Question

Two solvent A and B have $K_f$ values 1.86 and 2.79 K $mo{l}^{-1}$ kg respectively. A given amount of substance when dissolved in 500 g of A, it completely dimerizes and when same mass of substance is dissolved in 500 g of B, the solute undergoes trimerization.

The ratio of observed lowering of freezing points in two cases is 1:(?).

Answer 1

$\Delta T_f=i\times K_f\times m$ (where m is molality, i is van 't Hoff factor )

For both solutions m is same,

$\frac{\Delta T_f^A}{\Delta T_f^B}=\frac{i_A\times K_f^A\times m}{i_B\times K_f^B\times m}$

$\frac{\Delta T_f^A}{\Delta T_f^B}=\frac{0.5\times 1.86}{1/3\times 2.79}=1/1$

Hence, the statement is correct.