Equilibrium in chemical systems

The degrees of freedom F in the phase rule refer to the number of externally controllable conditions of the system which must be specified to define uniquely the state of the system at equilibrium. In chemical systems the controllable variables are the temperature, pressure, and the proportions of the components of the system. The degree of freedom has a direct parallel in algebra where the "phase rule" is... 

There are many important functions of state. Those of importance in chemistry determine the conditions of equilibrium in chemical systems and hence the equilibrium distribution of different reactants and products among the various phases. 

The conditions that must be satisfied for a reversible change are the same as the conditions that must be satisfied for the system to be in equilibrium. Even though it appears to contribute little to our understanding of equilibrium in mechanical systems, the idea of reversible processes as the limiting behaviour of observable processes is of great importance in the study of equilibrium in chemical systems. 

In following the most direct path from the principles of thermodynamics to the understanding of equilibrium in chemical systems, we have bypassed many useful thermodynamic relations that involve the properties of perfect and imperfect gases. These are summarized in this chapter. 

In later chapters, the inequality of Eq. 4.6.6 will turn out to be one of the most useful for deriving conditions for spontaneity and equilibrium in chemical systems The entropy of an isolated system continuously increases during a spontaneous, irreversible process until it reaches a maximum value at equilibrium. 

Steady state pi oblems. In such problems the configuration of the system is to be determined. This solution does not change with time but continues indefinitely in the same pattern, hence the name steady state. Typical chemical engineering examples include steady temperature distributions in heat conduction, equilibrium in chemical reactions, and steady diffusion problems. 

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. 

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

Dynamic equilibria occur frequently in chemical systems. Chemical processes reach a state of equilibrium if allowed to continue for a sufficient time. Nevertheless, molecular activity always goes on after equilibrium has been reached. The following example, illustrated schematically in Figure 2-9. should help you grasp this important idea. 

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