The concept of free energy

In order to minimize the effects of variables, scientists usually prefer to conduct experiments at constant pressure and temperature. When this is done and only the system being studied is considered, a new function— called the Gibbs free energy (hereafter called the free energy)—has been introduced. It is defined as follows  

H = enthalpy or heat content (joules), which is essentially a measure of the potential energy S = entropy (joules/degree Celsius) 

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The concept of free energy appears in other areas of science, notably biology. 

The coexistence of four phases in a one-component system has never been observed and is ruled out by a famous result from thermodynamics. The same Gibbs who introduced the concept of free energy derived this result by considering a system consisting of c components (individual... 

In this chapter we discuss thermodynamic quantities. We then expand the discussion to show how the concept of free energy is used in predicting biochemical pathways, and we explore the central role of ATP in providing energy for biochemical reactions. 

This expression serves as a precise mathematical definition of temperature. It is interesting to note that temperature, a variable with which we have intuitive and sensory familiarity, is defined based on entropy, one with which we may be less familiar. In fact, we shall see that entropy and temperature are intimately related in the concept of free energy, in which temperature determines the relative importances of energy and entropy in driving thermodynamic processes. 

The concept of free energy surfaces has proven its vitality over many years of fruitful applications to electron transfer kinetics. The direct connection... 

The chemical potential of species j indicates the free energy associated with that species and available for performing work. Because there are many concepts to be mastered before understanding such a statement, we first briefly explore the concept of free energy. (Further details are presented later in this chapter, in Chapters 3 and 6, and in Appendix IV.) We will introduce specific terms in the chemical potential of species j and then consider the extremely important case of water. 

The concept of free energy is introduced in Chapter 2 (Section 2.2A,B) in presenting the chemical potential of species /, fij. The chemical potential is actually the partial molal Gibbs free energy with respect to that species that is, fij equals (8G/drij)TPEh (Eq. IV.9 in Appendix IV), where the subscripts on the partial derivative indicate the variables that are held constant. We must consider the Gibbs free energy of an entire system to determine the chemical potential of species j. In turn, G depends on each of the species present, an appropriate expression being... 

Obviously the sea is an open, dynamic system with variable inputs and outputs of mass and energy for which the state of equilibrium is a construct. As we have seen, the concept of free energy, however, is no less important in dynamic systems. In considering equilibria and kinetics in ocean systems, it is useful to recall that different time scales need to be identified for the various processes. When a particular reaction of a phase or species has—within the time scale of consideration—a negligible rate, it is permissive to define a metastable equilibrium state. Similarly, in a flow system the time-invariant condition of a well-mixed volume approaches chemical equilibrium when the residence time is sufficiently large relative to the appropriate time scale of the reaction. 

In this appendix, we discuss briefly the concept of free energy of mixing and entropy of mixing, and the relatively newly defined concept of assimilation. A more detailed discussion of this topic may be found elsewhere (Ben-Naim 1987a,b). 

Use the concepts of free-energy change (AG) and electrochemical potential to predict active or passive transport. 

This means that we should talk about thermodynamics—but only a little bit. As you know it deals with the quantities of enthalpy (AH), enthropy (AS), free energy (AG), heat capacity (AC), pressure (p), and temperature (T). Thermodynamics is characterized by a plethora of formulas and has an antiquated reputation. The latter is no surprise, in that it goes back to the nineteenth century. The concept of free energy, for example, was introduced by Josiah Willard Gibbs in 1878. 

Structure is interpreted based on the concept of free energy, that is, the concept of equihbrium statistical mechanics. However, if the folding processes take place far from equilibrium, the concept of equilibrium statistical mechanics cannot be applied. On the other hand, from our point of view, the funnel-like structure would give a typical example where the strong dynamical correlation exists. If we can analyze how stable and unstable manifolds intersect in the folding processes, we can have an alternative explanation concerning the funnel, which is a future project from our approach. 

The concept of free energy is introduced, by Josiah Willard Gibbs to explain chemical equilibria. 

The concept of free energy is useful in defining the possibility of a reaction and in determining its limiting or equilibrium conversion. The formal definition of the equilibrium state of a chemical reaction is the state for which the total free energy is a minimum. Thus the well-known rule reaction can occur if AG is negative it cannot occur if AG is positive. Now we shall present the main features of the equilibrium state for ideal and nonideal gases. 

CP size has also been modeled using the concept of free energy by Cates and Deutsch (1986). Here, the conformational free energy of a CP in a melt of pure CPs is the sum of two terms and is given as... 

It is also possible to derive the Nernst distribution law from thermodynamic considerations using the concept of free energy (Lewis and Randall 1923). At equilibrium, the chemical potential of a solute X has to be the same in the aqueous and the organic phase, i.e.. 

The rate of most chemical reactions increases rapidly with temperature slow reactions can be transformed into fast reactions by heat. The effect was first explained and quantified in terms of activation energy. Later on (Section 3.1.4), when discussing the transition state theory, we shall use the concept of free energy of activation instead, but for now let us see how the simpler concept of energy of activation accounts for the effect of temperature on reaction rates. 

In this appendix, we will explain two important thermodynamic concepts needed in this book in diflFerent places The first concept is thermal activation of processes, the second the concept of free energy. A detailed discussion of thermodynamics can be found, for example, in Reif [116]. 

It is very convenient to define a new thermodynamic quantity in terms of H and S that will be directly useful as a criterion of spontaneity. For this purpose, the American physicist J. Willard Gibbs (1839-1903) introduced the concept of free energy, G, which is a thermodynamic quantity defined by the equation G = H — TS. This quantity gives a direct criterion for spontaneity of reaction. 

Of books published in 1969, that by Mayer gives a formal and rigorous approach to statistical mechanics, with a few examples of application and with little comparison between theory and experiment. Morton and Beckett s Basic Thermodynamics deals with sixth-form, O.N.C., and undergraduate courses, but only about one-sixth of the book is directly related to chemical aspects. However, applications to chemistry include the use of the concepts of free energy and activity and the determination of equilibrium constants. Appendices treat units, bond dissociation energies, standard electrode potentials, questions, and sources of useful equipment, and provide further information. 

In this chapter, an attempt will first be made to present the concept of free energy in a simple, descriptive way in order to introduce the nature of the concept. Then various methods of obtaining free energy data will be... 

Introduction of the concept of free energy was the origin of the development of a number of significant calculation methods for equilibrium systems. In this chapter, the concept of the Gibbs free energy is introduced and the practical application of this quantity is illustrated through problems. 

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