$K_{s p}:$ At definition temperature the produce of concentration of ions of sparingly soluble salt in its saturated solution is called solubility product $\mathrm{K}_{s p}$.

e.g., $\mathrm{BaSO}_{4(\mathrm{~s})} \square \quad \mathrm{Ba}_{(\mathrm{aq})}^{2+}+\mathrm{SO}_{4(\mathrm{aq})}^{2-}$ $\mathrm{K}_{s p}=\left[\mathrm{Ba}_{(\mathrm{aq})}^{2+}\right]\left[\mathrm{SO}_{(4)}^{2-}\right] \quad \ldots($ Eq.-i $)$

$\mathrm{Q}_{s p}$ : When two solutions of Sparingly soluble salts mix together than the product of concentration of ions of that two salts is called ionic product $\mathrm{Q}_{s p}$.

e.g. 0.1 M $\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$ mix with $0.05 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ in mixture : $\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \rightarrow \mathrm{Ba}^{2+}+2 \mathrm{NO}_{3}^{-}$ and $\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{SO}_{4}^{2-}+2 \mathrm{H}^{+}$

In this mixture the product of concentration of $\mathrm{Ba}^{2+}$ and $\mathrm{SO}_{4}^{2-}$ is called ionic product $\mathrm{Q}_{s p} \mathrm{BaSO}_{4}$. $\mathrm{Q}_{s p}\left(\mathrm{BaSO}_{4}\right)=\left[\mathrm{Ba}^{2+}\right]\left[\mathrm{SO}_{4}^{2-}\right] \quad \ldots($ Eq.-ii)

Reaction between $\mathrm{K}_{s p}$ and $\mathrm{Q}_{s p}$ :

If $Q_{s p}=K_{s p}$ equilibrium is established.

If $\mathrm{Q}_{s p}<\mathrm{K}_{s p}$ precipitation not take place

If $\mathrm{Q}_{s p}>\mathrm{K}_{s p}$ precipitation will take place.

By comparing the value of " $\mathrm{Q}_{s p}$ and $\mathrm{K}_{s p}$ precipitation will take place or not can be predicted.