At 100 degrees C, pure H2O has a vapor pressure of 760 torr. An aqueous solution has a concentration of 1.90 M MgCl2. The van't Hoff factor is 2.45. The density of the solution is 1.09 g/mL. Calculate the vapor pressure of the solution.
You need to find the mole fraction of H2O.
1 L of the solution has a mass of
1000 mL x 1.09 g/mL = 1090 grams.
There are 1.90 mols MgCl2 in that 1 L and that has a mass of
1.90 x molar mass MgCl2 = approx 170 but you need to do it more accurately. This is just an estimate.
Grams of H2O in that 1 L solution = 1090-170 = approx 900 g or 900/18 = approx 50 mols.
mols MgCl2 from above = ? and that x i = ? mols corrected for i.
mols H2O from above = ?
XH2O = mols H2O/total mols where total mols = mols H2O + corrected mols MgCl2.
Then
psolution = XH2O*PoH2O
Post your work if you get stuck.
VP(Soln) = VP(Solvent) - VP(Lowering Factor)
Using the following:
=> VP(Lowering Factor) = VP(LF)
=> VP(Solvent) = VP(Solv)
=> Mole Fraction Solute = X(Solute) = X(Solu)
=> van 't Hoff factor = (VHF)
VP(Soln) = VP(Solv) - VP(LF)
--VP(LF-ionic Soln) = VP(Solv)·X(Solu)·(VHF)
Therefore...
VP(Ionic Soln) = VP(Solv) - [(VP-Solv)(X-Solu)(VHF)]
Given:
VP(Solv) = 760Torr = 760 mmHg @100-deg.C
[MgCl2] = 1.90M
VHF = 2.45
Density Soln = 1.09 g/ml
VP(MgCl2 Soln) = VP(HOH)@100C - [VP(HOH)·X(MgCl2)·(VHF)]
X(MgCl2):
1.9M(MgCl2)= (1.9mol(MgCl2)/L Soln)
= 1.9mol(MgCl2)/1000-ml Soln)
= [1.9mol(MgCl2)/(1000-ml Soln)(1.09 g/ml Soln)]
= 1.9mol(MgCl2)/1090 gms Soln)
Grams MgCl2 = 1.90mol(95.22g/mol) = 180.92 gms MgCl2
Grams HOH = 1090 gms Soln - 180.92 gms MgCl2 = 909.08 gms HOH.
Moles HOH = (909.08 gms/18 gms/mol) = 50.5 moles HOH
X(MgCl2) = [(moles MgCl2)/(moles MgCl2) + moles(HOH)]
= [(1.90)moles/(1.9 + 50.2)moles] = 0.036
VP(ionic soln) = VP(solv) - [(VP-Solv)(X-Solu)(VHF)]
= (760-mmHg) - [(760-mmHg)(0.036)(2.45)]
= (760 - 75.24)mmHg = 684.76mmHg = 684.76Torr.
To calculate the vapor pressure of the solution, we can use Raoult's law. Raoult's law states that the vapor pressure of a solution is proportional to the mole fraction of the solvent in the solution.
Step 1: Calculate the mole fraction of the solvent (water).
The concentration of the magnesium chloride (MgCl2) solution is given as 1.90 M (molar concentration). The van't Hoff factor is 2.45, which represents the number of particles the compound dissociates into when dissolved in water. In this case, it means that for every magnesium chloride (MgCl2) molecule, it dissociates into 2.45 particles (2 Mg2+ ions and 2 Cl- ions).
Since MgCl2 is a strong electrolyte, we can assume complete dissociation. Therefore, the concentration of chloride ions (Cl-) is twice the concentration of the magnesium chloride solution.
Concentration of Cl- ions = 2 * 1.90 M = 3.80 M
To calculate the mole fraction of water, we need to divide the concentration of water by the sum of the concentrations of water and Cl- ions:
Mole fraction of water = concentration of water / (concentration of water + concentration of Cl- ions)
Since the concentration of water is 55.6 M (from the density given: 1.09 g/mL * (1000 mL/L) / (18.015 g/mol)), the mole fraction of water is:
Mole fraction of water = 55.6 M / (55.6 M + 3.80 M) = 0.936
Step 2: Calculate the vapor pressure of the solution.
According to Raoult's law, the vapor pressure of the solution (P_solution) is equal to the mole fraction of the solvent (water) multiplied by the vapor pressure of the pure solvent (P_solvent).
P_solution = mole fraction of water * P_solvent
Given that the vapor pressure of pure water (P_solvent) is 760 torr, the vapor pressure of the solution is:
P_solution = 0.936 * 760 torr = 711.36 torr
Therefore, the vapor pressure of the solution is approximately 711.36 torr.