How much water (in litres) must be added to 1 text L of an aqueous HCl solution with a pH of 1 to result in a final solution with a pH of 2?

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EEJ MAIN Chemistry QUESTION #7183

Question 1

How much water (in litres) must be added to $1 \text{ L}$ of an aqueous $HCl$ solution with a $pH$ of $1$ to result in a final solution with a $pH$ of $2$?

$0.1 \text{ L}$
$0.9 \text{ L}$
$2.0 \text{ L}$
$9.0 \text{ L}$✔️

Correct Answer Explanation

Using the definition of $pH = -\log[H^{+}]$:

Initial $[H^{+}] = 10^{-1} = 0.1 \text{ M}$.
Final $[H^{+}] = 10^{-2} = 0.01 \text{ M}$.
Using dilution formula $M_{1}V_{1} = M_{2}V_{2}$:
$0.1 \times 1 = 0.01 \times V_{2} \implies V_{2} = 10 \text{ L}$.
Volume to be added = $V_{2} - V_{1} = 10 - 1 = 9 \text{ L}$.

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