Step-by-step explanation:
Raoult's law states that the vapor pressure of a solvent that is a over a solution is equal to the vapor pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent.
Psolution = Xsolvent * P°solvent
Where Psolution is the vapor pressure of the solution, X is the molar fraction of the solvent and P°solvent is the vapor pressure of the pure solvent.
Our solvent is chloroform, we know its vapor pressure.
P°solvent = 120 mmHg
We still have to find the molar fraction of the solvent. The molar fraction of the solvent will be defined like:
Xsolvent = moles of solvent/(total number of moles)
We know that the concentration of the solution is 0.200 m. That means that we have 0.200 moles of solute in each kg of solvent.
In order to find the mole fraction we have to suppose that the solution has 1 kg of solvent.
mass of solvent = 1 kg
molality = 0.200 m
molality = moles of solute/(mass of solvent in kg)
0.200 m = moles of solute/1 kg
moles of solute = 0.200 m * 1 kg
moles of solute = 0.200 moles
So our solution has 0.200 moles of solute in 1 kg of solvent. The solvent is chloroform (CHCl₃). We can convert the mass of solvent into moles using the molar mass of it.
molar mass of CHCl₃ = 119.38 g/mol
mass of solvent = 1 kg = 1 kg * 1000 g/kg
mass of solvent = 1000 g
moles of solvent = 1000 g * 1 moles/(119.38 g)
moles of solvent = 8.377 moles
Our solution has 8.377 moles of solvent and 0.200 moles the non-volatile solute.
total number of moles = moles of solute + moles of solvent
total number of moles = 8.377 moles + 0.200 moles
total number of moles = 8.577 moles
Xsolvent = moles of solvent/(total number of moles)
Xsolvent = 8.377 moles/(8.577 moles)
Xsolvent = 0.977
Finally we found the mole fraction of the solvent and we can find the answer to our problem.
Psolution = Xsolvent * P°solvent
Psolution = 0.977 * 120 mmHg
Psolution = 117.2 mmHg
Answer: The vapor pressure of the solution is 117.2 mmHg.