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Answer :
To find the total vapor pressure above the solution, we will use Raoult's Law, which states that the partial vapor pressure of each component in a solution is equal to the product of the mole fraction of the component in the solution and the vapor pressure of the pure component.
Here are the steps to solve the problem:
1. Determine the moles of each component:
- Cyclohexane: 1.40 moles
- Acetone: 2.50 moles
2. Calculate the total number of moles in the solution:
[tex]\[
\text{Total moles} = 1.40 \, \text{mol (cyclohexane)} + 2.50 \, \text{mol (acetone)} = 3.90 \, \text{mol}
\][/tex]
3. Calculate the mole fractions of each component:
- Mole fraction of cyclohexane ([tex]\(x_{cy}\)[/tex]):
[tex]\[
x_{cy} = \frac{1.40}{3.90} \approx 0.359
\][/tex]
- Mole fraction of acetone ([tex]\(x_{ac}\)[/tex]):
[tex]\[
x_{ac} = \frac{2.50}{3.90} \approx 0.641
\][/tex]
4. Use Raoult's Law to find the partial pressures:
- Partial pressure of cyclohexane ([tex]\(P_{cy}^{\, \text{partial}}\)[/tex]):
[tex]\[
P_{cy}^{\, \text{partial}} = x_{cy} \times 97.6 \, \text{torr} \approx 35.0 \, \text{torr}
\][/tex]
- Partial pressure of acetone ([tex]\(P_{ac}^{\, \text{partial}}\)[/tex]):
[tex]\[
P_{ac}^{\, \text{partial}} = x_{ac} \times 229.5 \, \text{torr} \approx 147.1 \, \text{torr}
\][/tex]
5. Calculate the total vapor pressure above the solution:
[tex]\[
P_{\text{total}} = P_{cy}^{\, \text{partial}} + P_{ac}^{\, \text{partial}} \approx 35.0 \, \text{torr} + 147.1 \, \text{torr} \approx 182.2 \, \text{torr}
\][/tex]
So, the total vapor pressure above the solution is approximately [tex]\(182.2\)[/tex] torr.
Here are the steps to solve the problem:
1. Determine the moles of each component:
- Cyclohexane: 1.40 moles
- Acetone: 2.50 moles
2. Calculate the total number of moles in the solution:
[tex]\[
\text{Total moles} = 1.40 \, \text{mol (cyclohexane)} + 2.50 \, \text{mol (acetone)} = 3.90 \, \text{mol}
\][/tex]
3. Calculate the mole fractions of each component:
- Mole fraction of cyclohexane ([tex]\(x_{cy}\)[/tex]):
[tex]\[
x_{cy} = \frac{1.40}{3.90} \approx 0.359
\][/tex]
- Mole fraction of acetone ([tex]\(x_{ac}\)[/tex]):
[tex]\[
x_{ac} = \frac{2.50}{3.90} \approx 0.641
\][/tex]
4. Use Raoult's Law to find the partial pressures:
- Partial pressure of cyclohexane ([tex]\(P_{cy}^{\, \text{partial}}\)[/tex]):
[tex]\[
P_{cy}^{\, \text{partial}} = x_{cy} \times 97.6 \, \text{torr} \approx 35.0 \, \text{torr}
\][/tex]
- Partial pressure of acetone ([tex]\(P_{ac}^{\, \text{partial}}\)[/tex]):
[tex]\[
P_{ac}^{\, \text{partial}} = x_{ac} \times 229.5 \, \text{torr} \approx 147.1 \, \text{torr}
\][/tex]
5. Calculate the total vapor pressure above the solution:
[tex]\[
P_{\text{total}} = P_{cy}^{\, \text{partial}} + P_{ac}^{\, \text{partial}} \approx 35.0 \, \text{torr} + 147.1 \, \text{torr} \approx 182.2 \, \text{torr}
\][/tex]
So, the total vapor pressure above the solution is approximately [tex]\(182.2\)[/tex] torr.
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