To calculate the vapor pressure of hexane above the solution, we need to use Raoult's law, which states that the vapor pressure of a component in an ideal solution is directly proportional to its mole fraction in the solution.
First, we need to find the mole fraction of hexane in the solution. The mole fraction is the ratio of the moles of hexane to the total moles of all components in the solution.
To find the moles of hexane, we can divide the mass of hexane by its molar mass:
Molar mass of hexane (C6H14) = (6 * atomic mass of carbon) + (14 * atomic mass of hydrogen)
= (6 * 12.01 g/mol) + (14 * 1.01 g/mol) = 86.18 g/mol
Now, let's calculate the moles of hexane:
moles of hexane = mass of hexane / molar mass of hexane
= (100 g - 11.39 g) / 86.18 g/mol
= 88.61 g / 86.18 g/mol
= 1.027 mol
Next, we need to find the moles of naphthalene in the solution. We can calculate this using the mass of naphthalene and its molar mass:
Molar mass of naphthalene (C10H8) = (10 * atomic mass of carbon) + (8 * atomic mass of hydrogen)
= (10 * 12.01 g/mol) + (8 * 1.01 g/mol)
= 128.18 g/mol
Now, let's calculate the moles of naphthalene:
moles of naphthalene = mass of naphthalene / molar mass of naphthalene
= 11.39 g / 128.18 g/mol
= 0.0889 mol
To find the mole fraction of hexane, we divide the moles of hexane by the total moles of both components:
mole fraction of hexane = moles of hexane / (moles of hexane + moles of naphthalene)
= 1.027 mol / (1.027 mol + 0.0889 mol)
= 0.920
Now, we can use Raoult's law to calculate the vapor pressure of hexane above the solution:
vapor pressure of hexane = mole fraction of hexane * vapor pressure of pure hexane
= 0.920 * 151 torr
= 138.32 torr
Therefore, the vapor pressure of hexane above the solution is 138.32 torr at 25 °C.