Equilibrium Calculations Optional

Equilibrium calculations cover a wide range of problem types. A thorough understanding of these calculations is essential to understanding many chemical phenomena in the laboratory, in industry, and in living organisms. We will sample only a few in this section. 

You should write two things before attempting to solve any equilibrium problem. First is the equilibrium equation. Second is the equilibrium constant expression. 

The numbers used in the equilibrium constant expression are concentrations in moles per liter. These concentrations are sometimes given, but sometimes we must figure them out from the available information. The figuring-out process uses the mole relationships expressed in the coefficients in an equation. For example, suppose you were to prepare two 500-mL (0.5-L) solutions. In the first, you dissolve 0.1 mole of NaCl in the second you dissolve 0.1 mole of CaCl2. The molarities of both solutions would be 

But the concentrations used in equilibrium problems are usually ion concentrations. What are the Na+, Ca +, and Cr concentrations in the two solutions To answer these questions, we must examine the dissolving equations  

The NaCl equation shows that one mole of NaCl yields one mole of Na ion and one mole of Cl ion. Therefore, the ion concentrations are the same as the solute concentration  

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This optional chapter provides tools to compute the concentrations of species in systems with many simultaneous equilibria.3 The most important tool is the systematic treatment of equilibrium from Chapter 8. The other tool is a spreadsheet for numerical solution of the equilibrium equations. We will also see how to incorporate activity coefficients into equilibrium calculations. Later chapters in this book do not depend on this chapter. 

Under the pressure change option, the user can specify a lower and upper pressure range and an incremental pressure interval (AP) at which equilibrium is calculated at a fixed temperature (e.g., 1 to 1001 bars with AP = 100 bars would result in equilibrium calculations at 1, 101,. ..and 1001 bars). Under equilibrium crystallization , solid phases that have precipitated are allowed to dissolve and repreciptate as different solids when environmental drivers such as temperature, pressure, or evaporation change. Under fractional crystallization , a precipitated solid phase is not allowed to subsequently dissolve and reprecipitate when environmental drivers change this option allows for hypothetical removal (layering) of precipitates in basins when environmental drivers change. 

In 10.1 we present the basic thermodynamic relations that are used to start phase-equilibrium calculations we discuss vapor-liquid, liquid-liquid, and liquid-solid calculations. We have seen that the most interesting phase behavior occurs in nonideal solutions, but when we describe nonidealities using an ideal solution as a basis, we must select an appropriate standard state. Common options for standard states are discussed in 10.2 they include pure-component standard states and dilute-solution standard states. 

For complicated equilibrium calculations, the G-minimization technique is a useful option for the evaluation of phase equilibria, especially if both phase and reaction equilibria are involved. In contrast to the equilibrium conditions, the minimum of G is not only a necessary but a sufficient equilibrium condition. As well, for complicated equilibria it is often the only way to keep the overview. The only knowledge that must be available is the functional relationship for the Gibbs energy g and a clear concept for the minimum evaluation task. The following example shall illustrate the method. 

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