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

Molecule X associates according to the equation: \(X ⇌ (X)_n\). The van’t Hoff factor (i) is given as 0.80, and the fraction of associated molecules (α) is 0.3. The objective is to determine the value of ‘n’.

The formula for the van’t Hoff factor in association is:

\(i = 1 - α + \frac αn\)

Substituting the provided values yields:

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

Simplifying the equation results in:

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

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

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

\(n = 3\)

Therefore, the value of 'n' is \(3\).