The vapor pressure of water (at 50.0 o C) is lowered by 17.0 torr when 36.1 g of an unknown non-electrolyte is added to 65.56 g water. Determine the molecular weight of the unknown.
Density solution = 1.05 g/mL
Vapor pressure H2O @ 50oC = 92.5 torr
To determine the molecular weight of the unknown non-electrolyte, we can use Raoult's Law, which relates the vapor pressure of a solution to the mole fraction of the solute.
Raoult's Law states:
P(total) = X(solvent) * P(solvent)
where P(total) is the total vapor pressure of the solution,
X(solvent) is the mole fraction of the solvent, and
P(solvent) is the vapor pressure of the pure solvent.
In this case, we are given the vapor pressure of water (P(solvent)) and the change in vapor pressure of the solution (P(total) - P(solvent)).
To determine the mole fraction of the solvent, we need to calculate the number of moles of water and the number of moles of the unknown solute.
First, we calculate the number of moles of water:
moles of water = mass of water / molar mass of water
Given:
mass of water = 65.56 g
molar mass of water = 18.015 g/mol
moles of water = 65.56 g / 18.015 g/mol
Next, we calculate the number of moles of the unknown non-electrolyte:
moles of unknown solute = mass of the unknown / molar mass of the unknown
Given:
mass of the unknown = 36.1 g
To calculate the molar mass of the unknown, we will use the equation:
molar mass of the unknown = (mass of the unknown) / (moles of the unknown solute)
Finally, we can substitute the known values into Raoult's Law to solve for the molar mass of the unknown non-electrolyte.
Molecular weight of the unknown = molar mass of the unknown