Application of Equilibrium Criteria to Chemical Reactions

In Sec. 14.3 it is shown that the total Gibbs energy of a closed system at constant T and P must decrease during an irreversible process and that the condition for equilibrium is reached when G attains its minimum value. At this equilibrium state, 

Each of tliese may serve as a criterion of equilibrium. Thus, we may write an expression for G as a function of s and seek the value of e which minimizes G, or we may differentiate the 

Although the equilibrium expressions are developed for closed systems at constant T and P, they are not restricted in application to systems that are achially closed and reach equilibrium states along paths of constant T and P. Once an equilibrium state is reached, no further changes occur, and the system continues to exist in tliis state at fixed T and P. How this state was actually attained does not matter. Once it is known that an equilibrium state exists at given T and P, the criteria apply. 

3 THE STANDARD GIBBS-ENERGY CHANGE AND THE EQUILIBRIUM CONSTANT 

Equation (71.2), the fundamental property relation for single-phase systems, provides an expression for the total differential of the Gibbs energy  

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The chemical potential pi plays a vital role in both phase and chemical-reaction equilibria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence pi, is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, pi approaches negative infinity when either P or Xi approaches zero. While these characteristics do not preclude the use of chemical potentials, the application of equilibrium criteria is facilitated by introduction of the fugacity, a quantity that takes the place of p. but which does not exhibit its less desirable characteristics. 

A revised, updated suinmary of equilibrium constants and reaction enthalpies for aqueous ion association reactions and mineral solubilities has been compiled from the literature for common equilibria occurring in natural waters at 0-100 C and 1 bar pressure. The species have been limited to those containing the elements Na, K, Li, Ca, Mg, Ba, Sr, Ra, Fe(II/III), Al, Mn(II,III,IV), Si, C, Cl, S(VI) and F. The necessary criteria for obtaining reliable and consistent thermodynamic data for water chemistry modeling is outlined and limitations on the application of equilibrium computations is described. An important limitation is that minerals that do not show reversible solubility behavior should not be assumed to attain chemical equilibrium in natural aquatic systems. 

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. 

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