Spontaneous change Gibbs energy criteria

The decrease in Gibbs free energy as a signpost of spontaneous change and AG = 0 as a criterion of equilibrium are applicable to any kind of process, provided that it is occurring at constant temperature and pressure. Because chemical reactions are our principal interest in chemistry, we now concentrate on them and look for a way to calculate AG for a reaction. 

Thermodynamics is used to predict whether reactants have a spontaneous tendency to change into products. This tendency is associated with a decrease in the free energy or Gibbs energy of the system (G) to a minimum. As a consequence, the thermodynamic criterion for spontaneous change at constant temperature and pressure is AG < 0. Under standard conditions (concentrations = 1 M, and P = 1 atm), the standard Gibbs energy variation (AG°) is related with the equilibrium constant (A) by equation 11 ... 

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. 

The Legendre transform that defines the further transformed Gibbs energy G", which provides the criterion for spontaneous change and equilibrium in dilute... 

Since coenzymes, and perhaps other reactants, are in steady states in living cells, it is of interest to use a Legendre transform to define a further transformed Gibbs energy G" that provides the criterion for spontaneous change and equilibrium at a specified pH and specified concentrations of coenzymes. This process brings in a further transformed entropy S" and a further transformed enthalpy H", but the relations between these properties have the familiar form. 

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... 

The transformed Gibbs energy provides the criterion for spontaneous change and equilibrium in systems of enzyme-catalyzed reactions when the independent variables for the system are T, P, pH, and Wc - Notice that making this Legendre transform has introduced ) as a natural variable, but it has not changed the number of natural variables because there is now one less component that is conserved, the hydrogen atom component. 

When the pH is specified, the criterion for spontaneous change and equilibrium is provided by the transformed Gibbs energy and the reactants can be taken to be HgvM, HgvMOa, and O2 that are involved in the following biochemical reaction. 

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. 

Equation 8.30 provides an extremely useful criterion for determining the direction of spontaneous changes and the nature of physical and chemical equilibrium, hi addition, the changes in the Gibbs free energy function enable us to determine the amount of work that can be done in a process at constant temperature and pressure. To see this, start with the expression for AG for a process at constant temperature and pressure (Equation 8.29) ... 

The Gibbs free energy change as a criterion of spontaneity is summarized as follows ... 

Fig. 2.13 The criterion of spontaneous change is the increase in total entropy of the system and its surroundings. Provided we accept the limitation of working at constant pressure and temperature, we can focus entirely on the properties of the system and express the criterion as a tendency to move to lower Gibbs energy.

Our interest in chemical potentials (and activities) arises from the fact that the Gibbs energy of a mixture can be expressed in terms of the amounts of the substances and their chemical potentials, as shown by equations (13.31) and (13.32). These two equations, and the second law of thermodynamics, can be used to develop the criterion for predicting the direction of spontaneous chemical change. 

Gibbs energy, G, is a thermodynamic function designed to produce a criterion for spontaneous change when considering processes that occur at constant temperature and constant pressure. It is defined through the equation G = H — TS. 

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. 

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 ... 

It emerges from thermodynamics that the overall thermodynamic criterion for spontaneity is vested in a quantity defined as the Gibbs (free) energy change, AG which, for an isothermal (Frame 1) process, is defined by the equation ... 

The change in the Gibbs free energy provides a criterion for the spontaneity of any process occurring at constant temperature and pressure (Fig. 13.11). To predict whether a chemical reaction is spontaneous at given values of T and P, it is... 

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