Question

Concentrated aqueous sulpheric acid is 98% $H_{2}S{O}_4$ by mass and has a density of $1.80{\text{g mL}}^{-1}$. Volume of acid required to make one litre of $0.1\text{M}{H}_{2}S{O}_4$ solution is:

• A. $16.65\text{mL}$
• B. $22.20\text{mL}$
• C. $5.5\text{mL}$
• D. $11.10\text{mL}$

Answer 1

The correct option is C $5.5\text{mL}$

$\text{Molarity}=\frac{\text{number of moles}}{\text{Volume in litre}}$

Volume of $98\%$ by mass of $H_{2}S{O}_4$:

$V=\frac{\text{mass}}{\text{density}}$

$\Rightarrow V=\frac{100\text{g}}{1.8{\text{g mL}}^{-1}}=55.55\text{mL}=0.055\text{L}$

$\text{Number of moles,}n=\frac{\text{given weight}}{\text{molar mass}}$

$\Rightarrow n=\frac{98}{98}=1\text{mol}$

$\Rightarrow \text{Molarity}\left(M\right)=\frac{1}{0.055}=18.18\text{M}$
We know:
$M_1\times V_1=M_2\times V_2$
$\Rightarrow 18.18\times V_1=0.1\times 1$
$\Rightarrow V_1=\frac{0.1}{18.18}$
$\Rightarrow V_1=5.5\times {10}^{-3}\text{L}=5.5\text{mL}$