What is the vapor pressure at 23 ¢ªC of a solution of 1.20 g of naphthalene, C10H8, in 25.6 g of benzene, C6H6? The vapor pressure of pure benzene at 23 ¢ªC is 86.0 mmHg; the vapor pressure of naphthalene can be neglected. Calculate the vapor pressure lowering of the solution.
mols naphthalene = grams/molar mass
mols benzene = grams/molar mass
Xnaph = nnaph/total mols
Xbenzene = nbenzene/total mols
pbenzene = Xbenzene*Pobenzene
plowering = Xnaph*Pobenzene
To calculate the vapor pressure lowering of the solution, we need to use Raoult's Law. Raoult's Law states that the vapor pressure of a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution.
First, let's calculate the mole fraction of benzene in the solution. To do this, we need to calculate the moles of benzene and naphthalene in the solution.
Step 1: Calculate the moles of benzene.
Molar mass of benzene (C6H6) = 78.11 g/mol
moles of benzene = mass of benzene / molar mass of benzene
moles of benzene = 25.6 g / 78.11 g/mol
Step 2: Calculate the moles of naphthalene.
Molar mass of naphthalene (C10H8) = 128.17 g/mol
moles of naphthalene = mass of naphthalene / molar mass of naphthalene
moles of naphthalene = 1.20 g / 128.17 g/mol
Step 3: Calculate the mole fraction of benzene.
mole fraction of benzene = moles of benzene / (moles of benzene + moles of naphthalene)
Now that we have the mole fraction of benzene, we can use Raoult's Law to calculate the vapor pressure of the solution.
Step 4: Calculate the vapor pressure of the solution.
vapor pressure of the solution = vapor pressure of pure benzene * mole fraction of benzene
Finally, to calculate the vapor pressure lowering, subtract the vapor pressure of the solution from the vapor pressure of pure benzene.
vapor pressure lowering = vapor pressure of pure benzene - vapor pressure of the solution.