Biphenyl, C12?H10 (molar mass =154.22 g/mol ), is a non-volatile, nonionizing solute that is soluble in benzene, C6?H6? (molar mass =78,12 g/mol ). At 25°C, the vapour pressure of pure benzene is 100.84 tort. What is the vapour pressure, in tort, of a solution made from dissolving 15.2 g of biphenyl in 31.3 g of benzene? Vapour pressure = tort. Report your answer to three significant figures. Do NOT include units in your answer.
The Correct Answer and Explanation is :
To find the vapor pressure of the solution, we can use Raoult’s Law:
[
P_{\text{solution}} = X_{\text{solvent}} \cdot P_{\text{solvent}}^{\text{pure}}
]
Where:
- ( P_{\text{solution}} ) is the vapor pressure of the solution.
- ( X_{\text{solvent}} ) is the mole fraction of the solvent (benzene) in the solution.
- ( P_{\text{solvent}}^{\text{pure}} ) is the vapor pressure of the pure solvent (benzene).
Step 1: Calculate the moles of biphenyl (solute) and benzene (solvent).
Moles of biphenyl:
[
\text{moles of biphenyl} = \frac{\text{mass of biphenyl}}{\text{molar mass of biphenyl}} = \frac{15.2\ \text{g}}{154.22\ \text{g/mol}} = 0.0985\ \text{mol}
]
Moles of benzene:
[
\text{moles of benzene} = \frac{\text{mass of benzene}}{\text{molar mass of benzene}} = \frac{31.3\ \text{g}}{78.12\ \text{g/mol}} = 0.400\ \text{mol}
]
Step 2: Calculate the mole fraction of benzene.
The mole fraction of benzene ((X_{\text{benzene}})) is:
[
X_{\text{benzene}} = \frac{\text{moles of benzene}}{\text{moles of benzene} + \text{moles of biphenyl}} = \frac{0.400}{0.400 + 0.0985} = \frac{0.400}{0.4985} = 0.802
]
Step 3: Apply Raoult’s Law.
Now, use Raoult’s Law to find the vapor pressure of the solution:
[
P_{\text{solution}} = X_{\text{benzene}} \cdot P_{\text{benzene}}^{\text{pure}} = 0.802 \cdot 100.84\ \text{torr} = 80.9\ \text{torr}
]
Final Answer:
The vapor pressure of the solution is 80.9 torr (to three significant figures).
Explanation:
This calculation assumes ideal behavior of the solution (no significant deviations from Raoult’s Law). The mole fraction of benzene, which is the solvent, influences the vapor pressure. As biphenyl is non-volatile, it does not contribute to the vapor pressure, so the solution’s vapor pressure depends solely on the benzene. By using Raoult’s Law, we adjusted the vapor pressure of pure benzene based on its mole fraction in the solution.