To calculate the vapor pressure of a solution containing urea (a nonvolatile solute) in water, we can use Raoult's Law, which states:
\[ P_{\text{solution}} = X_{\text{solvent}} \times P^0_{\text{solvent}} \]
where:
- \( P_{\text{solution}} \) is the vapor pressure of the solution,
- \( X_{\text{solvent}} \) is the mole fraction of the solvent (water),
- \( P^0_{\text{solvent}} \) is the vapor pressure of the pure solvent (water).
Step 1: Calculate the number of moles of urea and water.
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Moles of urea: \[ \text{Moles of urea} = \frac{11.5 \text{ grams}}{124.16 \text{ g/mole}} \approx 0.0927 \text{ moles} \]
-
Moles of water: \[ \text{Moles of water} = \frac{137.5 \text{ grams}}{18.02 \text{ g/mole}} \approx 7.634 \text{ moles} \]
Step 2: Calculate the total number of moles in the solution.
\[ \text{Total moles} = \text{Moles of urea} + \text{Moles of water} \approx 0.0927 + 7.634 \approx 7.7267 \text{ moles} \]
Step 3: Calculate the mole fraction of water.
\[ X_{\text{water}} = \frac{\text{Moles of water}}{\text{Total moles}} = \frac{7.634}{7.7267} \approx 0.988 \]
Step 4: Calculate the vapor pressure of the solution using Raoult's Law.
Given that \( P^0_{\text{water}} = 71.93 \text{ mmHg} \):
\[ P_{\text{solution}} = X_{\text{water}} \times P^0_{\text{water}} = 0.988 \times 71.93 \text{ mmHg} \approx 71.08 \text{ mmHg} \]
Final Result
The vapor pressure of the solution at 45.0°C is approximately 71.08 mmHg.
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