Question

The mole fraction of solute in some solution is $\frac{1}{n}$. If $50\%$ of the solute molecules dissociates into two parts and remaining $50\%$ get dimerized and new mole fractions of solvent become $\frac{4}{5}$ Find the value of n

Answer 1

Given, mole fraction of solute $=\frac{1}{n}=\frac{1}{1+(n-1)}$
So, original moles of solute = 1
Again, $50$ of the solute dissociates and $50\%$ of the solute dimerize and hence new number of moles = $1.25$
New mole fraction of solvent = $\frac{4}{5}$ and hence new mole fraction of the solute = $\frac{1}{5}$
$\therefore \frac{1}{5}=\frac{1.25}{1.25+(n-1)}$
$\Rightarrow 1.25+n-1=6.25$
$\Rightarrow n=6$