Acid-base equilibrium problems approximations

Obviously, all acid-base equilibrium constants depend on the pH scale used. It is possible to convert approximately an equilibrium constant determined in one scale to that of another scale. The problem of different definitions of equilibrium constants needs attention when applying an infinite dilution scale complex formation constant,—for example, for CuC03(aq)—in a seawater medium. 

If we make the same x is small approximation that we make for weak acid or weak base equilibrium problems, we can consider the equilibrium concentrations of HA and A to be essentially identical to the initial concentrations of HA and A (see step 4 of Example 16.1). Therefore, to determine [H30 ] for any buffer solution, we multiply by the ratio of the... 

We can now write some general rules for solving chemical equilibrium problems, using the approximation approach. These rules should be applicable to acid-base dissociation, complex formation, oxidation-reduction reactions, and others. That is, all equilibria can be treated similarly. 

Graphical presentation of redox equilibria, like the graphical treatment of acid-base, complexation, and precipitation equilibria is helpful in understanding complicated problems and in obtaining approximate solutions to equilibrium questions. For redox systems in natural waters the equilibrium condition is truly a boundary condition. In many cases, natural systems are not at equilibrium from a redox standpoint. The diagrams usually present an idea of what is possible, not necessarily of the existing or imminent situation. The graphical presentations of redox equilibria are seldom simple because redox reactions usually involve... 

Here we proposed a physically based approximation to get around this problem. We separate the coordinate set X into two domains X " and where slow and fast are with respect to the rate of approaching equilibrium. For example, we argue that the translation and rotation degrees of freedom of a bulk water molecule relax to equilibrium more rapidly than the protein dihedral angles of an amino acid i. 

The thermodynamic properties of the solution—such as the equilibrium constants of reactions involving ions—can then be derived in the same way as for ideal solutions but with activities in place of concentrations. However, when we want to relate the results we derive, we need to know how to relate activities to concentrations. We ignored that problem when discussing acids and bases and simply assumed that all activity coefficients were 1. The cytoplasm and other fluids in organisms have ion concentrations that are far too high to behave ideally, so y = 1 is a poor approximation in this chapter, we see how to improve that approximation. 

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