Question

A dilute solution contains ${}^{\prime }{x}^{\prime }$ moles of solute $A$ in $1\text{kg}$ of solvent with molal elevation constant $K_b$. The solute dimerises in the solution according to the following equation.
$2A\rightleftharpoons A_2$
The degree of association is $\left(\alpha \right)$. The molar mass observed will be :
[1 Mark]

• A. Greater than the actual molar mass
• B. Lesser than the actual molar mass
• C. Equal to the actual molar mass
• D. Cannot be predicted by the data given

Answer 1

The correct option is A Greater than the actual molar mass

Given,
$\begin{array}{cccc}& 2A& \rightleftharpoons & A_2\\ \text{At t=0}& 1& & 0\\ \text{At}t=t_{\text{eq}}& 1-\alpha & & \frac{\alpha }{2}\end{array}$

$\therefore \text{van't Hoff factor}\left(i\right)=1-\alpha +\frac{\alpha }{2}=1-\frac{\alpha }{2}$
Again,
$i=\frac{\text{Normal molar mass}}{\text{Observed molar mass}}$
Since value of $i$ here is less than 1, hence The molar mass observed will be greater than the actual molar mass.