A solution contains naphthalene (C10H8) dissolved in hexane (C6H14) at a concentration of 11.39{\rm \\%} 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.
11.39% w/w is 11.39g naph/100 g solution.
100 g soln = 11.30g naph + 88.61g hexane.
n = mols naph = nnaph = grams/molar mass
nhexane = grams/molar mass.
Take sum of mols =
ntotal = nnaph + nhexane.
Xhex = nhexane/total mols
psolution = Xhexane*Pohexane</sub
psoln = Xhexane*Pohexane
To calculate the vapor pressure of hexane above the solution, we need to apply Raoult's Law. According to Raoult's Law, the vapor pressure above a solution is equal to the mole fraction of the solvent multiplied by its vapor pressure in its pure state.
First, let's calculate the mole fraction of hexane (C6H14) in the solution.
1. Calculate the mole fraction of naphthalene (C10H8):
Molar mass of naphthalene (C10H8) = 128 g/mol
Molar mass of hexane (C6H14) = 86 g/mol
Moles of naphthalene in 100 g of solution:
mass of naphthalene = (11.39/100) * 100 g = 11.39 g
moles of naphthalene = 11.39 g / 128 g/mol = 0.0889 mol
Moles of hexane in 100 g of solution:
mass of hexane = (100 - 11.39) g = 88.61 g
moles of hexane = 88.61 g / 86 g/mol = 1.0303 mol
Mole fraction of hexane (C6H14) in the solution:
mole fraction of hexane = moles of hexane / (moles of hexane + moles of naphthalene)
= 1.0303 mol / (1.0303 mol + 0.0889 mol)
= 0.9208
Next, we calculate the vapor pressure of hexane above the solution:
Vapor pressure of hexane above the solution = mole fraction of hexane * vapor pressure of pure hexane
= 0.9208 * 151 torr
= 139.15 torr
Therefore, the vapor pressure at 25 °C of hexane above the solution is 139.15 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 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.