JEE Advanced 2025 · Paper 2, Chemistry question 13

At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density $= 1.00\ \mathrm{g\,cm^{-3}}$) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule is $2.00\ \mathrm{g\,dm^{-3}}$, the molar mass of the macromolecule is calculated to be $\boldsymbol{X}\times10^4\ \mathrm{g\,mol^{-1}}$. The value of $\boldsymbol{X}$ is _____.

Use: Universal gas constant (R) $= 8.3\ \mathrm{J\,K^{-1}\,mol^{-1}}$ and acceleration due to gravity ($g$) $= 10\ \mathrm{m\,s^{-2}}$