Activity Coefficient: Definition & Equation

Instructor: Scott Larkin
Ionic solutions are not ideal solutions. The ionic strength of the solution changes the behavior of the ions in the solution. The activity coefficient is used to show how much the solution deviates from the ideal.

Ideal Solutions are not Ideal

Equilibrium expressions for solutions are calculated assuming the expression applies to an ideal solution. Ideal solutions assume there is no interaction between ions once the ions are in solution. But, ions solution do interact with other ions and solvents. The activity coefficient of an electrolyte solution is used to factor in the concentration-dependent interactions between ions in a solution.

In the lab, sometimes emulsions form and there is no separation between an aqueous phase and organic phase. A common practice to separate them is to add a saturated solution of NaCl. This causes water to become 'more polarized'. Addition of a salt increases the ionic strength of the aqueous phase, which in turn separates the components of an emulsion into polar and nonpolar layers.

Causes of Non-Ideal Behavior

Ionic Atmosphere

Ions in solution travel near other ions. So, cations will encounter cations and anions. Cations are more attracted to anions than cations. Ions of opposite charges shield the effective charge of an ion as shown in Figure 1. The effect is to make anions and cations less attracted to one another.

Figure 1: Partial charges surround ions and shield the effective ionic charge
cloud of opposite charge that surrounds ion

As the ionic strength of the solution increases, the ionic atmosphere around an ion becomes stronger. You can see this visually in Figure 2.

Figure 2: Stronger ionic strength leads to a stronger ionic atmosphere and less attraction between ions
compared ionic atmosphere

For our discussion and calculations, we are working with concentrations of no greater than 0.1 M. To account for the influence of the ionic atmosphere, two factors are included:

1. Ionic Strength

Ionic strength calculates the degree to which charges on ions influence how far a solution deviates from ideal behavior. This a combination of concentration and unaltered charge and concentration of a given ion as seen in Equation 1.

Equation 1: ionic strength of solution
equation for ionic strength of solution

  • Ci is the concentration of the ith component
  • Zi is the charge on the on the ion in question
  • μ is the symbol for the total ionic strength of a solution

Example 1 shows how a salt's ionic strength is different than its molar concentration. The apparent and real concentrations are not the same.

Example 1: Calculation of ionic strength of MgCl 2
Calculation of ionic strength of MgCl2

2. Effective Ionic Radius

Smaller ions have a larger effective radius. This is because the solvent cage of water is larger. The other factor associated effective ionic radius is the charge. A higher charge (a magnitude whether it is positive or negative) attracts more oppositely charged ions.

Activity Coefficient Tables

Fortunately for most of us, activity coefficients are provided on tables in physical chemistry or analytical chemistry texts. You can also find them online by typing 'activity coefficient table'. For the following two sample calculations, a shortened table of activities is presented here in Table 1. Cross index ionic strength with the desired ion.

Table 1: Selected activity coefficients
table of activity coefficients

Sample Calculations

The calculation of pH and molar solubility are two examples where the activity coefficient has a measurable effect on a common calculation. A similar process is used for each.

  1. calculate the ionic strength
  2. interpolate the value of the activity coefficient from known values
  3. plug in activity coefficients times concentration

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