in a solvent 50% of benzoic acid dimerises while the rest ionises. determine molar mass of acid which is observed and also its van't hoff factor.

Formula to calculate i ( Van't haff factor) using $\alpha $ (degree of ionizaion) is as follows:

i = (1-$\alpha $) + $\frac{\alpha}{n}$

Here,

$\alpha $ = 50/100 = 0.5

n = 2 (dimerisation)

i = (1.0-0.5) + 0.5/2

= 0.75

i = $\frac{\mathrm{Observed}\mathrm{molar}mass}{\text{ActualMolarmass}}$

0.75 = $\frac{\mathrm{Observed}\mathrm{molar}mass}{122\text{g/mol}}$

Observed Molar mass = 0.75 x 122 g/mol

= 91.5 g/mol

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