Concentrated aqueous sulphuric acid is $98 %$ $H_{2} S O_{4}$ by mass and has a density of $1.80 g m L^{- 1} .$ Volume of acid required to make $1$ litre of $0.1 M H_{2} S O_{4}$ solution is :

5.55 m L

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11.10 m L

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16.65 m L

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22.20 m L

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Solution

The correct option is A $5.55 m L$
Let the volume of $98 %$ by mass $H_{2} S O_{4}$ solution required to make $1$ litre of $0.1 M H_{2} S O_{4}$ solution be $V m L$ .
Now, moles of $H_{2} S O_{4}$ required $= m o l a r i t y \times v o l u m e o f s o l u t i o n (L) = 0.1 \times 1 = 0.1 m o l$
Thus, mass of $H_{2} S O_{4}$ required $= m o l e s \times m o l a r m a s s = 0.1 \times 98 = 9.8 g$
The solution given to us is $98 %$ by mass $H_{2} S O_{4}$ i.e. per $100 g$ of solution we have $98 g$ of $H_{2} S O_{4}$ .
or we can say, $98 g$ of $H_{2} S O_{4}$ is present in $100 g$ of solution.
$∴ 9.8 g$ of $H_{2} S O_{4}$ will be present in $= \frac{100 \times 9.8}{98} = 10 g$
Hence, the volume of $98 %$ by mass $H_{2} S O_{4}$ solution required is $= \frac{m a s s o f H_{2} S O_{4} s o l u t i o n}{d e n s i t y o f H_{2} S O_{4} s o l u t i o n} = \frac{9.8}{1.80} \approx 5.55 m L$

Hence, the correct answer is option (a).

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Conc. Aqueous sulpuric acid is 98%H2SO4 by mass and has density of 1.80 g/ml. Volume of acid required to make 1 litre of 0.1M H2SO4 solution is

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