A molecule \(X\) associates in a given solvent as per the following equation:

\(X ⇌ (X)_n\)

For a given concentration of \(X\), the van't Hoff factor was found to be 0.80 and the fraction of associated molecules was \(0.3\). The correct value of 'n' is:

3

The correct answer is option 3. 3.

The given equation is

\(X ⇌ (X)_n\)

Given,

\(\text{van't Hoff factor, i }= 0.80\)

\(\text{Fraction of associated molecules }, \alpha = 0.3\)

We know,

\(i = 1 + \alpha \left(\frac{1}{n} - 1\right)\)

or, \(0.80= 1 + 0.3 \left(\frac{1}{n} - 1\right)\)

or, \(0.80= 1 +  \frac{0.3}{n} - 0.3\)

or, \(0.80= 0.70 +  \frac{0.3}{n} \)

or, \(0.10=   \frac{0.3}{n}\)

or, \(n=   \frac{0.3}{0.10}\)

or, \(n =   3\)