Ionic Strength, activity coefficient and solubility

Ions	Concentration		Weight [g/mole]	Concentration[mmole/L]
Ca2+		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	40.1		4
Mg2+		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	24.3		4
Na+		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	23.0		1
K+		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	39.1		1
HCO3-		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	61.0		1
SO42-		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	96.1		4
Cl-		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	35.5		1
NO3-		mg/L g/m3 ppm eq/L meq/L mol/L mmol/L	62.0		1
Sum

The ionic strength is calculated with formula (1):

(1)

where:

	= ionic strength
	= concentration of the ith species, mole/L
	= valence (or oxidation) number of the ith species

The activity coefficient is calculated with formula (2):

so

(2)

where:

=activity coefficient

This activity coefficient is used in the calculation of the pH_s (saturation pH) but it can also be used to determine the minimum concentration of a dissolved element required to be in equilibrium with its solid (salt) element. You can for example determine the minimum concentration of calcium that would be required in solution to be in equilibrium with the solid calcium carbonate.

The equilibrium constant K_sp of this equilibrium equation is called the solubility product constant. It can be calculated with the following equation:

The molar concentrations of calcium and carbonate ions are the same, in addition calcium and carbonate ions are both divalent ions so they have the same activity coefficient.

and

so

The minimal concentration for an equilibrated water regarding calcium carbonate is:

Use the following calculator to determine the minimal concentration of calcium that would be required in solution to be in equilibrium with solid calcium carbonate. Use the activity coefficient of the divalent ion calculated above.

Remark: The calculation above shows only the ions that are usually present in drinking water. If you have for example Silicates and Fluorides in your water, the ionic strength is not accurate.