2. A 3.37 gram sample of a nonvolatile nonelectrolyte ( no ions) is dissolved in 23.7 grams of hexane (C6H14) at 25.0 degrees calcius. The vapor pressure of pure hexane at this temperature is 438 tort, and the vapor pressure of the solution is 419.3 torr. Calculate the molecular weight of the nonelectrolyte.
Psoln = Xhexane*Pohexane
Solve for Xhexane. Then 1-Xhexane = Xunknown.
nunknown/total mols = Xunknown.
Total mols = nunknown + nhexane. You have grams hexane and molar mass hexane; therefore you have n hexane. Solve for n unknown.
Then n unknown = grams/molar mass.
Solve for molar mass unknown.
To calculate the molecular weight of the nonelectrolyte, we need to use Raoult's law and the concept of vapor pressure.
Raoult's law states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution. Mathematically, it can be represented as:
Psolution = Xsolute * Psolvent,
where Psolution is the vapor pressure of the solution, Xsolute is the mole fraction of the solute, and Psolvent is the vapor pressure of the pure solvent.
In this case, the solute is the nonvolatile nonelectrolyte, and the solvent is hexane. We are given the following information:
Mass of solute (nonvolatile nonelectrolyte): 3.37 g
Mass of solvent (hexane): 23.7 g
Temperature: 25.0 °C
Vapor pressure of pure hexane (Psolvent): 438 torr
Vapor pressure of the solution (Psolution): 419.3 torr
First, we need to calculate the mole fraction of hexane in the solution.
Mole fraction (Xsolute) = Moles of solute / Total moles in the solution.
To find the moles of solute, we need to convert the mass of the solute to moles using its molecular weight. Since we are looking to find the molecular weight, we'll assume an arbitrary value for now.
Next, we'll find the number of moles of hexane using its molecular weight and the mass of the solvent.
Finally, we can use the mole fractions and the vapor pressure values to apply Raoult's law and solve for the molecular weight of the nonelectrolyte.
Let's go step by step to calculate the molecular weight:
1. Calculate the moles of solute:
Moles of solute = Mass of solute / Molecular weight of solute
Since the mass of the solute is given as 3.37 g and its molecular weight is unknown, we'll assume an arbitrary value for now (let's use "M" for molecular weight).
Moles of solute = 3.37 g / M
2. Calculate the moles of hexane:
Moles of hexane = Mass of hexane / Molecular weight of hexane
Moles of hexane = 23.7 g / (molecular weight of hexane)
3. Calculate the mole fraction of hexane:
Mole fraction of hexane (Xsolute) = Moles of hexane / (Moles of solute + Moles of hexane)
4. Apply Raoult's law:
Psolution = Xsolute * Psolvent
Rearrange the equation to solve for the molecular weight of the solute (nonelectrolyte):
M = (Xsolute * Psolvent) / Psolution
Substitute the values and solve for M.
By following these steps, you can calculate the molecular weight of the nonelectrolyte.