Equilibrium criteria for

Kinetic-molecular theory provides an explanation on a molecular level for this equilibrium. Evaporation from the liquid occurs as fast moving molecules on the surface escape from the liquid. In turn, molecules in the gas phase strike the liquid and condense, As the concentration (pressure) of gas molecules builds up in the gas phase, the rate of condensation increases. Eventually, a pressure is reached where the rate of condensation and rate of evaporation just balance, and equilibrium is achieved. The equilibrium pressure is denoted by p and is known as the vapor pressure. The magnitude ofp depends upon the substance, composition of the liquid, and any two of our thermodynamic variables such as temperature and total pressure. The criteria for equilibrium that we will now derive provide the thermodynamic relationships that will help... 

To obtain the criteria for equilibrium we combine equations (5.76) and (5.77) to give... 

Equation (5.81) gives us the criteria for equilibrium or spontaneity. For example, for equilibrium in the reaction leading to the formation of ammonia... 

The chapter also outlines the criteria for equilibrium in terms of the Gibbs function and chemical potential, together with the criteria for spontaneity. 

Now that we have developed convenient criteria for equilibrium and for spontaneity we can apply the laws of thermodynamics to problems of interest. In this chapter, we will deal with changes of phase in one-component systems, which are transformations of concern to the chemist and of particular concern to the geologist and the materials scientist. 

However, these potentials do not yet express the second law in the form most convenient for chemical applications. Open laboratory vessels exposed to the temperature and pressure of the surroundings are subject neither to constraints of isolation (as required for entropy maximization) nor to adiabatic constant-volume conditions (as required for energy minimization). Hence, we seek alternative thermodynamic potentials that express the criteria for equilibrium under more general conditions. 

The basic question in all of thermodynamics is A certain system is under such and such constraints, what is the equilibrium state that it can go to spontaneously The amazing thing is that this question can be answered by making macroscopic measurements. Thermodynamics does not deal with the question as to how long it will take to reach equilibrium. We now have seven criteria for equilibrium in a one-phase system with one species and only PV work. The criteria of equilibrium provided by these thermodynamic potentials are (dt/)S K n 0, (dH)SPn < 0, (d/4)r K 0, (dG)rp <0, (dC/[/r])s v >(1 < 0,... 

These equations give criteria for equilibrium similar to those obtained from Eqs. (20)-(24). For example, at constant T, P, and generalized driving forces Lt, a process is at equilibrium if dG = 0 and proceeds spontaneously if dG < 0. 

This last result makes it possible to formulate criteria for equilibrium. 

On the basis of standard criteria for equilibrium, stability limits, and criticality yielding coexistence curve (binodal), spinodal line, and critical point, the phase behavior maybe predicted using Eq. (1) ... 

There seems to be a law of nature that, in an equilibrium system, the chemical hardness and the physical hardness have maximum values, compared with nearby non-equilibrium states. However, it must not be inferred that these maximum principles are being proposed to take the place of estabished criteria for equilibrium. Instead, they are necessary consequences of these fundamental laws. It is very clear that the Principle of Maximum Hardness for electrons is a result of the quantum mechanical criterion of minimum energy. Similarly, Sanchez has recently derived the relationship (dB/dP) = 5 by a straightforward manipulation of the thermodynamic equation of state.The PMPH is a result of the laws of thermodynamics. 

In all of the these relations, choosing the inequality provides the criteria for spontaneous change. Choosing the equal sign gives us the criteria for equilibrium under the conditions specified. 

Since these equations follow directly from the equality of the molar Gibbs energy in each phase at phase equilibrium, EqS. 7.4-7 can be used as criteria for equilibrium. They will be used for this purpose in this book. 

The criteria for equilibrium are very important, and may be summarized as follows ... 

CRITERIA FOR EQUILIBRIUM AMONG COEXISTING PHOSPHATES AND OTHER PHASES... 

Equilibrium conditions are those in which the forces resisting the process are just balanced by those which cause it. Therefore, any small change that would take place would have to be a reversible one if no dissipative actions are involved. Since a reversible process is one which takes place always at equilibrium conditions, the criteria of reversibility must include the criteria for equilibrium conditions at constant pressure and temperature. 

Of the several criteria for equilibrium and spontaneity, we shall have the most use for the one involving dG or AG, simply because most chemical reactions and phase transformations are subject to the conditions, constant T and p. If we know how to compute the change in Gibbs energy for any transformation, the algebraic sign of AG tells us whether... 

In this chapter we apply the general criteria for equilibrium developed in Chap. 6 to systems in which chemical reactions may occur. In Sec. 8-1, we present a general discussion of chemical equilibrium in homogeneous and heterogeneous systems. The concept of a progress variable is introduced, and the conditions for chemical equilibrium are derived. The equilibrium constant is defined, and some of its properties are developed. A discussion of the Le Chatelier-Braun principle applied to chemical reactions is presented. In Sec. 8-2, the results of Sec. 8-1 are applied to chemical reactions in mixtures of real gases. 

The application of the general criteria for equilibrium to systems in which chemical reactions may occur involves the ability to freeze the chemical reactions at any desired point. Thus, a system containing r substances which may undergo a chemical reaction must be considered to be made up of r independent components. At equilibrium, of course, the number of moles of any component is determined by specifying the numbers of moles of the r — l other components and the values of the other pertinent thermodynamic parameters. 

The criteria for equilibrium in the system can be written in variational form... 

By remembering that AG = ( a, - i ), application of these criteria for equilibrium to Equation 8.31 leads to the first derivative of that equation... 

This distinction in the choice of appropriate dependent variables will influence om-development of the criteria for equilibrium, whiA appears in Chapter 7. 

The chapter divides in two in early sections we describe the behavior of nomeact-ing systems, while in later sections we deal with systems in which reactions occur. In 7.1 we combine the first and second laws to obtain criteria for identifying limitations on the directions of processes and for identifying equilibrium in closed multiphase systems. Then in 7.2 we develop the analogous relations for heat, work, and material transfers in open systems. With the material in 7.2 as a basis, we then present in 7.3 the thermodynamic criteria for equilibrium among phases. 

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