Concentrated aqueous sulphuric acid is $98 %$ $H_{2} S O_{4}$ by mass and has a density of $1.80$ gm $L^{- 1}$ . What is the volume of acid required to make one litre of $0.1$ M $H_{2} S O_{4}$ solution?

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Solution

$98$ % $H_{2} {S O}_{4}$ by mass

$98 g$ of $H_{2} {S O}_{4}$ in $100 g$ of solution.

Moles of $H_{2} {S O}_{4} = \frac{98 g}{98 {g m o l}^{- 1}} = 1 m o l$

Density= ${1.80 m o l}^{- 1}$

$D = \frac{M}{V}$

$V = \frac{M}{D} = \frac{100}{1.80} = 55.55 m L = 55.55 \times 10^{- 3} L$

Volume of solution= $55.55 \times 10^{- 3} L$

$M o l a r i t y o f s o l u t i o n = \frac{N o . o f m o l e s}{V o l u m e o f s o l u t i o n i n L} = \frac{1 m o l}{55.55 \times 10^{- 3} L}$

$ =18.001\ M$

We will use formula

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

$M_{1} = 18 M M_{2} = 0.1$

$V_{1} = ? V_{2} = 1 L$

$18 \times V_{1} = 0.1 \times 1$

$V_{1}$ $= \frac{0.1 \times 1}{18} = 0.0055 L$

The volume of acid required to make one litre of solution is $0.0055 L$ or $5.55 m L$

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Concentrated aqueous sulphuric acid is $98 %$ $H_{2} S O_{4}$ by mass and has a density of $1.80$ gm $L^{- 1}$ . What is the volume of acid required to make one litre of $0.1$ M $H_{2} S O_{4}$ solution?