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Question

In case a solute associates in solution, the van’t Hoff factor is :


A
i>1
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B
i=1
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C
i<1
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D
None of these
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Solution

The correct option is C $$i < 1$$
if a fraction $${\displaystyle \alpha }$$  of $${\displaystyle n}$$ moles of solute associate to form one mole of an n-mer (dimer, trimer, etc.), then

$${\displaystyle i=1-\left(1-{\frac {1}{n}}\right)\alpha .}$$

For the dimerisation of acetic acid in benzene

$$2CH_3COOH ⇌ {(CH_3COOH)}_2$$

2 moles of acetic acid associate to form 1 mole of dimer, so that

$${\displaystyle i=1-\left(1-{\frac {1}{2}}\right)\alpha =1-{\frac {\alpha }{2}}.}$$

For association in the absence of dissociation, the van 't Hoff factor is: $${\displaystyle i<1}$$

Hence, the correct option is $$\text{C}$$

Chemistry

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