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Question
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?
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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 Kfm
Calculation:
ΔTf = `"T"_"f"^0` – Tf
= 0 °C – (–4.3 °C) = 4.3 °C = 4.3 K
Now, using the formula,
ΔTf = i Kf.m
∴ i = `(Δ"T"_"f")/("K"_"f"."m")`
`= (4.3 "K")/(1.86 "k kg mol"^-1 xx 0.1 "mol kg"^-1)`
= 23.11
The value of van’t Hoff factor is 23.11.
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