# Solubility and Solubility Product

Table of Content:

## What is Solubility?

Solubility is the amount of the substance (ionic or other) soluble to make a saturated solution at a specified temperature and in a fixed volume of solvent.

Solubility changes with the nature of the substance, solvent, temperature, presence of common ions.

Sparingly soluble substances have very low solubility (AgCl, BaSO4) in water. Being ionic substances, in spite of the low solubility, it can be considered to form a saturated solution and the ions are in equilibrium with the undissolved solid.

$AgCl\rightleftharpoons Ag^+Cl^-$

(Undissolved ) (Dissolved)

Equilibrium constant of dissociation $=Kc=\frac{{{\left[ Ag \right]}^{+}}{{\left[ Cl \right]}^{-}}}{\left[ AgCl \right]}$

Silver chloride being solid, the concentration is taken to be constant, such that, a new equilibrium constant, can be considered.

Solubility Product $=Ksp=Kc\left[ AgCl \right]=\left[ A{{g}^{+}} \right]\left[ C{{l}^{-}} \right]=$ Product of the concentration of the ions.

For a sparingly insoluble salt of general formula, AxBy

$AxBy(s)\rightleftharpoons xA^y(aq)+yB^x-(aq)$ $Ksp=[xA^{y+}][yB^{x-}]^{y}$

The value is constant for the substance and varies only with temperature.

## Significance of Solubility Product

• Presence of common ion may affect the equilibrium and hence the concentration (solubility) but not solubility product.
• Precipitation of the solutes occurs when the ionic product exceeds the ksp

### Relationship Between Solubility and Solubility Product

$AxBy\rightleftharpoons xA^{Y+}+yB^{x-}$

At equilibrium C Cx Cy

Ksp = [xAY+ ]x[yBx-]y = [Cx]x [Cy]y = [C]x [x]x [C]y [y]y

Ksp = [C]x [C]y [x]x [y]y = [C]x+y [x]x [y]y

Ksp = [S]x+y [x]x [y]y S is the solubility= C= mole/l

Solubility = [S]x+y = $\frac{Ksp}{x^{x}y^{y}}$

Example: For silver chromate, $Ag_2CrO_4\rightleftharpoons2Ag^{+}+CrO_{4}^{2-}$

Ksp = (2S)2 S = 4S3

Also Read: pH Change By Common-Ion