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%

Answer: (B)

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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 \(n_{\text{FeCl}_2}\).
5. 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.