A molecule $M$ associates in a given solvent according to the equation $\mathrm{M}…
A molecule $M$ associates in a given solvent according to the equation $\mathrm{M} \rightleftharpoons(\mathrm{M})_n$. For a certain concentration of M, the van't Hoff factor was found to be $0.9$ and the fraction of associated molecules was $0.2$. The value of $n$ is:
3
5
2
4
Solution
van't Hoff factor (i) and the degree of association are related as below :
$
\begin{aligned}
& i=1-\alpha\left(1-\frac{1}{n}\right) \\
& 0.9=1-0.2\left(1-\frac{1}{n}\right)
\end{aligned}
$
On solving,
$
\begin{aligned}
& \left(1-\frac{1}{n}\right)=\frac{1}{2} \\
& \frac{1}{n}=1-\frac{1}{2}=\frac{1}{2} \\
& \therefore n=2
\end{aligned}
$