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The normal boiling point of methanol is 64.7°C. A solution containing a nonvolatile solute dissolved in methanol has a vapor pressure of 417.0 torr at 64.7°C. What is the mole fraction of methanol in this solution?
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14. Solutions
Vapor Pressure Lowering (Raoult's Law)
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What is the vapor pressure of a solution made by dissolving 150.0 grams of sucrose (C12H22O11) in 250.0 grams of water at 25.0 °C? The molar mass of sucrose is 342.34 g/mol, the molar mass of water is 18.02 g/mol, and the vapor pressure of pure water at 25.0 °C is 23.8 mmHg.
A
23.1 mmHg
B
24.5 mmHg
C
23.8 mmHg
D
22.5 mmHg
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Calculate the number of moles of sucrose (C12H22O11) using its mass and molar mass. Use the formula: \( \text{moles of sucrose} = \frac{\text{mass of sucrose}}{\text{molar mass of sucrose}} \).
Calculate the number of moles of water using its mass and molar mass. Use the formula: \( \text{moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} \).
Determine the mole fraction of water in the solution. The mole fraction of water is given by: \( X_{\text{water}} = \frac{\text{moles of water}}{\text{moles of water} + \text{moles of sucrose}} \).
Apply Raoult's Law to find the vapor pressure of the solution. Raoult's Law states: \( P_{\text{solution}} = X_{\text{water}} \times P^0_{\text{water}} \), where \( P^0_{\text{water}} \) is the vapor pressure of pure water.
Substitute the values into the equation from Raoult's Law to calculate the vapor pressure of the solution.
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