What volumes of $0.200 M {HNO}_{2}$ and $0.200 M {NaNO}_{2}$ are required to make 500 mL of a buffer solution with $pH = 3.00 ? [K_{a}$ for ${HNO}_{2} = 4.00 \times 10^{- 4}$ ].

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250 mL of each

$143 mL$ of ${HNO}_{2}$ and $357 mL$ of ${NaNO}_{2}$

$357 mL$ of ${HNO}_{2}$ and $143 mL$ of ${NaNO}_{2}$

$200 mL$ of ${HNO}_{2}$ and $300 mL$ of ${NaNO}_{2}$

answer is D.

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Detailed Solution

$\begin{array}{l} 3 = 4 - \log 4 + \log [\frac{0 .2 \times V}{0 .2 \times (500 - V)}] \\ \Rightarrow V = \frac{1000}{7} \\ V = = 143 ml of {NaNO}_{2} and 357 ml of {HNO}_{2} \end{array}$

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