Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to $$4 kg$$  of water to prevent it from freezing at $$ - {6^ \circ }C$$  will be : ( $${K_f}$$ for water = $$1.86\,K\,kg\,mo{l^{ - 1}},$$    and molar mass of ethylene glycol = $$62\,g\,mo{l^{ - 1}}$$   )

Solution :
\[\begin{align} & \text{Given}\,{{K}_{f}}=1.86\,K\,kg\,mo{{l}^{-1}} \\ & \Delta {{T}_{f}}=0-\left( -6 \right)={{6}^{\circ }}C \\ & \text{As we know that} \\ & \Delta {{T}_{f}}={{K}_{f}}\times \text{molality} \\ & \text{=}\frac{{{K}_{f}}\times 1000\times \text{mass of solute}}{\begin{align} & \text{molar mass of}\,\text{solute }\times \text{ mass of solvent in kg} \\ & \text{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \\ \end{align}} \\ & \text{Substituting given values in formula} \\ & 6=\frac{1.86\times 1000\times w}{62\times 4};\,w=0.8\,kg=800\,gm \\ & \\ \end{align}\]