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Answer :
Final answer:
The vapor pressure of the methanol-glycerol solution at 40°C is calculated using Raoult's law to be approximately 85.8 torr.
Explanation:
The question concerns the vapor pressure of a solution made by dissolving glycerol, a nonvolatile nonelectrolyte, in methanol. Using Raoult's law, which states that the vapor pressure of a solvent in a solution is equal to the mole fraction of the solvent times the vapor pressure of the pure solvent, we can calculate the vapor pressure of the solution.
Firstly, calculate the moles of methanol and glycerol:
- Moles of methanol = 95.7 g / 32.00 g/mol = 2.99125 moles
- Moles of glycerol = 38.0 g / 92 g/mol = 0.41304 moles
Next, calculate the mole fraction of the solvent (methanol) which is the ratio of moles of methanol to the total moles of both components:
- Mole fraction of methanol = Moles of methanol / (Moles of methanol + Moles of glycerol) = 2.99125 / (2.99125 + 0.41304) = 0.8785
Now, apply Raoult's law:
- Vapor pressure of the solution = Mole fraction of methanol * Vapor pressure of pure methanol
- Vapor pressure of the solution = 0.8785 * 97.7 ker (should be corrected to torr)
- Vapor pressure of the solution ≈ 85.8 torr
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