an aqueous solution was prepared by dissolving 1438.0g of a nonelectrolyte in 469.0g of water at 25*c. the Vapor pressure of the resulting solution was found to be 20.5 torr. what is the molar mass of the unknown compound? the vapor pressure of the water at 25*c is 23.76torr.
delta Psoln = Xsolute*PoH2O
23.76-20.5 = Xsolute*Psolvent
Solve for Xsolute.
Then
nsolute/(n solute + n H2O) = Xsolute
n H2O = 469/molar mass H2O.
Solve for n solute, then
n = grams/molar mass and rearrange to
molar mass = grams/n. Solve for molar mass.
To find the molar mass of the unknown compound, we need to use Raoult's law, which states that the vapor pressure of a solution depends on the mole fraction of the solvent and the vapor pressure of the pure solvent.
The mole fraction of the solvent (water) can be calculated using the formula:
Mole fraction of water = Moles of water / Total moles of solute and solvent
First, let's calculate the moles of water:
Moles of water = Mass of water / Molar mass of water
Given:
Mass of water = 469.0 g
Molar mass of water = 18.015 g/mol (approximately the molar mass of water)
Moles of water = 469.0 g / 18.015 g/mol ≈ 26.030 mol
Next, let's calculate the moles of the non-electrolyte compound:
Moles of non-electrolyte = Mass of non-electrolyte / Molar mass of non-electrolyte
Given:
Mass of non-electrolyte = 1438.0 g
Molar mass of non-electrolyte = ?
We can rearrange Raoult's law formula to solve for the molar mass of the non-electrolyte:
Vapor pressure of solution = Mole fraction of water * Vapor pressure of pure water
Rearranging for the molar mass of non-electrolyte:
Molar mass of non-electrolyte = Mass of non-electrolyte / (Mole fraction of water * Vapor pressure of pure water)
Now, let's calculate the mole fraction of water:
Mole fraction of water = Moles of water / (Moles of water + Moles of non-electrolyte)
Mole fraction of water = 26.030 mol / (26.030 mol + Moles of non-electrolyte)
Substituting the given numbers:
20.5 torr = (26.030 mol / (26.030 mol + Moles of non-electrolyte)) * 23.76 torr
Now, we can solve for Moles of non-electrolyte:
Moles of non-electrolyte = Moles of water * [(23.76 torr / 20.5 torr) - 1]
Substituting the values:
Moles of non-electrolyte = 26.030 mol * [(23.76 torr / 20.5 torr) - 1]
Once you have the value for Moles of non-electrolyte, you can calculate the molar mass of the non-electrolyte compound:
Molar mass of non-electrolyte = Mass of non-electrolyte / Moles of non-electrolyte
Substituting the given values:
Molar mass of non-electrolyte = 1438.0 g / Moles of non-electrolyte
Finally, calculate the molar mass of the unknown non-electrolyte compound by substituting the value of Moles of non-electrolyte into the equation.