Question

A solution is 98% by mass of sulphuric acid in water. The density of the solution is 1.8. The sum of the molality and the molarity of the solution is:

Answer 1

Assuming 100 g of the solution,
Mass of $H_{2}S{O}_4=98\text{g}$
molar mass of $H_{2}S{O}_4=98\text{g/mol}$
mass of $H_{2}O=2\text{g}$
moles of $H_{2}S{O}_4=1\text{mol}$
molality = $\frac{\text{moles of}{H}_{2}S{O}_4}{\text{mass of the solvent in kg}}=\frac{1}{0.002}=500$
Volume = $\frac{\text{mass}}{\text{density}}=\frac{100}{1.8}$

molarity = $\frac{\text{moles}}{\text{volume (L)}}=\frac{1\times 1.8\times 1000}{100}=18M$
sum of molarity and molality = 500 + 18 = 518