MCQ
How many litres of water must be added to $1\,\, litre$ of an aqueous solution of $HCl$ with a $pH$ of $1$ to create an aqueous solution with $pH$ of $2$?.......$L$
- A$0.1$
- B$0.9$
- C$2$
- ✓$9$
✓
Answer
Correct option: D.
$9$
d
$\cup \operatorname{sing} \mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$
$\cup \operatorname{sing} \mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$
Initial $\mathrm{pH}=1$, i.e. $\left[\mathrm{H}^{+}\right]=0.1 \mathrm{mole} / \mathrm{L}$
New $\mathrm{pH}=2$
i.e. $\left[\mathrm{H}^{+}\right]=0.01 \mathrm{mole} / \mathrm{L}$
In case of dilution: $\mathrm{M}_{1} \mathrm{V}_{1}=\mathrm{M}_{2} \mathrm{V}_{2}$
$\therefore \quad 0.1 \times 1=0.01 \times \mathrm{V}_{2}$
$\mathrm{V}_{2}=10 \mathrm{L}$
Volume of water added,
$=\mathrm{V}_{2} \text { - volume of } \mathrm{HCl}=10-1=9 \mathrm{L}$
The volume of water added = $9 \mathrm{L}$
Hence, the correct option is $\mathrm{D}$.
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