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 = Tf = – 4.3 °C 
Kf of water = 1.86 K kg mol–1

To find: van’t Hoff factor

Formula: ΔTf = i Kf m

Calculation: 

ΔTf = Tf0 - Tf

= 0 °C - (- 4.3 °C) = 4.3 °C = 4.3 K

Now, using formula,

ΔTf = i Kf m

∴ i = TfKfm

=4.3K1.86k kg mol-1×0.1mol kg-1

= 23.1

The value of van’t Hoff factor is 23.1.