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Answer :
To find the total vapor pressure above the solution, we can use Raoult's Law. Raoult's Law states that the vapor pressure of each component in an ideal solution is equal to the mole fraction of the component multiplied by its vapor pressure when pure. The total vapor pressure is the sum of the partial pressures of each component.
Here are the steps to find the total vapor pressure above the solution:
1. Identify the number of moles for each component:
- Cyclohexane: 1.70 mol
- Acetone: 2.50 mol
2. Identify the vapor pressure of each component when pure:
- Cyclohexane: [tex]\( P_{\text{cy}}^{\circ} = 97.6 \)[/tex] torr
- Acetone: [tex]\( P_{\text{ac}}^{\circ} = 229.5 \)[/tex] torr
3. Calculate the total moles in the solution:
[tex]\[
\text{Total moles} = 1.70 + 2.50 = 4.20 \text{ moles}
\][/tex]
4. Calculate the mole fraction of each component:
- Mole fraction of cyclohexane:
[tex]\[
x_{\text{cy}} = \frac{1.70}{4.20} \approx 0.4048
\][/tex]
- Mole fraction of acetone:
[tex]\[
x_{\text{ac}} = \frac{2.50}{4.20} \approx 0.5952
\][/tex]
5. Calculate the partial pressure of each component using Raoult's Law:
- Partial pressure of cyclohexane:
[tex]\[
P_{\text{cy}} = x_{\text{cy}} \times P_{\text{cy}}^{\circ} = 0.4048 \times 97.6 \approx 39.50 \text{ torr}
\][/tex]
- Partial pressure of acetone:
[tex]\[
P_{\text{ac}} = x_{\text{ac}} \times P_{\text{ac}}^{\circ} = 0.5952 \times 229.5 \approx 136.61 \text{ torr}
\][/tex]
6. Find the total vapor pressure above the solution:
[tex]\[
P_{\text{total}} = P_{\text{cy}} + P_{\text{ac}} = 39.50 + 136.61 \approx 176.11 \text{ torr}
\][/tex]
Therefore, the total vapor pressure above the solution is approximately 176.11 torr.
Here are the steps to find the total vapor pressure above the solution:
1. Identify the number of moles for each component:
- Cyclohexane: 1.70 mol
- Acetone: 2.50 mol
2. Identify the vapor pressure of each component when pure:
- Cyclohexane: [tex]\( P_{\text{cy}}^{\circ} = 97.6 \)[/tex] torr
- Acetone: [tex]\( P_{\text{ac}}^{\circ} = 229.5 \)[/tex] torr
3. Calculate the total moles in the solution:
[tex]\[
\text{Total moles} = 1.70 + 2.50 = 4.20 \text{ moles}
\][/tex]
4. Calculate the mole fraction of each component:
- Mole fraction of cyclohexane:
[tex]\[
x_{\text{cy}} = \frac{1.70}{4.20} \approx 0.4048
\][/tex]
- Mole fraction of acetone:
[tex]\[
x_{\text{ac}} = \frac{2.50}{4.20} \approx 0.5952
\][/tex]
5. Calculate the partial pressure of each component using Raoult's Law:
- Partial pressure of cyclohexane:
[tex]\[
P_{\text{cy}} = x_{\text{cy}} \times P_{\text{cy}}^{\circ} = 0.4048 \times 97.6 \approx 39.50 \text{ torr}
\][/tex]
- Partial pressure of acetone:
[tex]\[
P_{\text{ac}} = x_{\text{ac}} \times P_{\text{ac}}^{\circ} = 0.5952 \times 229.5 \approx 136.61 \text{ torr}
\][/tex]
6. Find the total vapor pressure above the solution:
[tex]\[
P_{\text{total}} = P_{\text{cy}} + P_{\text{ac}} = 39.50 + 136.61 \approx 176.11 \text{ torr}
\][/tex]
Therefore, the total vapor pressure above the solution is approximately 176.11 torr.
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