At \( 300 \, \text{K} \), an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (\( h \)) of the solution (density \( = 1.00 \, g \, \text{cm}^{-3} \)) where \( h \) is equal to \( 2.00 \, \text{cm} \). If the concentration of the dilute solution of the macromolecule is \( 2.00 \, g \, \text{dm}^{-3} \), the molar mass of the macromolecule is calculated to be \( X \times 10^{4} \, g \, \text{mol}^{-1} \). The value of \( X \) is __________.
Use: Universal gas constant (\( R \)) \( = 8.3 \, J \, K^{-1} \, \text{mol}^{-1} \) and acceleration due to gravity (\( g \)) \( = 10 \, \text{m} \, \text{s}^{-2} \).
