Activity & Ionic Strength
Activity vs. Concentration (Non-ideal Solutions)
Ions in solution interact with each other and with H2O molecules. In this way, ions behave chemically like they are less concentrated than they really are (or measured). This effective concentration, which is available for reactions, is called activity:
| (1) | activity ai = effective concentration ≤ real concentration ci |
In (infinitely) dilute solutions, i.e. at low concentrations ci and at low background salt concentrations, the ionic interactions can be ignored, and we have
| (2) | ideal solution: ai = ci |
Usually, solutions are non-ideal. Hence, all hydrochemical calculations with aqion are based on activities (rather than concentrations).
Activity Coefficient
Once we know the concentration of the free ion ci we convert it to the activity ai by the free-ion activity coefficient γi:
| (3) | ai = γi ci | ( activity = γi × concentration ) |
In the very limit of infinitely dilute systems the activity coefficient becomes 1:
| (4) | ideal solution: γi = 1 |
γi corrects for electrostatic shielding by other ions; hence, γi depends on the ionic strength (i.e. the concentration of electrical charge). There are several approaches to calculate the activity coefficients.
Ionic Strength
The ionic strength of a solution is a function of the concentration of all ions present in a solution:
| (5) | \(\large I = \frac{1}{2} \, \sum\limits_{i}z_{i}^{2} \, c_{i}\) |
Here, ci and zi are the molar concentration and the charge of ion i. The sum is taken over all ions in the solution. Due to the square of zi, multivalent ions contribute particularly strongly to the ionic strength. [Note: In literature the ionic strength, I, is also abbreviated by the Greek symbol μ.]
aqion displays the ionic strength of each aqueous solution in the output tables. For comparison: Typical ionic strengths of natural waters are
| surface water | I = 0.001 – 0.005 M |
| potable water, groundwater | I = 0.001 – 0.02 M |
| seawater | I = 0.7 M |
The ionic strength is related to both EC and TDS, respectively.
Example: Ionic Strength of CaCl2
The ionic strength of a CaCl2 solution is calculated as follows:
| \(\begin{align*} I \ &= \ \frac{1}{2} \left\{ z_{Ca}^2 \,[Ca^{+2}] + z_{Cl}^2\, [Cl^{-}] \,\right \} \\ &= \ \frac{1}{2} \left\{ z_{Ca}^2\, [CaCl_2] + z_{Cl}^2 \,2\, [CaCl_2] \,\right \} \\ &= \ \frac{1}{2} \left\{ 2^2 \,[CaCl_2] + (-1)^2 \,2\, [CaCl_2] \,\right \} \\ &= \ \ 3 \ [CaCl_2] \\ \end{align*}\) |
Here, rectangular brackets [..] symbolize molar concentrations. Note the stoichiometric factor 2 of Cl- in the second line.
Based on this equation, a 0.5 molar CaCl2 solution has an ionic strength of I = 3 × 0.5 M = 1.5 M.
[You can check this result with aqion: Click on H2O, activate the upper checkbox mol and enter Ca = 500 mM and Cl = 1000 mM, then Click Start. In the output table, row “ionic strength” you will find: 1.5 mol/L.]