Question

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?

Answer 1

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 = `"T"_"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 = `(triangle "T"_"f")/("K"_"f" * "m")`

`= (4.3 "K")/(1.86 "k kg mol"^-1 xx 0.1 "mol kg"^-1)`

= 23.1

The value of van’t Hoff factor is 23.1.