Final answer:
Using Raoult's Law and the mole fraction of ethanol, the vapor pressure of the solution is calculated to be 112.72 torr, which is close to the measured vapor pressure of 113 torr. This validates the information given that pure ethanol has a vapor pressure of 135.28 torr at 40°C.
Step-by-step explanation:
To find the vapor pressure of pure ethanol at 40°C using the given solution data, we can apply Raoult's Law. Raoult's Law states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent. Since glycerin is nonvolatile, it will not contribute to the vapor pressure, meaning the vapor pressure of the solution is solely due to the ethanol.
- First, we need to calculate the mole fractions of ethanol (C₂H₅OH) and glycerin (C₃H₈O₃) in the solution:
- The molar mass of glycerin is approximately 92.09 g/mol, and the molar mass of ethanol is about 46.07 g/mol.
- Using these molar masses, we can calculate the moles of each substance:
- Moles of glycerin = 53.6 g / (92.09 g/mol) = 0.582 moles
- Moles of ethanol = 133.7 g / (46.07 g/mol) = 2.902 moles
- Next, calculate the total moles of substance in the solution by adding the moles of glycerin and ethanol:
- Total moles = 0.582 moles (glycerin) + 2.902 moles (ethanol) = 3.484 moles
- Now, find the mole fraction of ethanol, which is the ratio of moles of ethanol to the total moles:
- Mole fraction of ethanol = 2.902 moles / 3.484 moles = 0.833
- Since the vapor pressure of pure ethanol at 40°C is given as 0.178 atm, and 1 atm is equivalent to 760 torr:
- Vapor pressure of pure ethanol in torr = 0.178 atm * 760 torr/atm = 135.28 torr
- To find the vapor pressure of ethanol in the solution using Raoult's Law:
- Raoult's Law: P_solution = X_ethanol * P_pure_ethanol
- P_solution = 0.833 * 135.28 torr = 112.72 torr
However, the measured vapor pressure is 113 torr, which is reasonably close to the calculated value, considering experimental uncertainties and the approximation that the solution behaves ideally.