Question

If the maximum concentration of $PbCl _{2}$ in water is $0.01 \,M$ at $25^{\circ} C$, its maximum concentration in $0.1 \,M \,NaCl$ will be

• A. $2 \times 10^{-3} \,M$
• B. $1 \times 10^{-4} \,M$
• C. $1.6 \times 10^{-2} \,M$
• D. $4 \times 10^{-4}\, M$

Answer 1

Answer: (D)

$\underset{S}{ PbCl _{2}} \longrightarrow \underset{S}{ Pb ^{2+}}+\underset{2 S}{2 Cl ^{-}}$
$K_{ sp } =S(2 S)^{2}=4 S^{3} $
$=4 \times\left(10^{-2}\right)^{3}=4 \times 10^{-6} $
In $0.1\, M \,NaCl ,\left[ Cl ^{-}\right]=0.1+2 \times 10^{-2} \approx 0.1\, M$
As $0.01 \,M \,PbCl _{2} \equiv 0.02\, M \,Cl ^{-}$
$\left[ Pb ^{2+}\right]\left[ Cl ^{-}\right]^{2}=K_{ sp }$
or $\left[ Pb ^{2+}\right](0.10)^{2}=4 \times 10^{-6}$
or $\left[ Pb ^{2+}\right]=4 \times 10^{-4}\, M$