Q. When 20 g of Naphthoic acid $\left(\right.C_{11}H_{8}O_{2}\left.\right)$ is dissolved in 50 g of benzene $\left(\right.K_{f}=1.72$ $Kkgmol^{- 1}\left.$ , a freezing point depression of 2 K is observed. The Van’t Hoff factor (i) is

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A

1

B

3

C

0.5

D

2

Solution:

The Van 't Hoff factor(i ) (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute on colligative properties such as osmotic pressure, relative lowering in vapour pressure, boiling-point elevation and freezing-point depression. The Van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass.
$\Delta T_{f}=K_{f}\times molality\times i$
$2=1.72\times \frac{20}{172}\times \frac{1000}{50}\times i$
$i=0.5.$

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