Final answer:
The student’s question concerns calculating the vapor pressure of a water-glycerin solution at 20.0°C using Raoult’s Law. The nonvolatile glycerin does not contribute to vapor pressure, but it does lower the ratio of water molecules in the solution, leading to a reduced vapor pressure compared to pure water.
Step-by-step explanation:
The student is asking to calculate the vapor pressure of a solution after glycerin is added to water at a specific temperature. Because glycerin (C3H8O3) is a nonvolatile solute, it won't contribute to the vapor pressure of the solution; only the solvent (water in this case) will. The vapor pressure of the solution can be found using Raoult's Law, which states that the vapor pressure of the solution (Psolution) is equal to the vapor pressure of the pure solvent (Psolvent) multiplied by the mole fraction (Xsolvent) of the solvent in the solution.
To use Raoult's Law, we need to calculate the mole fraction of water in the solution. First, we find the moles of glycerin by dividing its mass by its molar mass. Next, we find the mass of water using its density and the volume provided, and then convert this mass to moles. The mole fraction of water is the moles of water divided by the total moles of both water and glycerin. Then, we can calculate Psolution by multiplying this mole fraction by the given vapor pressure of pure water.
Assuming ideal behavior and ignoring any colligative properties that glycerin might introduce to the solution (which can be valid if the concentration of glycerin is low), the calculation for the vapor pressure of the solution will yield a value in torr. This value will be lower than the original vapor pressure of the pure water due to the addition of glycerin because the glycerin molecules take up space in the solution, reducing the number of water molecules present at the surface and thus their ability to escape into the vapor phase.