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<p>Understanding Raoult's Law & Vapor Pressure Lowering</p>
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9. Solutions
Vapor Pressure Lowering (Raoult's Law)
Multiple Choice
The vapor pressure of water at 100.0ºC is 0.720 atm. Determine the mass percent of iron (II) chloride, FeCl2, needed to reduce its vapor pressure to 0.655 atm. (MW of FeCl2 is 126.756 g/mol)
A
67.7%
B
18.9%
C
22.5%
D
58.3%
Verified step by step guidance1
Identify the given data: vapor pressure of pure water at 100.0ºC (\(P^0 = 0.720\) atm), vapor pressure of the solution (\(P = 0.655\) atm), and molar mass of FeCl\(_2\) (126.756 g/mol). The goal is to find the mass percent of FeCl\(_2\) in the solution.
Use Raoult's Law, which relates the vapor pressure of the solvent in solution to the mole fraction of the solvent:
\[P = X_{\text{solvent}} \times P^0\]
Rearrange to find the mole fraction of water (\(X_{\text{water}}\)):
\[X_{\text{water}} = \frac{P}{P^0}\]
Express the mole fraction of water in terms of moles of water and moles of FeCl\(_2\):
\[X_{\text{water}} = \frac{n_{\text{water}}}{n_{\text{water}} + n_{\text{FeCl}_2}}\]
Assume a basis of 1 mole of water to simplify calculations, then solve for \(n_{\text{FeCl}_2}\) using the mole fraction found in step 2.
Convert moles of FeCl\(_2\) to grams using its molar mass:
\[\text{mass of FeCl}_2 = n_{\text{FeCl}_2} \times 126.756 \text{ g/mol}\]
Also, calculate the mass of water (since 1 mole of water has a molar mass of approximately 18.015 g).
Calculate the mass percent of FeCl\(_2\) in the solution using the formula:
\[\text{mass \% FeCl}_2 = \frac{\text{mass of FeCl}_2}{\text{mass of FeCl}_2 + \text{mass of water}} \times 100\%\]
This will give the required mass percent to reduce the vapor pressure to 0.655 atm.
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