If osmotic pressure of 4 \%(w / v) solution of sucrose is same as 2...

$4 \%$ 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 $\pi=\frac{n}{V} R T$; where $n=$ number of moles of solute. Since, $\pi_1$ (for sucrose solution) $=\pi_2$ (for X solution) $\therefore \quad \frac{\mathrm{n}_1}{\mathrm{~V}_1} \mathrm{RT}=\frac{\mathrm{n}_2}{\mathrm{~V}_2} \mathrm{RT}$$\begin{aligned} & \Rightarrow \quad \frac{4}{342}=\frac{2}{\text{ Molecular weight }} \\ & {\left[\because \mathrm{n}=\frac{\text{ Mass\text{ of } solute }}{\text{ Molar mass of solute }}\right]} \\ & \Rightarrow \text{ Molecular weight }=\frac{2}{4} \times 342\end{aligned}$$$Molecular weight$=171 \mathrm{~g} \mathrm{~mol}^{-1}$