(N/A) $K_{sp}$: At a defined temperature,the product of the concentrations of the ions of a sparingly soluble salt in its saturated solution is called the solubility product,$K_{sp}$.
Example: $BaSO_{4(s)} \rightleftharpoons Ba^{2+}_{(aq)} + S{O_{4}}^{2-}_{(aq)}$
$K_{sp} = [Ba^{2+}] [SO_{4}^{2-}] \quad \dots (Eq.-I)$
$Q_{sp}$: When two solutions containing ions of a sparingly soluble salt are mixed,the product of the concentrations of these ions at any given moment is called the ionic product,$Q_{sp}$.
Example: When $0.1 \ M \ Ba(NO_{3})_{2}$ is mixed with $0.05 \ M \ H_{2}SO_{4}$,the product of the concentrations of $Ba^{2+}$ and $SO_{4}^{2-}$ is the ionic product,$Q_{sp}$.
$Q_{sp}(BaSO_{4}) = [Ba^{2+}] [SO_{4}^{2-}] \quad \dots (Eq.-II)$
Relationship between $K_{sp}$ and $Q_{sp}$:
$1$. If $Q_{sp} = K_{sp}$,the solution is saturated and equilibrium is established.
$2$. If $Q_{sp} < K_{sp}$,the solution is unsaturated and no precipitation occurs.
$3$. If $Q_{sp} > K_{sp}$,the solution is supersaturated and precipitation will take place.
Thus,by comparing $Q_{sp}$ and $K_{sp}$,we can predict whether precipitation will occur.