One mole of a solute A is dissolved in a given volume of a solvent. The association of the solute take place as follows $n A ⇌ A_{n}$ . If a is the degree of association of A, the Van’t Hoff factor i is expressed as

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$i = 1 - α$

$i = 1 + \frac{α}{n}$

$i = 1 - α + \frac{α}{n}$

$i = 1$

answer is C.

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Detailed Solution

$n A \underset{}{⇌} A_{n}$

at Initial mole =1 , $n_{i} = 1$

At equilibrium state.

$\begin{array}{l} 1 - α \frac{α}{n}, \\ \Rightarrow n_{eq} = 1 - α + \frac{α}{n} \end{array}$ ( i = Van’t Hoff factor)

$\begin{array}{l} ∴ i = \frac{n_{eq}}{n_{i}} \\ = \frac{1 - α + \frac{α}{n}}{1} \end{array}$ ( i = Van’t Hoff factor) $i = 1 - α + \frac{α}{n}$

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