Determine the mass(w/w%) percent of CaCl2 given the following information. The vapor pressure of a CaCl2 solution is 81.6 mmHg at 50degrees C. The vapor pressure of pure water at this temp is 92.6mmHg. Assume that you have 1.00mol of water.[Raoult's Law: P(solution)=X(solvent)P^o
(solvent)]
psoln = XH2O*PoH2O
81.6 = XH2O*92.6
XH2O = 81.6/92.6 = approx 0.88 but you need a more accurate number than that estimate.
Set up mole fraction expression for H2O.
[nH2O/(nH2O + nCaCl2)] = 0.88
nH2O = 1 in the problem;solve for nCaCl2 (as ions) and I get about 0.135. The van't Hoff factor is 3 for CaCl2 so mols CaCl2 in the molecular form is 0.135/3 = about 0.045 and convert that to grams CaCl2. That's approximately 5.0 grams.
% w/w = (mass solute/mass solution)*100 = ?
% = [(5.0/(5.0+ 18)]*100 = about 22% w/w.
Another way to do this is
vapor pressure LOWERING or
delta P = i*XCaCl2*PoH2O
92.6-81.6 = 11 = XCaCl2*92.6 and solve for XCaCl2. XCaCl2 = about 0.12 so XH2O = 1.0-0.12 = about 0.88 and go from there.
To determine the mass(w/w%) percent of CaCl2 in the solution, we need to use Raoult's Law and the given vapor pressure data.
Raoult's Law states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent in the solution. It can be written as:
P(solution) = X(solvent) * P°(solvent)
Where:
P(solution) is the vapor pressure of the solution
X(solvent) is the mole fraction of the solvent
P°(solvent) is the vapor pressure of the pure solvent
In this case, the solvent is water, and we are given that the vapor pressure of pure water (P°(solvent)) at 50 degrees C is 92.6 mmHg.
First, let's calculate the mole fraction of water (X(solvent)) in the solution using the given information.
Since we have 1.00 mol of water, and we know that the solution contains both water and CaCl2, the total moles of solute and solvent in the solution is also 1.00 mol.
Mole fraction (X) is defined as the ratio of the moles of a component to the total moles in the solution.
The mole fraction of water (X(solvent)) can be calculated as follows:
X(solvent) = moles of water / total moles
= 1.00 mol / (1.00 mol + moles of CaCl2)
Now, we can use Raoult's Law to find the vapor pressure of the CaCl2 solution (P(solution)). We are given that the vapor pressure of the solution is 81.6 mmHg.
81.6 mmHg = X(solvent) * 92.6 mmHg
Now, we can rearrange the equation to solve for X(solvent):
X(solvent) = 81.6 mmHg / 92.6 mmHg
Finally, to determine the mass(w/w%) percent of CaCl2 in the solution, we need to find the mole fraction of CaCl2 (X(solute)) in the solution.
Since the sum of mole fractions of all components in a solution is equal to 1, we can calculate X(solute) as:
X(solute) = 1 - X(solvent)
Once we have X(solute), we can convert it to mass percent by multiplying by 100.
Mass(w/w%) percent of CaCl2 = X(solute) * 100
So, by following these calculations, you should be able to determine the mass(w/w%) percent of CaCl2 in the solution.