$31g$ of ethylene glycol $\left(C_2{H}_6{O}_2\right)$ is mixed with $500g$ of solvent ($K_f$ of the solvent is $2K$ $kg$ ${mol}^{-1}$). What is the freezing point of the solution (in $K$)?

[Freezing point of solvent $=273K$]

The correct option is B $271$
Given, $W_B=$ mass of solute (ethylene glycol) $=31g$

$W_A=$ mass of solvent $=500g$

$M_B=$ Ethylene glycol $\left(C_2{H}_6{O}_2\right)$

$=(2\times 12+6+2\times 16)=62g$

$K_f=2K$ $kg$ ${mol}^{-1}$

$\Delta T_f=K_f\frac{W_B}{M_B}\times \frac{1000}{W_A}$

$\Delta T_f=\frac{2\times 31\times 1000}{62\times 500}=2K$

$\because \Delta T_f=T_f^o-T_f$

$T_f=T_f^o-2$ ($\because$ Depression in freezing point $=2K$)

$\therefore T_f=273-2=271K$