What volume of $6.0 {MH}_{2} {SO}_{4}$ should be mixed with $10 L$ of $1.0 M H_{2} {SO}_{4}$ to make $20 L$ of $3.0 {MH}_{2} {SO}_{4}$ upon dilution to volume?

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5.0 L

1.7 L

8.3 L

10 L

answer is C.

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Detailed Solution

It is known that,

$\begin{array}{l} N_{1} V_{1} + N_{2} V_{2} = N_{3} V_{3} \\ M_{1} V_{1} + M_{2} V_{2} = M_{3} V_{3} \\ = 6 V_{1} + (1 \times 10) = (3 \times 20) \\ 6 (V_{1} + 10 = 60 \end{array}$
So,

$V_{1} = \frac{50}{6} = 8.3 L$

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