Final answer:
The vapor pressure of a solution containing equal masses of methanol and ethanol can be calculated using Raoult's Law. After determining the moles of each component and their respective mole fractions, the vapor pressures of methanol and ethanol are added together based on their mole fractions. The calculated vapor pressure is 73 torr.
Step-by-step explanation:
The question asks to calculate the vapor pressure of a solution containing methanol (CH3OH) and ethanol (CH3CH2OH) using their respective pure component vapor pressures at a given temperature. We can use Raoult's Law to find the solution's vapor pressure.
To calculate the mole fractions, first find the moles of methanol and ethanol using their molar masses:
- Molar mass of methanol (CH3OH): 32.04 g/mol
- Molar mass of ethanol (CH3CH2OH): 46.07 g/mol
Moles of methanol = 50.0 g / 32.04 g/mol = 1.560 mol
Moles of ethanol = 50.0 g / 46.07 g/mol = 1.085 mol
Total moles = 1.560 mol + 1.085 mol = 2.645 mol
Mole fraction of methanol = 1.560 mol / 2.645 mol = 0.590
Mole fraction of ethanol = 1.085 mol / 2.645 mol = 0.41
Now apply Raoult's Law:
Vapor pressure of solution = (Mole fraction of methanol × Vapor pressure of methanol) + (Mole fraction of ethanol × Vapor pressure of ethanol)
Vapor pressure of solution = (0.590 × 92 torr) + (0.410 × 45 torr)
Vapor pressure of solution = 54.28 torr + 18.45 torr
Vapor pressure of solution = 72.73 torr
Therefore, the closest answer to the calculated vapor pressure is 73 torr (Option A).