The vapor pressure of pure water at 10C is 9.2 torr. How many grams of MgCl2 would you need to add to 500 mL of water to drop the vapor pressure to 8.0?
delta P = i*Xsolute*Po
delta P is 9.2-8.0 = >
Po = 9.2
i = 3 for MgCl2.
Solve for Xsolute and use nsolute/(nsolute+nsolvent) = X
(Note that n solvent is 500/18). Solve for nsolute, convert to grams MgCl2.
To solve this problem, we need to use Raoult's law, which relates the vapor pressure of a solution to the mole fraction of the solute and the vapor pressure of the pure solvent.
Step 1: Calculate the mole fraction of the solute (MgCl2) in the solution.
To find the mole fraction, we need to know the amount in moles of MgCl2 and the amount in moles of water. However, the problem only provides information about the volume of water, so we need to use the density of water to convert the volume to mass and then to moles.
Step 2: Determine the mass of water in the solution using its density.
Since the problem states that the volume of water is 500 mL, we can use the density of water (which is approximately 1 g/mL) to find the mass of water in grams.
Mass of water = Volume of water x Density of water
Mass of water = 500 mL x 1 g/mL = 500 grams
Step 3: Calculate the mole fraction of the solute.
Mole fraction (x) = Moles of solute / Total moles of solute and solvent
Moles of solute = Mass of solute / Molar mass of solute
We need to determine the mass of MgCl2 needed to change the vapor pressure.
Step 4: Calculate the moles of MgCl2 needed.
We can use the formula:
Moles of solute = Mass of solute / Molar mass of solute
Since we need the mass of MgCl2 to achieve a certain vapor pressure, we'll rearrange the formula to find the mass:
Mass of solute = Moles of solute x Molar mass of solute
Step 5: Determine the molar mass of MgCl2.
The molar mass is the sum of the atomic masses of one magnesium atom and two chlorine atoms. The atomic masses can be found on the periodic table.
Atomic mass of Mg = 24.31 g/mol
Atomic mass of Cl = 35.45 g/mol
Molar mass of MgCl2 = (1 x Atomic mass of Mg) + (2 x Atomic mass of Cl)
Step 6: Calculate the mass of MgCl2.
Using the equation:
Mass of solute = Moles of solute x Molar mass of solute
Substituting the known values:
Mass of solute = Moles of solute x Molar mass of MgCl2
Now, we can use Raoult's law to determine the moles of MgCl2 needed to achieve the desired vapor pressure.
The mole fraction of the solute is given by:
x = (P_solute / P_solvent)
Where:
P_solute: Vapor pressure of the solute (unknown)
P_solvent: Vapor pressure of pure solvent (9.2 torr)
Since the vapor pressure is inversely proportional to the mole fraction, we can write:
P_solvent / P_solute = 1 / x
P_solute = P_solvent / x
Substituting the known values:
P_solute = 9.2 torr / x
Step 7: Determine the moles of solute from the vapor pressure.
We can use the equation:
Moles of solute = Moles of solvent x (P_solvent - P_solute) / P_solute
Substituting the known values:
Moles of solute = Moles of solvent x (8.0 torr - 9.2 torr) / 9.2 torr
Step 8: Calculate the mass of MgCl2.
Using the equation:
Mass of solute = Moles of solute x Molar mass of solute
Substituting the known values:
Mass of MgCl2 = Moles of solute x Molar mass of MgCl2
Following these steps will allow you to calculate the number of grams of MgCl2 needed to drop the vapor pressure of water to 8.0 torr.