Activity And Activity Coefficients

Equilibrium relationships are frequently applied to equilibria involving salts, acids, bases, gases, and other molecules in aqueous solution. As solutions of these materials become more concentrated, then- quantitative effect on equilibria becomes progressively less than that calculated solely on the basis of changes in concentration. Thus the effective concentration, or activity, of ions and molecules is changed from that of the actual concentration. When activity does not equal concentration, the species is behaving nonideally. This has been explained partially as resulting from forces of attraction between positive and negative ions and is related to the thermodynamics of the reaction. Ideal behavior occurs when activity equals concentration.

Therefore, activities or effective concentrations, rather than actual concentrations, should be used in equilibrium relationships for accurate results.

where the braces { } distinguish activity from concentration.

We need some general rules for expressing activity in these relationships. In many texts, activity and concentration are related as follows:

where y,- = activity coefficient for species i {i} = activity of species i [/] = concentration of species i

To be strictly correct, the concentration of species i needs to be reported relative to a reference state for species i as follows:

where [i]0 is the concentration of species; in the reference state.

So, activity {¡} is actually unkless. The reference state for ions and molecules dissolved in water is typically 1.0 M. The reference state for solvents is the pure solvent with a mole fraction = 1.0. The reference state for solids is the pure solid with a mole fraction = 1.0. The reference state for gases is pure gas (i.e., 1 atm pressure). Thus, in most cases, [;']„ = 1.0, and Eq, (2.25) reduces to Eq. (2.24). We will use Eq. (2.24) in this book.

Unfortunately, the activity coefficient is not usually an easy number to determine with precision. Although numerical calculations from equilibrium relationships may be in error if actual concentrations are used in place of activities, the error is not very great for dilute aqueous solutions. Also, a high degree of precision is seldom required in equilibrium analytical computations. For this reason, activity coefficients will in general be assumed to be unity for equilibrium calculations in this book. A more detailed discussion of this subject, together with methods for estimating the activity coefficient, is given in Sec. 4.3.

It is up to the individual to decide whether to use concentrations or activities in the equilibrium relationships. This will of course depend on the nature and concentration of ions and molecules making up the solution of interest. However, certain conventions for expressing concentrations or activities of solvents, solutes, solids, and gases need to be understood, especially if published values for equilibrium constants are to be used. The methods of expression are as follows.

1. For ions and molecules in solution:

[i] = concentration of species i, mol/L % = activity coefficient for species i

In dilute solutions, y-t approaches 1.0 and {¿} = [ij.

2. For a solvent in solution or for mixtures of liquids:

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