(a) Calculate the vapor pressure of water above a solution prepared by adding 22.5 g of lactose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) to 200.0 \(\mathrm{g}\) of water at 338 \(\mathrm{K}\) . (Vapor-pressure data for water are given in Appendix B.) (b) Calculate the mass of propylene glycol \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{2}\right)\) that must be added to 0.340 \(\mathrm{kg}\) of water to reduce the vapor pressure by 2.88 torr at \(40^{\circ} \mathrm{C}\) .

a) The vapor pressure of water above the lactose solution at 338 K is calculated using the molality of the lactose solution and Raoult's Law. We find that the molality is \(\frac{moles\,of\,lactose}{0.200\,kg}\), and then use the mole fraction of water and the vapor pressure of pure water at 338 K to find the vapor pressure: \(P_{water} = X_{water} * P_{water}^{*}\). b) To calculate the mass of propylene glycol to be added to reduce the vapor pressure by 2.88 torr at $40^{\circ} \mathrm{C}$, we first determine the molality of the propylene glycol solution, then use this to find the moles of propylene glycol in the mixture. Finally, we find the mass of propylene glycol needed by multiplying the moles by the molar mass (76 g/mol).