Question

At 298 K, the solubility product of $PbC{{l}_{2}}$is $1.0\times {{10}^{-6}}$. What will be the solubility of $PbC{{l}_{2}}$in moles/litre?
(A) $6.3\times {{10}^{-3}}$
(B) $1.0\times {{10}^{-3}}$
(C) $3.0\times {{10}^{-3}}$
(D) $4.6\times {{10}^{-14}}$

Answer 1

Hint: When a salt is stirred in water and only a small amount of it gets dissolved but a large amount of it remains undissolved, then the salt is known as sparingly soluble salt. The solubility product of a sparingly soluble salt forming a saturated solution in water is calculated as the product of the concentrations of the ions raised to a power equal to the number of the ions occurring in the equation representing the dissociation of the electrolyte. The solubility product is denoted by ${{K}_{sp}}$.

Formula Used: For a salt $A{{B}_{2}}$, The solubility product is ${{K}_{sp}}=\left[ A \right]{{\left[ B \right]}^{2}}$

Complete Step by Step Solution:
$PbC{{l}_{2}}$ gets dissociated as

Let solubility be s.
${{K}_{sp}}=\left[ P{{b}^{2+}} \right]{{\left[ C{{l}^{-}} \right]}^{2}}$
${{K}_{sp}}=s\times {{(2s)}^{2}}$
${{K}_{sp}}=4{{s}^{3}}$
The given solubility product is ${{K}_{sp}}=1.0\times {{10}^{-6}}$ .

Comparing the given value and calculated value of solubility product.
$4{{s}^{3}}=1.0\times {{10}^{-6}}$
${{s}^{3}}=1.0\times {{10}^{-6}}\div 4$
${{s}^{3}}=250\times {{10}^{-9}}$
$s=6.3\times {{10}^{-3}}$
Hence, the solubility of $PbC{{l}_{2}}$in moles/litre is $6.3\times {{10}^{-3}}$ moles/litre.
Correct Option: (A) $6.3\times {{10}^{-3}}$.

Additional Information: A saturated solution is a solution in which the solute gets completely dissolved in the solvent. A solute can be highly soluble, sparingly soluble or insoluble in the solvent. When a salt is dissolved in water, then there is an equilibrium formed between the reactant and the products.

Note: The solubility product depends upon the temperature. It increases with an increase in temperature. This is because with an increase in temperature, solubility increases. Solubility means the tendency of a solute to get dissolved in a solvent to form a solution. It also depends on the common-ion effect; that is, if a common ion is present in the solution, then the solubility product gets lowered.