A solution contains naphthalene (C10H8) dissolved in hexane (C6H14) at a concentration of 11.07 % naphthalene by mass.
Calculate the vapor pressure at 25 ∘C of hexane above the solution. The vapor pressure of pure hexane at 25 ∘C is 151 torr.
To calculate the vapor pressure of hexane above the solution, we need to use Raoult's Law, which states that the vapor pressure of the solvent above the solution is directly proportional to the mole fraction of the solvent in the solution. The mole fraction of a component in a mixture is the ratio of the number of moles of that component to the total number of moles in the mixture.
Here's how you can calculate the vapor pressure of hexane above the solution:
1. Convert the mass percentage of naphthalene in the solution to the mole fraction of hexane:
- First, calculate the mass of naphthalene in the solution: mass_naphthalene = mass_solution * (mass_percentage / 100)
- Calculate the mass of hexane in the solution: mass_hexane = mass_solution - mass_naphthalene
- Calculate the number of moles of naphthalene: moles_naphthalene = mass_naphthalene / molar_mass_naphthalene
- Calculate the number of moles of hexane: moles_hexane = mass_hexane / molar_mass_hexane
- Calculate the mole fraction of hexane: mole_fraction_hexane = moles_hexane / (moles_naphthalene + moles_hexane)
2. Use Raoult's Law to calculate the vapor pressure of hexane above the solution:
- Calculate the vapor pressure of hexane: vapor_pressure_hexane = mole_fraction_hexane * vapor_pressure_hexane(pure)
Substituting the values, we have:
- mass_solution = mass_naphthalene + mass_hexane
- mass_percentage = 11.07%
- molar_mass_naphthalene = 128 g/mol
- molar_mass_hexane = 86.18 g/mol
- vapor_pressure_hexane(pure) = 151 torr
After calculating the mole fraction of hexane, you can substitute the values into the formula to find the vapor pressure of hexane above the solution.