# Solubility: Is the common ion effect proportional to individual solubility values?

I'm trying to grasp how solubility works in real applications. Is it so that in a solution with only one salt, it's solubility will change upon the addition of another salt with a common ion in a manner strictly proportional to the latter salt's solubility in water alone? (i.e. that highly soluble salts will decrease the solubility of common ion salts the most and vice versa) If so, is the solubility of each salt in a combined solution a ratio of their respective solubility values when alone in the solution?

• It is more complicated than that. Do you know what is a solubility product? – Ivan Neretin Jun 19 '19 at 13:57
• Not yet! I'll read into it. Thanks for the hint! – Veritas Jun 21 '19 at 7:35

There are basically 3 effects.

The solubility is controlled by the solubility product, the constant being the multiplication of ion activities

$$K_\mathrm{sp}={a_\mathrm{M}}^m\cdot {a_\mathrm{X}}^n$$ for a salt $$\ce{M_{m}X_{n}}$$

For low concentration of ions, it can be approximated by concentrations, related to activities via activity coefficients $$\gamma$$, that are supposed to be equal to 1.

$$K_\mathrm{sp}={c_\mathrm{M}}^m\cdot {c_\mathrm{X}}^n$$

where $$a_\mathrm{M}=\gamma_\mathrm{M} \cdot c_\mathrm{M}$$, the same for $$\text{X}$$

Therefore the presence of other salt with the common ion decreases the salt solubility, as the common ion contributes to the rate of precipitation.

The second effect is general effect of dissolved non common ions, given by ionic strength

$$I=\sum_i {c_\mathrm{i}\cdot {z_\mathrm{i}}^2}$$

and its effect on the ion activity, given for diluted solutions approximately by Debye-Hueckel equation

$$\log \gamma=-0.5 \cdot z_+ \cdot z_- \cdot \sqrt I$$

where $$\gamma$$ is the mean activity coefficient for given salt and $$z$$ are respective ion charges. The coefficient $$0.5$$ is rounded up.

For a particular ion, it is often written as

$$\log \gamma=-0.5 \cdot {z}^2 \cdot \sqrt I$$

For less diluted solutions, it is often modified as

$$\log \gamma=-0.5 \cdot {z}^2 \cdot \frac {\sqrt I}{c + \sqrt I}$$

where $$c$$ is ion dependent constant close to 1.

Generally, the higher is overall ion concentration, the higher is salt solubility. But the effect is smaller than effect of common ions.

For high concentration of general salts, ion activity coefficients revert their decreasing trend and start raising. For very high concentration to values much higher than 1.

As result, the solubility decreases.