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Concentrated aqueous sulphuric acid is 98% $H_2SO_4$ by mass and has a density of 1.80 g mL$^{-1}$. Volume of acid required to make one litre of 0.1 M $H_2SO_4$ solution is
A
16.65 mL
B
22.20 mL
C
5.55 mL
D
11.10 mL
Detailed Solution
Molarity of the concentrated $H_2SO_4$ solution $= \dfrac{\text{mass percent} \times \text{density} \times 10}{\text{molar mass}}$
$= \dfrac{98 \times 1000}{98 \times 100} \times 1.80$
$= 18.0$ M (the source solution takes this as 18.02 M)
Suppose $V$ mL of this $H_2SO_4$ is used to prepare 1 litre of 0.1 M $H_2SO_4$.
Using $M_1V_1 = M_2V_2$: $V \times 18.02 = 1000 \times 0.1$
$V = \dfrac{1000 \times 0.1}{18.02}$
$V = 5.55$ mL
$= \dfrac{98 \times 1000}{98 \times 100} \times 1.80$
$= 18.0$ M (the source solution takes this as 18.02 M)
Suppose $V$ mL of this $H_2SO_4$ is used to prepare 1 litre of 0.1 M $H_2SO_4$.
Using $M_1V_1 = M_2V_2$: $V \times 18.02 = 1000 \times 0.1$
$V = \dfrac{1000 \times 0.1}{18.02}$
$V = 5.55$ mL