Ionic strength is sometimes stated as having units of molal (or molar) and other times stated as being unitless, depending on the book you read. The easiest way to see how to apply this formula is to consider a few examples. First consider 100 mM NaCl. Upon dissolving, one obtains 100 mM Na+ and 100 mM Cl-. Thus

The ionic strength of a solution is a measure of the amount of ions present. As you might guess a divalent ion (a 2+ or 2- ion, like Ca2+) does more to make the solution ionic than a monovalent ion (e.g., Na+). This must be taken into account. The other very critical thing to remember is that the ionic strength of a solution depends on the concentrations of all the ions in the solution, not just the ion pair that you are calculating the activity coefficient for. Thus, if you are calculating the average activity coefficient of dissolved CaCl2, but there is also dissolved NaCl present, the

ionic strength you use has contributions from all the ions.The formula for ionic strength is:

. First consider 100 mM NaCl. Upon dissolving, one obtains 100 mM Na+ and 100 mM Cl-. Thus Notice that for a simple salt of two monovalent ions, the ionic strength is just the concentration of the salt.

This is not true for a salt with one or more multivalent ions like MgCl2. For a 100 mM solution of this salt:

Note that the Mg cation is divalent and thus it has a big effect since the charge is squared. Also note that the chloride anion is present at twice the concentration since there are two chloride ions per molecule of salt.

What is the ionic strength of a solution of 100 mM NaCl plus 100 mM of acetic acid which has been titrated with NaOH until the pH of the solution is 4.75 (the pKA of acetic acid)? When the pH equals

the pKA, that means that half of the acetic acid has been converted

to the conjugate base, sodium acetate. Acetic acid is uncharged and does not contribute to the ionic strength. However sodium acetate ionizes completely to form acetate anions and sodium cations. Since half was converted, there are 50 mM of each. Then we must add in the 100 mM of NaCl. So there is 50 mM acetate anion, 150 mM sodium anion, and 100 mM chloride anion:

ACTIVITY COEFFICIENT is in essence a "correction factor" that accounts for the apparent decrease of concentration because of interaction with other ions in solution. The value of γ can be estimated using one of the existing activity models. Finding appropriate activity coefficients for aqueous species especially in concentrated multicomponent solutions is one of the most important (but troublesome) task in calculating equilibrium relations.

If you imagine an aqueous solution for a moment, where charged ions are dispersed in the solvent, Coulomb's Law tells us that the electrostatic forces acting on ions vary inversely with the square of the distance. Hence, the activity coefficient is expected to decrease (i.e., "effective concentration" decrease) as the concentrations of ions increase. The Coulombic forces increase as the ion density increases. This phenomenon was known for a long time, even before we were able to formulate ways of estimating activity coefficients.

Calculating Activity Coefficients.Now we actually will use the Debye-Huckel limiting law itself. There are three very important things about applying the Debye-Huckel theory. First, it only applies to ions. Molecules that are not charged have an activity coefficient of 1.0 according to this theory (in reality, that is not true, but their activity coefficients will be much closer to 1 than will that of an ion). Second, the charges that appear in the equation are only those of the salt you are calculating the activity coefficient for. Finally, all you can only ever calculate are average activity coefficient of the two ions which make up the salt you are considering. For MgCl2, you cannot

use this theory to calculate the activity coefficient of Mg2+ separately from Cl-, you can only calculate the geometric average of the two activities,

.

The Debye-Huckel limiting law is

Notice that the ionic strength is that of the whole solution, while the charges are those of the sodium acetate ions we are calculating the activity coefficient for.

where A=0.509 for water at 25 C. (A is an empirical constant.) In the acetate/acetic acid example given above, the sodium acetate ions would have an average activity coefficient given by