Chemistry - Liquid Solution Question with Solution | TestHub

A non-volatile solid solute X is dissolved in 1 kg of a liquid solvent S having a cryoscopic constant ${\mathrm{K}}_{\mathrm{f}}=0.5\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$. In this solution, $X$ simultaneously undergoes dimerization $\left(2X\rightleftharpoons {\mathrm{X}}_2\right)$ and dissociation $\left(X\rightleftharpoons A^{+}+B^{-}\right)$, and at equilibrium $20\%$ of the initial moles of $X$ remain as monomeric $X,40\%$ of the initial moles combine to form the dimer ${\mathrm{X}}_2$, while the remaining moles undergo complete dissociation into ${\mathrm{A}}^{+}$and ${\mathrm{B}}^{-}$. If the observed depression in freezing point is 3.0 K , calculate the initial number of moles of X added, assuming the solution is dilute and the mass of the solvent remains 1 kg .