Question

If in a solvent, $n$ simple molecules of solute combine to form an associated molecule, $\alpha$ is the degree of association, the van’t Hoff factor is equal to

• A. $\frac{1}{1 - n\alpha}$
• B. $1 - \alpha + n\alpha$
• C. $1 - \alpha + \frac{\alpha}{n}$
• D. $\frac{\alpha}{n} - 1 + \alpha$

Hint:

Association ↓ particles → $i<1$.

Answer 1

The Correct Option is C

Concept: Association reduces number of particles.

Step 1: Initial particles = 1.

Step 2: Fraction associated = $\alpha$, so remaining = $1 - \alpha$.

Step 3: Associated particles = $\textcolor{red}{\alpha/n}$ (since $n$ combine into 1).

Step 4: Total particles: \[ i = \textcolor{red}{(1 - \alpha) + \frac{\alpha}{n}} \] Conclusion:
van’t Hoff factor = $1 - \alpha + \frac{\alpha}{n}$