Chemistry - Liquid Solution Question with Solution | TestHub

$4\%$ solution of sucrose $(\mathrm{w}/\mathrm{v})$ means 4 g of sucrose is dissolved in 100 mL of solution. Similarly, $2\%(\mathrm{w}/\mathrm{v}$ ) solution of ' X ' means 2 g of X present in 100 mL of solution. As we know that, osmotic pressure $(\pi )=$ CRT or $\pi =\frac{n}{V}RT$; where $n=$ number of moles of solute. Since, ${\pi }_1$ (for sucrose solution) $={\pi }_2$ (for X solution) $\therefore \frac{{\mathrm{n}}_1}{{\mathrm{V}}_1}\mathrm{RT}=\frac{{\mathrm{n}}_2}{{\mathrm{V}}_2}\mathrm{RT}$ $\begin{array}{rl}& \Rightarrow \frac{4}{342}=\frac{2}{\text{ Molecular weight }}\\ & \left[\because \mathrm{n}=\frac{\text{ Mass of solute }}{\text{ Molar mass of solute }}\right]\\ & \Rightarrow \text{ Molecular weight }=\frac{2}{4}\times 342\end{array}$ Molecular weight $=171\mathrm{g}{\mathrm{mol}}^{-1}$