A 0.1 m solution of K2SO4 in water has a freezing point of – 4.3 °C. What is the value of van’t Hoff factor if Kf for water is 1.86 K kg mol–1?

Exercise | Q 2.04 | Page 45

Answer the following in one or two sentences.

A 0.1 m solution of K2SO4 in water has a freezing point of – 4.3 °C. What is the value of van’t Hoff factor if Kf for water is 1.86 K kg mol–1?

Solution

Given: Molality of K₂SO₄ solution = m = 0.1 m 
Freezing point of solution = T_f = – 4.3 °C 
K_f of water = 1.86 K kg mol^–1

To find: van’t Hoff factor

Formula: ΔT_f = i K_f m

Calculation: 

ΔT_f = ${\displaystyle {\text{T}}_{\text{f}}^0}$ - T_f

= 0 °C - (- 4.3 °C) = 4.3 °C = 4.3 K

Now, using formula,

ΔT_f = i K_f m

∴ i = ${\displaystyle \frac{△{\text{T}}_{\text{f}}}{{\text{K}}_{\text{f}}\cdot \text{m}}}$

${\displaystyle =\frac{4.3\text{K}}{1.86{\text{k kg mol}}^{-1}\times 0.1{\text{mol kg}}^{-1}}}$

= 23.1

The value of van’t Hoff factor is 23.1.