Editing Solubility equilibrium (section)

=== Common-ion effect ===
The [[common-ion effect]] is the effect of decreased solubility of one salt when another salt that has an ion in common with it is also present. For example, the solubility of [[silver chloride]], AgCl, is lowered when sodium chloride, a source of the common ion chloride, is added to a suspension of AgCl in water.<ref>{{Housecroft3rd}} Section 6.10.</ref>
<math display="block">\mathrm{AgCl(s) \leftrightharpoons Ag^+ (aq) + Cl^- (aq) }</math>
The solubility, ''S'', in the absence of a common ion can be calculated as follows. The concentrations [Ag<sup>+</sup>] and [Cl<sup>−</sup>] are equal because one mole of AgCl would dissociate into one mole of Ag<sup>+</sup> and one mole of Cl<sup>−</sup>. Let the concentration of [Ag<sup>+</sup>(aq)] be denoted by ''x''. Then
<math display="block">K_\mathrm{sp}=\mathrm{[Ag^+] [Cl^-]}= x^2</math>
<math display="block"> \text{Solubility} = \mathrm{[Ag^+]=[Cl^-]} = x = \sqrt{K_\mathrm{sp}}  </math>
''K''<sub>sp</sub> for AgCl is equal to {{val|1.77|e=-10|u=mol<sup>2</sup> dm<sup>−6</sup>}} at 25&nbsp;°C, so the solubility is {{val|1.33|e=-5|u=mol dm<sup>−3</sup>}}.

Now suppose that sodium chloride is also present, at a concentration of 0.01&nbsp;mol dm<sup>−3</sup> = 0.01 M. The solubility, ignoring any possible effect of the sodium ions, is now calculated by
<math display="block">K_\mathrm{sp}=\mathrm{[Ag^+] [Cl^-]}=x(0.01 \,\text{M} + x)</math>
This is a quadratic equation in ''x'', which is also equal to the solubility.
<math display="block"> x^2 + 0.01 \, \text{M}\, x - K_{sp} = 0</math>
In the case of silver chloride, ''x''<sup>2</sup> is very much smaller than 0.01 M ''x'', so the first term can be ignored. Therefore
<math display="block">\text{Solubility}=\mathrm{[Ag^+]} = x = \frac{K_\mathrm{sp}}{0.01 \,\text{M}} = \mathrm{1.77 \times 10^{-8} \, mol \, dm^{-3}}</math>
a considerable reduction from {{val|1.33|e=-5|u=mol dm<sup>−3</sup>}}. In [[gravimetric analysis]] for silver, the reduction in solubility due to the common ion effect is used to ensure "complete" precipitation of AgCl.