Q32 / 150 · MHT CET 2009 · Chemistry
The number of hydroxyl ions in $10 \mathrm{~cm}^{3}$ of $0.2 \mathrm{M}$ HCl solution is
- A$5 \times 10^{-14}$
- B$3 \times 10^{9}$
- Correct answerC$3 \times 10^{12}$
- D$5 \times 10^{-12}$
Solution
$\left[\mathrm{H}^{+}\right]=0.2 \mathrm{M}$ (given, $\mathrm{HCl}=0.2 \mathrm{M}$ )
$\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]=10^{-14}$
$\left[\mathrm{OH}^{-}\right]=\frac{10^{-14}}{0.2}=5 \times 10^{-14} \mathrm{M}$
Concentration of hydroxyl ions in $0.2 \mathrm{M} \mathrm{HCl}$
$$
=5 \times 10^{-14} \mathrm{M}
$$
$\therefore$ The number of moles of hydroxyl ions
$$
=5 \times 10^{-14} \times 1000
$$
The number of $\mathrm{OH}^{-}$ in $10 \mathrm{~cm}^{3}$
$$
\begin{array}{l}
=\frac{5 \times 10^{-14} \times 1000 \times 6.023 \times 10^{23}}{10} \\
=3 \times 10^{12}
\end{array}
$$
Hence, the correct answer is option: 'C'.