Question

An antifreeze solution is prepared from $222.6\, g$ of ethylene glycol, $C_{2}H_{4}(OH)_{2}$ and $200\, g$ of water. If the density of the solution is $1.072\, g\, mL^{-1}$, the molality of the solution will be

• A. $20.9\, m$
• B. $17.95\, m$
• C. $25.5\, m$
• D. $35.7\, m$

Answer 1

Answer: (B)

Mass of the solute, $C_{2}H_{4}(OH)_{2} = 222.6\, g$
Molar mass of solute $C_{2}H_{4}(OH)_{2} = 62\, g\,$ mol $^{-1}$
$\therefore $ Moles of the solute $ = \frac{222.6\, g}{62 \,g\, mol^{-1}} = 3.59$
Mass of the solvent $= 200\, g = 0.200\, kg$
Volume of solution $ = \frac{422.6}{1.072 \,g\, mL^{-1}}$
$= 394.2\, mL = 0.3942\, L$
Molality $ = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}}$
$ = \frac{3.59}{0.2} = 17.95\,m$