$100$ ml of $2$ M NaOH solution is diluted by water and the final molarity becomes $0.5$ . The volume of water added to the solution is:

400

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300

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500

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200

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Solution

The correct option is B $300$ ml
Molarity $= \frac{n}{V (s o l u t i o n)}$

$M_{1} = \frac{n}{V_{1} (s o l u t i o n)}$ ...(1)

$M_{2} = \frac{n}{V_{2} (s o l u t i o n)}$ ...(2)

From (1) and (2)

$\frac{M_{1}}{M_{2}} = \frac{V_{2}}{V_{1}}$

substituting the values,

$V_{2} = \frac{2 M \times 100 m l}{0.5 M}$

$V_{2} = 400 m l$

Hence, $V_{2} - V_{1} = 400 m l - 100 m l = 300 m l$

Therefore, 300ml of water is added to the solution.

Option B is correct.

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