These chapters will introduce basic concepts of thermodynamics and kinetics for application to biochemical systems, such as biochemical synthesis, cel- lular metabolism and signaling processes, and gene regulatory networks. Although we have seen examples of chemical kinetics in previous chapters, notably in Sections 2.3 and 2.4, in those examples we developed the expressions governing the chemistry more from intuition than from a physical theory. One of the primary goals here will be to develop a formal physical/chemical foundation for analyzing and simulating complex biochemical systems. As is our practice throughout this book, these concepts will be applied to analyze real data (and understand the behavior of real systems) later in this chapter and elsewhere. Yet, because the rules governing the behavior of biochemical systems are grounded in thermodynamics, we must begin our investigation into chemical systems by establishing some fundamental concepts in chemical thermo- dynamics. The concept of free energy is particularly crucial to understanding thermodynamic driving forces in chemistry. We will see that both a physical definition and an intuitive understanding of free energy require physical definitions and intuitive understandings of temperature and entropy. All of this means that this chapter will begin with some abstract thought experiments and derivations of physical concepts. 5.1 Temperature, pressure, and entropy 5.1.1 Microstates and macrostates All thermodynamic theory arises from the fact that physical systems composed of many atoms and/or molecules attain a large number (often a practically infinite 146 Chemical reaction systems: thermodynamics and chemical equilibrium number) of microstates under defined macroscopic conditions, such as temper- ature, pressure, and volume.
eBook - PDF- Donald T. Haynie(Author)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
Chapter 4 Gibbs free energy – theory A. Introduction This chapter discusses a thermodynamic relationship that provides a basis for explaining spontaneous chemical reactivity, chemical equilibrium, and the phase behavior of chemical compounds. The relationship involves a thermodynamic state function that enables prediction of the direction of a chemical reaction at constant tem-perature and pressure . The constraints of fixed T and p might seem annoyingly restrictive, because they are less general than the requirements of the Second Law, but in fact the gains made on imposing the constraints will outweigh the losses. How is that? One reason is at any given time an individual organism is practically at uniform pressure and temperature (but be sure to see the Exercises at the end of the chapter). Another is that constant temperature and pressure are the very conditions under which nearly all bench-top biochemistry experiments are done. Yet another is that, although the total entropy of the universe must increase in order for a process to be spontaneous, evaluation of the total entropy change requires mea-surement of both the entropy change of the system and the entropy change of the surroundings. Whereas 1 S system can often be found without too much difficulty, albeit only indirectly, 1 S surroundings can be hard to measure! How could one measure the entropy change of the rest of the universe? The subject of the present chapter provides a way around the difficulty. A particularly clear example of the inadequacy of 1 S system to predict the direction of spontaneous change is given by the behavior of water at its freezing point. Table 4.1 shows the thermo-dynamic properties of water for the liquid ! solid phase transition. The decrease in internal energy (which is practically identical to the enthalpy as long as the number of moles of gas doesn’t change; see Chapter 2 ) would suggest that water freezes spontaneously in the range 263–283 K.
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
The name of this quantity recognizes the contributions of J. Willard Gibbs, a professor of mathematical physics at Yale from 1871 until the early 1900s, who some consider to be the greatest scientist produced by the United States. The Gibbs free energy of a system at any moment in time is defined as the enthalpy of the system minus the product of the temperature times the entropy of the system. The Gibbs free energy is therefore a state function because it is defined in terms of thermodynamic properties (enthalpy, entropy, and temperature) that are state functions. At a given temperature, the change in the Gibbs free energy of the sys- tem that occurs during a reaction is therefore equal to the change in the enthalpy of the system minus the product of the temperature times the change in entropy of the system. The beauty of the equation defining changes in the free energy of a system is its ability to determine the relative importance of the enthalpy and entropy terms for a particular reaction at a given temperature. The change in the free energy of the system that occurs during a reaction measures the balance between the two driving forces that determine whether a reaction is spontaneous. As we have seen, the enthalpy and entropy terms have different sign con- ventions. The enthalpy term is favorable when it is negative, whereas the entropy term is favorable when positive. ¢G = ¢H - T¢S G = H - TS The overall entropy of reaction is negative because the reaction transforms 4 moles of reactants into 2 moles of products. According to these calculations, ¢H° for the reaction is 92.2 kJ/mol rxn and ¢S° for the reaction is 198.8 J/mol rxn K. Enthalpy (¢H° 6 0) therefore drives the reaction toward the products, but entropy (¢S° 6 0) drives the reac- tion toward the reactants.
eBook - PDFChemistry
An Atoms First Approach
- Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
The situation is different for a chemical reaction system, as illustrated in Fig. 16.7(b). In Fig. 16.7(b) the ball will not get to point B because there is a lower po- tential energy at point C. Like the ball, a chemical system will seek the lowest possible free energy, which, for reasons we will discuss below, is the equilibrium position. Therefore, although the value of DG for a given reaction system tells us whether the products or reactants are favored under a given set of conditions, it does not mean that the system will proceed to pure products (if DG is negative) or remain at pure reactants (if DG is positive). Instead, the system will spontaneously go to the equilibrium posi- tion, the lowest possible free energy available to it. In the next section we will see that the value of DG8 for a particular reaction tells us exactly where this position will be. 16.8 Free Energy and Equilibrium When the components of a given chemical reaction are mixed, they will proceed, rap- idly or slowly depending on the kinetics of the process, to the equilibrium position. In Chapter 12 we defined the equilibrium position as the point at which the forward and reverse reaction rates are equal. In this chapter we look at equilibrium from a thermo- dynamic point of view, and we find that the equilibrium point occurs at the lowest value of free energy available to the reaction system. As it turns out, the two defini- tions give the same equilibrium state, which must be the case for both the kinetic and thermodynamic models to be valid. To understand the relationship of free energy to equilibrium, let’s consider the fol- lowing simple hypothetical reaction: As gd m Bs gd where 1.0 mole of gaseous A is initially placed in a reaction vessel at a pressure of 2.0 atm. The free energies for A and B are diagramed as shown in Fig.
- Peter V. Hobbs(Author)
- 2000(Publication Date)
- Cambridge University Press(Publisher)
2 Chemical thermodynamics Heat can be released or absorbed during a chemical reaction. This pro-vides a powerful method for studying chemical equilibrium by means of chemical thermodynamics. Thermodynamics is based on a few funda-mental postulates, called the first, second, and third laws of thermo-dynamics. We will discuss these laws first, and then apply them to chemical equilibria. 2.1 The first law of thermodynamics; enthalpy In addition to the macroscopic kinetic and potential energy that a body or system as a whole may possess, it also contains internal energy due to the kinetic and potential energy of its molecules or atoms. Increases in internal kinetic energy in the form of molecular motions are manifested as increases in the temperature of the system, while changes in the poten-tial energy of the molecules are caused by changes in their relative configurations. Let us suppose that a system of unit mass takes in a certain quantity of heat energy q (measured in joules). As a result, the system may do a certain amount of external work w (also measured in joules). The excess energy supplied to the system, over and above the external work done by the system, is q - w. Therefore, if there is no change in the macro-scopic kinetic and potential energy of the system, it follows from the principle of conservation of energy that the internal energy of the system must increase by q -w. That is, q - w = u 2 -Mi (2.1) where u x and u 2 are the internal energies of a unit mass of the system before and after the change. In differential form Eq. (2.1) becomes 17 18 Chemical thermodynamics dq-dw = du (2.2) where dq is the differential increment of heat added to a unit mass of the system, dw the differential increment of work done by a unit mass of the system, and du the differential increment in internal energy of a unit mass of the system. Equations (2.1) and (2.2) are statements of the first law of thermodynamics.
eBook - PDFAn Introduction to Chemical Metallurgy
International Series on Materials Science and Technology
- R. H. Parker, D. W. Hopkins(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
(3) Methods of experimental determination of free energy changes will be discussed in Section 2.14 at the end of the chapter. 2.9. Chemical Equilibrium: The Equilibrium Constant In any chemical reaction A+B = C + D, the reaction will proceed in the forward direction (left to right), and also in the reverse direction (right to left). If the substances A, B, C and D were placed together in a box, isolated from the chemical action of their surroundings, the forward and reverse reactions would proceed. The Law of Mass Action (C. M. Guldberg and P. Waage, 1867) states that the rate of chemical reaction is proportional to the active masses of the reacting substances. It is now understood that, by active masses, we can mean the concentrations of the reacting substances, or, in the case of gaseous reactants, their partial pressures, where PA = P . *A, (2.28) p A being partial pressure of A, x A its mole fraction, and P the total pressure of the gaseous system. The mole fraction of a substance in a phase is the number of molecules of the substance present, N A , divided by the total number of molecules present in the phase, N. ENTROPY, FREE ENERGY 6 7 ΧΑ = η£. (2-29) If we have pure solids or liquids involved in a reaction, their active masses can be considered to be unity for the purposes of this approach. This leads to the relationship involving generalized measure-ments of concentration c A , c B , etc., rate of forward reaction = k x . c A . c B , (2.30) rate of reverse reaction = k 2 . c c . c D . (2.31) (The significance of k t and k 2 , the velocity constants of reactions, will be discussed further in Chapter 4.) The two reactions will proceed until eventually the rate of the forward and reverse reactions are the same, provided the temperature and pressure remain unaltered. No further change in the overall composition of the system occurs, and the system is said to be in a state of chemical equilibrium.
eBook - PDF- Don Shillady(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
6 Gibbs ’ Free Energy and Equilibria INTRODUCTION In previous chapters, we have stressed that in nature energy tends to decrease while entropy tends to increase. A naive fi rst consideration of any machine or process is that energy is needed to continue operation and we often overlook energy expended on various repair activities that are a form of entropy management. It becomes more obvious that entropy is a factor when one studies chemical processes that ‘‘ should ’’ occur based on energy considerations but nevertheless require some sort of a catalyst or other special conditions, which imply geometric constraints that overcome the natural tendency of randomness to increase. The value of D S is a change in a state variable but the path can be modi fi ed by special conditions such as the introduction of a catalytic surface, which allows reactants to meet side-by-side compared to random collisions in the gas phase. Josiah Willard Gibbs (1839 – 1903) was a foremost U.S. scientist (Figure 6.1) who made important advances in thermo-dynamics applying the new idea of ‘‘ chemical potential ’’ ( D G = n ) as a free energy per mole of a substance in phase diagrams and applied to equilibria. At the time of his work, few people understood it but it was later developed into the idea of free energy and greatly affected thinking, teaching, and problem solving in chemical engineering. Gibbs ’ research used what was advanced mathematics in his time but remained at what we call ‘‘ classical physics ’’ today since he predated quantum mechanics. Gibbs is especially noteworthy in that he carried out research in the United States at a time when the turmoil of the U.S. Civil War and settling in the West were not as conducive to research as was the case in Europe in the late 1800s. However, Gibbs had spent a year each in Paris, Berlin, and Heidelberg and had written contact with foremost scientists in Europe.
eBook - PDFStatistical Physics of Biomolecules
An Introduction
- Daniel M. Zuckerman(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
Once the conditions are set, the pertinent free energy is all of the following: (1) It is the logarithm of that partition function obeying the conditions, multiplied by ( − k B T ) . (2) It quantifies the amount of work that can be done by the system under the condi-tions. (3) It tends to become minimized if the system is initially out of equilibrium, as we will see below. The notation for free energies uses the conditions (the parameters held constant) as “natural” variables. Therefore, each free energy should always be written in a way that make the corresponding conditions obvious. The free energies we have discussed are • F ( T , V , N ) = E − TS , the Helmholtz free energy • G ( T , P , N ) = F + P V , the Gibbs free energy • ( T , V , μ ) = F − N μ , the grand canonical potential Note that the total energy is the sum of kinetic and potential contributions—that is, E = KE + U . 174 Statistical Physics of Biomolecules: An Introduction 7.6.2 F REE E NERGIES A RE “S TATE F UNCTIONS ” As we have seen more than enough times, a free energy is defined from a partition function. In turn, the partition function simply integrates to some number once the natural variables—for example, T , V , N in Z ( T , V , N ) —are fixed. Thus, the natural variables define the free energy: once you specify the variables, the free energy is some number. A free energy is called a “state function” because it comes from a definite integral depending only on the equilibrium “state” of the system—that is, only on the natural variables. It does not depend on how that state was reached (maybe by a weird nonequilibrium process) because this doesn’t change the equilibrium integral. The notion of a state function is important in understanding free energy differ-ences generally, and especially in understanding “thermodynamic cycles,” which we shall study in the context of binding in Chapter 9.
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