Answer:
To calculate the total vapor pressure above a mixture of two liquids, we can use Raoult's Law, which states that the partial vapor pressure of each component in a mixture is proportional to its mole fraction in the mixture.
The formula for calculating the partial vapor pressure of a component in a mixture is:
Partial Vapor Pressure = Mole Fraction * Vapor Pressure of Pure Component
Given:
- Vapor pressure of pure water (P₁) = 118 mm Hg
- Vapor pressure of ethanol (P₂) = 144 mm Hg
- Mass of ethanol (m₁) = 77.0 g
- Molar mass of ethanol (M₁) = 46.0 g/mol
- Mass of water (m₂) = 32.0 g
- Molar mass of water (M₂) = 18.0 g/mol
First, calculate the moles of each component:
Moles of ethanol (n₁) = m₁ / M₁
Moles of water (n₂) = m₂ / M₂
Calculate the total moles of the mixture:
Total moles (n_total) = n₁ + n₂
Calculate the mole fractions:
Mole fraction of ethanol (χ₁) = n₁ / n_total
Mole fraction of water (χ₂) = n₂ / n_total
Now, use Raoult's Law to calculate the partial vapor pressures:
Partial Vapor Pressure of ethanol (P₁') = χ₁ * P₁
Partial Vapor Pressure of water (P₂') = χ₂ * P₂
Finally, the total vapor pressure above the mixture is the sum of the partial vapor pressures:
Total Vapor Pressure = P₁' + P₂'
Substitute the given values and calculated values to find the total vapor pressure above the mixture.