Multiple Choice
Which of the following statements correctly describes the effect of adding a nonvolatile solute to a solvent according to Raoult's Law?
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14. 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 type of solution and the relevant colligative property. Since the problem involves lowering the vapor pressure of water by adding a solute (FeCl\_2), we use Raoult's Law, which relates vapor pressure lowering to mole fraction of the solvent.
Write Raoult's Law for the solvent (water):
\[ P_{\text{solution}} = X_{\text{water}} \times P^\circ_{\text{water}} \]
where \(P_{\text{solution}}\) is the vapor pressure of the solution, \(X_{\text{water}}\) is the mole fraction of water, and \(P^\circ_{\text{water}}\) is the vapor pressure of pure water.
Calculate the mole fraction of water using the given vapor pressures:
\[ X_{\text{water}} = \frac{P_{\text{solution}}}{P^\circ_{\text{water}}} \]
Substitute the given values for \(P_{\text{solution}} = 0.655\) atm and \(P^\circ_{\text{water}} = 0.720\) atm.
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 \(n_{\text{FeCl}_2}\).
Convert moles of FeCl\_2 to mass using its molar mass:
\[ \text{mass of FeCl}_2 = n_{\text{FeCl}_2} \times 126.756 \text{ g/mol} \]
Calculate the mass percent of FeCl\_2 in the solution using:
\[ \text{mass \% FeCl}_2 = \frac{\text{mass of FeCl}_2}{\text{mass of FeCl}_2 + \text{mass of water}} \times 100\% \]
Use the mass of water as 18.015 g (molar mass of water) for 1 mole.
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