Question

A solution of $\text{H}_2\text{SO}_4$ is 31.4% $\text{H}_2\text{SO}_4$ by mass and has a density of $1.25 \, \text{g/mL}$. The molarity of the $\text{H}_2\text{SO}_4$ solution is _____ M (nearest integer).
[Given molar mass of $\text{H}_2\text{SO}_4 = 98 \, \text{g/mol}$]

Answer 1

To find the molarity (M), use the formula:

$M = \frac{n_{\text{solute}}}{V} \times 1000$

Given that the solution is 31.4% $H_2SO_4$, with a density of 1.25 g/mL:

Step 1 : Calculate the mass of $H_2SO_4$ in 100 g of solution:

Mass of $H_2SO_4 = 31.4 \, \text{g}$

Step 2 : Convert this to moles:

$\frac{31.4}{98} = 0.32 \, \text{mol}$

Step 3 : Find the volume of the solution:

$\text{Volume} = \frac{\text{Mass of solution}}{\text{Density}} = \frac{100}{1.25} = 80 \, \text{mL}$

Step 4 : Calculate molarity:

$M = \frac{0.32 \, \text{mol}}{80 \, \text{mL}} \times 1000 = 4.005 \approx 4 \, \text{M}$

So, the correct answer is: 4M