What volume of 0.10 M $H_{2} {SO}_{4}$ must be added to 50 mL of a 0.10 M $NaOH$ solution to make a solution in which the molarity of the $H_{2} {SO}_{4}$ is 0.050 M?

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100 mL

400 mL

50 mL

150 mL

answer is B.

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Detailed Solution

Volume (V) can be find out as,

$\begin{array}{l} \frac{0.01 V - 0.0025}{v + 50} \times 1000 = 0.05 M \\ \frac{100 V - 2.5}{V + 50} = 0.05 \\ \frac{100 V - 2.5}{V + 50} 2.5 + 2.5 \\ 99.95 V = 5 \\ V = 0.05002 L \\ V = 50.02 ML \end{array}$

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