A solution of glucose has 22.5 g in each litre…

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A solution of glucose has $22.5\ \text{g}$ in each litre. A solution of a non-electrolyte X has $3.4\ \text{g}$ in $400\ \text{mL}$ . At the same temperature the two solutions are isotonic. Find the molar mass of X. The molar mass of glucose is $180\ \text{g/mol}$ .

Need a reminder? The key ideaShow

The osmotic pressure of a dilute solution is $\pi = CRT$ , with $C$ in mol/L and $T$ in kelvin. $R = 0.0821\ \text{L atm K}^{-1}\text{mol}^{-1}$ gives atm, and $R = 8.314\ \text{J K}^{-1}\text{mol}^{-1}$ gives kPa. Isotonic solutions have equal $\pi$ . A column of height $h$ of a liquid of density $\rho$ gives a pressure $\rho g h$ .

The worked solution

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