Question

The concentration of hydroxyl ion in solution left after mixing $100mL$ of $0.1MMgC{l}_2$ and $100mL$ of $0.2MNaOH$ $[K_{sp}$ of $Mg(OH{)}_2=1.2\times {10}^{-11}]$ is ?

• A. $2.8\times {10}^{-3}M$
• B. $2.8\times {10}^{-2}M$
• C. $2.8\times {10}^{-4}M$
• D. $2.8\times {10}^{-5}M$

Answer 1

Answer: (C)

$2.8\times {10}^{-4}M$

Given sata,

$MgC{l}_2=0.1M\left(100mL\right)$

$NaOH=0.2M\left(100mL\right)$

$K_{s}10=1.2\times {10}^{-11}$

$\underset{\mathrm{0.0.1}mole}{MgC{l}_2}+\underset{2NaOH}{2NaOH}⟶\underset{0.01}{Mg(OH{)}_2}+2NaCl$

$\underset{0.01}{Mg(OH{)}_2}⟶0.01M{g}^{2+}+\underset{2\times 0.01}{2O{H}^{-}}$

$K_{s/o}=5\times (25{)}^2={45}^3=1.2\times {10}^{-11}$

$5^3=0.3\times {10}^{-11}=3\times {10}^{-12}$

$5=(3\times {10}^{-12}{)}^{\frac{1}{3}}=1.44\times {10}^{-4}$

Concentration $=25=2\times 1.44\times {10}^{-4}$

$=2.8\times {10}^{-4}M$

option C