Question

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:

• A. 2
• B. 3
• C. 1
• D. 5

Answer 1

The Correct Option is B

A molecule X associates as per the equation: \(X ⇌ (X)_n\). Given: the van’t Hoff factor (i) is 0.80, and the fraction of associated molecules (α) is 0.3. We need to find the value of ‘n’.

For association, van’t Hoff factor is given by: 

\(i = 1 - α + \frac αn\)

Substitute the given values:

\(0.8 = 1 - 0.3 + \frac {0.3}{n}\)

Simplify the equation:

\(0.8 = 0.7 + \frac {0.3}{n}\)

\(0.1 = \frac {0.3}{n}\)

\(n = \frac {0.3}{0.1}\)

\(n = 3\)

Thus, the value of 'n' is \(3\).