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Question

If 5 g of Na2SO4 is dissolved in 45 g of H2O, the freezing point is changed by 3.72C. Calculate the van't Hoff factor for Na2SO4.
Given: Freezing point depression constant for water is 1.86C kg mol1

A
1.85
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B
2.56
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C
3.11
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D
3.8
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Solution

The correct option is B 2.56
van't Hoff factor is a correction factor by which actual extent of association/ dissociation can be expressed.
To correct the colligative property we multiply colligative property with 'i'.
The corrected colligative property of depression in freezing point is given by,
Tf=i×Kf×m
where,
Tf is the depression in freezing point.
Kf is molal depression constant.
m is molality of solution.
i is van't Hoff factor
Tf=i×Kf×wB×1000mB×wA
where,
wb is mass of solute
mB is molar mass of solute
wA is mass of solvent

Given:
Kf=1.86C kg mol1
Tf=3.72C
wb=5 g
mB=142 g/mol
wA=45 g

3.72=i×1.86×5×1000142×45
i=2.56

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