Carbon disulfide (CS2) has a boiling point of 46.2°C. ?What is the boiling point elevation of a
solution consisting of 13.7g ?phosphorus (P4) ?dissolved in 62.67g ?of CS2 ? ( {:CS2KK=2.34)
Use the Molar Mass:
C=12.01gmol
P=30.97gmol
S=32.06gmol
Round your answer to 3 ?significant figures.
Calculate the Vapor Pressure of a solution of 11.138g ?of aspirin (C9H8O4) ?in 65.271g ?of methanol
(CH3OH) ?at 21.2°C.
Methanol has a vapor pressure of 101 ?torr at this temperature.
Use the following Molar Mass:
C=12.01gmol
H=1.01gmol
O=16.00gmol
Round your answer to 5 ?significant figures.
The Correct Answer and Explanation is :
Part 1: Boiling Point Elevation Calculation
To calculate the boiling point elevation of the solution, we need to use the following formula:
[
\Delta T_b = K_b \times m
]
Where:
- (\Delta T_b) is the boiling point elevation,
- (K_b) is the ebullioscopic constant (boiling point elevation constant) of the solvent (CS2), which is given as 2.34 °C·kg/mol,
- (m) is the molality of the solution.
Step 1: Calculate the number of moles of phosphorus (P4)
To find the molality of the solution, we first need to calculate the number of moles of phosphorus (P4) that are dissolved in 62.67 g of CS2.
- Molar mass of phosphorus (P) is given as 30.97 g/mol.
- Molar mass of P4 is (4 \times 30.97 \, \text{g/mol} = 123.88 \, \text{g/mol}).
Now, calculate the moles of phosphorus (P4) in 13.7 g of phosphorus:
[
\text{moles of P4} = \frac{13.7 \, \text{g}}{123.88 \, \text{g/mol}} = 0.110 \, \text{mol}
]
Step 2: Calculate the molality of the solution
Molality ((m)) is the number of moles of solute (P4) per kilogram of solvent (CS2).
- Mass of CS2 is 62.67 g, which is 0.06267 kg.
[
m = \frac{0.110 \, \text{mol}}{0.06267 \, \text{kg}} = 1.756 \, \text{mol/kg}
]
Step 3: Calculate the boiling point elevation
Now, apply the formula for boiling point elevation:
[
\Delta T_b = K_b \times m = 2.34 \, \text{°C·kg/mol} \times 1.756 \, \text{mol/kg} = 4.11 \, \text{°C}
]
The boiling point elevation is 4.11 °C.
Step 4: Final boiling point
The boiling point of pure CS2 is 46.2°C, so the new boiling point of the solution is:
[
\text{Boiling point of solution} = 46.2 \, \text{°C} + 4.11 \, \text{°C} = 50.31 \, \text{°C}
]
Thus, the boiling point of the solution is 50.31°C.
Part 2: Vapor Pressure of the Aspirin Solution
To calculate the vapor pressure of a solution, we use Raoult’s Law:
[
P_{\text{solution}} = X_{\text{solvent}} \times P_{\text{solvent}}
]
Where:
- (P_{\text{solution}}) is the vapor pressure of the solution,
- (X_{\text{solvent}}) is the mole fraction of the solvent (methanol),
- (P_{\text{solvent}}) is the vapor pressure of the pure solvent (methanol), given as 101 torr.
Step 1: Calculate the number of moles of aspirin (C9H8O4)
To find the mole fraction of the solvent, we first need to calculate the moles of aspirin (C9H8O4).
- Molar mass of aspirin (C9H8O4): (9 \times 12.01 + 8 \times 1.01 + 4 \times 16.00 = 180.16 \, \text{g/mol}).
Now, calculate the moles of aspirin in 11.138 g:
[
\text{moles of aspirin} = \frac{11.138 \, \text{g}}{180.16 \, \text{g/mol}} = 0.0618 \, \text{mol}
]
Step 2: Calculate the moles of methanol (CH3OH)
Next, calculate the moles of methanol (CH3OH):
- Molar mass of methanol: (12.01 + 4 \times 1.01 + 16.00 = 32.04 \, \text{g/mol}).
[
\text{moles of methanol} = \frac{65.271 \, \text{g}}{32.04 \, \text{g/mol}} = 2.038 \, \text{mol}
]
Step 3: Calculate the mole fraction of methanol
The mole fraction of methanol is the ratio of the moles of methanol to the total moles (moles of methanol + moles of aspirin):
[
X_{\text{methanol}} = \frac{2.038 \, \text{mol}}{2.038 \, \text{mol} + 0.0618 \, \text{mol}} = \frac{2.038}{2.0998} = 0.9707
]
Step 4: Calculate the vapor pressure of the solution
Now, apply Raoult’s Law to calculate the vapor pressure of the solution:
[
P_{\text{solution}} = X_{\text{methanol}} \times P_{\text{methanol}} = 0.9707 \times 101 \, \text{torr} = 97.99 \, \text{torr}
]
Thus, the vapor pressure of the aspirin solution is 97.99 torr.
Summary:
- The boiling point elevation of the CS2 solution is 50.31°C.
- The vapor pressure of the aspirin solution in methanol is 97.99 torr.