Free energy change defined

Let us define the respective basicity by — AG in the gas phase and — AG" in aqueous solution. For discussions concerning the relative strength in basicity of a series of methyl-amines, only the relative magnitudes of these quantities are needed. Thus the free energy changes associated with the protonation of the methylamines relative to those of ammonia are defined as... 

Neither the principles of thermodynamics nor theories of reaction rates require that there should be such linear relationships. There are, in fact, numerous reaction series that fail to show such correlations. Some insight into the origin of die correlation can be gained by considering the relationship between the correlation equation and the free-energy changes involved in the two processes. The line in Fig 4.2 defines an equation in which m is the slope of the line ... 

But spontaneity depends on the concentrations of reactants and products. If the ratio [Bl YCA] is less than a certain value, the reaction is spontaneous in the forward direction if [Bl YCA] exceeds this value, the reaction is spontaneous in the reverse direction. Therefore, it is useful to define a standard free-energy change (AG°) which applies to a standard state where [A] = [B] = 1 M. 

In Section 8.2 solvation energy AGsoiv was defined as the free energy change upon transferring a solute from the gas into a solvent. We can now relate the transfer free energy to solvation energies ... 

The Unitary Part of a Free Energy Change. In this way we can obtain values for the unitary terms characteristic of processes of each of the four types discussed in Chapters 1 and 2. At this point it will be convenient to review what was said in those chapters and to relate that discussion to (71) and (72). In Sec. 11 the dissociation energy D was introduced by analogy with the dissociation energy T3tac, defined for the Bame molecule in a vacuum. In solution (as in a gas or vapor) the parts... 

The Gibbs-Helmholtz equation can be used to calculate the standard free energy of formation of a compound. This quantity, AGf, is analogous to the enthalpy of formation, AH . It is defined as the free energy change per mole when a compound is formed from the elements in their stable states at 1 atm. 

Equations (9.7) and (9.8) define K, the equilibrium constant for the reaction.b It is sometimes referred to as the thermodynamic equilibrium constant. As we shall see, this ratio of activities can be related to ratios of pressure or concentration which, themselves, are sometimes called equilibrium constants. But K, as defined in equations (9.7) and (9.8), is the fundamental form that is directly related to the free energy change of the reaction. 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

When the reactants are present in concentrations of 1.0 mol/L, AG is the standard free energy change. For biochemical reactions, a standard state is defined as having a pH of 7.0. The standard free energy change at this standard state is denoted by AG". ... 

When one chooses a radical as the reference system, the stability of a carbocation or carbanion can be defined by the free-energy change for discharging the ion in vacuum, and the change can be approximately described by the classical Born equation (3) (Bom, 1920), provided that the ion is represented by a conducting sphere on which the charge is located. 

In words, in any process that occurs at constant T and P, the free energy change for the system is negative whenever the total entropy change is positive that is, whenever the overall process is spontaneous. Defining a new function and imposing some restrictions provides a way to use properties of a system to determine whether a process is... 

When put into an appropriate model [N0rskov et al., 2004], the binding energy correlations directly define a limit to t/o on the metals obeying the linear relations shown in Fig. 3.7. Since all intermediates are dependent on Eq, it is possible to plot the heights of all the steps AGi 4 as functions of Eq at zero potential. The step with the smallest free energy change wUl define I/ork (Fig. 3.8) ... 

Before we will discuss the electrochemical system, it is important to define the properties and characteristics of each component, especially the electrolyte. In the following, we assume macroscopic amounts of an electrolyte containing various ionic and nonionic components, which might be solvated. In the case that this bulk electrolyte is in thermodynamic equilibrium, each of the species present is characterized by its electrochemical potential, which is defined as the free energy change with respect to the particle number of species i ... 

In order to have a consistent basis for comparing different reactions and to permit the tabulation of thermochemical data for various reaction systems, it is convenient to define enthalpy and Gibbs free energy changes for standard reaction conditions. These conditions involve the use of stoichiometric amounts of the various reactants (each in its standard state at some temperature T). The reaction proceeds by some unspecified path to end up with complete conversion of reactants to the various products (each in its standard state at the same temperature T). 

The free energy of chemical reactions may be estimated both under the standard conditions and under real, or physiological, conditions. The standard free energy, AG°, of a biochemical reaction is defined as a free energy change under the standard conditions, i.e. at the concentration of reactants 1 mol/litre, temperature 25 °C <298 X), and pH 7. 

Almost all problems that require knowledge of free energies are naturally formulated or can be framed in terms of (1.15) or (1.16). Systems 0 and 1 may differ in several ways. For example, they may be characterized by different values of a macroscopic parameter, such as the temperature. Alternatively, they may be defined by two different Hamiltonians, 3%o and 3%, as is the case in studies of free energy changes upon point mutation of one or several amino acids in a protein. Finally, the definitions of 0 and 1 can be naturally extended to describe two different, well-defined macroscopic states of the same system. Then, Q0 is defined as ... 

The change in free energy of a system between two states (A,B) (AG,) is calculated after each step of the transformation. Since the free energy is a state function the total free energy change, AG, is the sum of the intermediate AG,s. An intermediate state22 of the system is defined as,... 

The solvation free energy is defined as the free energy change to transfer a solute molecule from vacuum to solvent [13-15]. It can be considered to have three components ... 

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