Spontaneity Gibbs function change

The values of these functions change when thermodynamic processes take place. Processes in which the Gibbs energy decreases (i.e., for which AG<0), will take place spontaneously without specific external action. The Gibbs energy is minimal in the state of equilibrium, and the condition for equilibrium are given as... 

In the following sections, we introduce the concept of a thermodynamic universe (i.e. a system plus its surroundings). For a reaction to occur spontaneously in a system, we require the change in Gibbs function G to be negative. We then explore the thermodynamic behaviour of G as a function of pressure, temperature and reaction composition. 

Figure 5.2 Graph of molar Gibbs function Gm as a function of temperature. Inset, at temperatures below r(meit) the phase transition from liquid to solid involves a negative change in Gibbs function, so it is spontaneous...

The protons and oxide ions combine to form water. Again, the value of AGr for Equation (7.36) is negative, because the reaction is spontaneous. AG would be positive if we wrote Equation (7.36) in reverse. The change in sign follows because the Gibbs function is a function of state (see p. 83). 

The reaction also can be carried out reversibly if additional constraints are placed on the system, as in the cell illustrated by Figure 7.2. The H2 and CI2 electrodes are connected to a potentiometer. If the electromotive force of the cell is opposed by the eleetromotive force of the potentiometer, which is maintained at an infinitesimally lower value than that of the H2-CI2 cell, then the conversion to HCl can be carried out reversibly, although it would take an infinitely long time to obtain one mole of reaction. The change in the Gibbs function is the same for either the reversible or the explosively spontaneous path for carrying out the transformation, because the initial and final states are the same in both cases. However, the amount of useful (electrical) work is different, and, for the reversible path... 

CALCULATION OF CHANGE IN THE GIBBS FUNCTION FOR SPONTANEOUS PHASE CHANGE... 

Thus far we have restricted our attention to phase changes in which equilibrium is maintained. It also is useful, however, to find procedures for calculating the change in the Gibbs function in transformations that are known to be spontaneous, for example, the freezing of supercooled water at —10°C ... 

The method of determination from measurements of cell potentials depends on the possibility of carrying out a transformation reversibly in an electrical cell. (See Fig. 7.2.) In this case, the spontaneous tendency of the transformation wUl be opposed by an opposing potential just sufficient to balance the potential in the electrical ceU produced by that spontaneous tendency. The potential observed under such circumstances is related to the change of the Gibbs function for the reaction by Equation (7.84)... 

In Frame 13, section 13.2 we established the Gibbs function, G, as the index of spontaneous change. Equation (13.10) Frame 13 gave the relationship between G and the enthalpy, H and entropy, S namely ... 

You must know the Gibbs function, and, most importantly, that a negative AG indicates a spontaneous reaction. Realize that the Gibbs function deals with the change in enthalpy and entropy of a system. 

To use entropy as a criterion of spontaneous change, it is necessary to investigate both system and surroundings. For that reason, a further thermodynamic function, the free energy, or Gibbs function G, is used. This combines the enthalpy H and the entropy S and allows the combination of the effects of both H and S on the system only, generally at constant pressure. The quantities U, if, G and S are referred to as state functions, since they depend only on the state of the system. 

The Gibbs function expresses the direction of a spontaneous change If ArG < 0, the reaction proceeds A—> B, and if ArG > 0, the reaction proceeds B—>A. The condition of equilibrium can be further developed by introduction of the standard reaction Gibbs function at the standard pressure of 1.013 bar and reaction temperature T, ArG° ... 

The change t/Gsyst is negative when the process is spontaneous. As a result, at constant pressure and temperature, the molar reaction Gibbs function ArG must be negative in the case of a spontaneous process ... 

In other words, the Gibbs function of a system will always be minimized in a spontaneous process (dG < 0). When the Gibbs energy reaches a local minima, where the change is zero (dG = 0), the reaction stops and local thermodynamic equilibrium is achieved, as illustrated in Figure 3.10. 

There is no single criterion for the system alone that applies to all processes. However, if we restrict the conditions to constant temperature and pressure, there is a state function whose change for the system predicts spontaneity. This new state function is the free energy (G), which was introduced by the American J. Willard Gibbs and is defined by Equation G = H - T S As usual, H is enthalpy, T is absolute temperature, and S is entropy. 

Thus far we have observed that the Gibbs and Planck functions provide the criteria of spontaneity and equilibrium in isothermal changes of state at constant pressure. If we extend our analysis to systems in which other constraints are placed on the system, and therefore work other than mechanical work can be performed, we find that the Gibbs and Helmholtz functions also supply a means for calculating the maximum magnitude of work obtainable from an isothermal change. 

The free energy functions are defined by explicit equations in which the variables are functions of the state of the system. The change of a state function depends only on the initial and final states. It follows that the change of the Gibbs free energy (AG) at fixed temperature and pressure gives the limiting value of the electrical work that could be obtained from chemical transformations. AG is the same for either the reversible or the explosively spontaneous path (e.g. H2 -I- CI2 reaction) however, the amount of (electrical) work is different. Under reversible conditions... 

The use of this Legendre transform has introduced the intensive property T as an independent variable. It can be shown that the criterion for spontaneous change and equilibrium is given by (dG)rp 0. The Gibbs energy is so useful because T and P are convenient intensive variables to hold constant and because, as we will see shortly, if G can be determined as a function of T and P, then S, V, H, and U can all be calculated. 

However, using entropy as a criterion of whether a biochemical process can occur spontaneously is difficult, as the entropy changes of chemical reactions are not readily measured, and the entropy change of both the system and its surroundings must be known. These difficulties are overcome by using a different thermodynamic function, free energy (G), proposed by Josiah Willard Gibbs which combines the first and second laws of thermodynamics ... 

The choice of independent variables is a very important decision in thermodynamics (6). In chemical thermodynamics, the independent variables are usually T, P, and amounts of species, and the criterion of spontaneous change and equilibrium is provided by the Gibbs energy G. When G can be expressed as a function of T, P, and [nj], the total differential of G can be expressed by a fundamental equation made up of additive terms proportional to dT, dP, and [dnj]. For example, if g is a function of x and y, the total differential of g is given by... 

Spontaneous change or equilibrium is described when the RHS of Eq. 3.4 or 3.5 is > or =0, respectively. To restrict the evaluation to measurable properties of the system rather than of the surroundings, free energy functions have been derived (Gibbs, Helmholtz). Most protein-ligand interactions occur at constant temperature and pressure, so that the only work is -PAV The second law then is represented by... 

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