Question

A solution of acetone in heptane has a mole fraction 0.2. Its density 0.92 g/mL. Then the product of molality and molarity is

Answer 1

Assuming one mole of the solution,
moles of acetone = 0.2
molar mass of acetone = 60 g/mol
mass of acetone = 12 g
moles of heptane = 0.8
molar mass of heptane = 100 g/mol
mass of heptane = 80 g
$Molality=\frac{\text{moles of solute}}{\text{mass of the solvent in kg}}=\frac{0.2}{0.08}=2.5m$

Total mass of the solution = 80 + 12 = 92 g
density of the solution = 0.92 g/mL
Hence volume of the solution = $\frac{92}{0.92}=100mL$

$Molarity=\frac{\text{moles of solute}}{\text{volume of the solution (L)}}=\frac{0.2}{0.1}=2M$
Product of molarity and molality = $2\times 2.5=5$