As you saw in Part B, the vapor above the cyclohexane-acetone solution is composed of both cyclohexane vapor and acetone vapor.

Question 1:
What mole fraction of the vapor above the solution, [tex]X_{\text{cy (vapor)}}[/tex], is cyclohexane? Express your answer numerically.

Question 2:
A solution is composed of 1.10 mol cyclohexane ([tex]P_{\text{cy}} = 97.6 \text{ torr}[/tex]) and 2.20 mol acetone ([tex]P_{\text{ac}} = 229.5 \text{ torr}[/tex]). What is the total vapor pressure [tex]P_{\text{total}}[/tex] above this solution? Express your answer with the appropriate units.

Hint:
[tex]P_{\text{total}} = 186 \text{ torr}[/tex]

The mole fraction of cyclohexane in the vapor above the solution is approximately 0.333. The total vapor pressure above the solution is 185.34 torr.

Explanation:

To find the mole fraction of cyclohexane in the vapor above the solution, we need to calculate the mole fraction of cyclohexane in the total solution and then use it to calculate the mole fraction in the vapor phase.

Step 1: Calculate the mole fraction of cyclohexane in the total solution.

The total number of moles in the solution is the sum of the moles of cyclohexane and acetone:

Total moles = moles of cyclohexane + moles of acetone = 1.10 mol + 2.20 mol = 3.30 mol

The mole fraction of cyclohexane in the total solution is:

Mole fraction of cyclohexane = moles of cyclohexane / total moles = 1.10 mol / 3.30 mol = 0.333

Step 2: Calculate the mole fraction of cyclohexane in the vapor phase.

The mole fraction of cyclohexane in the vapor phase is equal to the mole fraction of cyclohexane in the total solution, as the vapor phase is in equilibrium with the solution:

Mole fraction of cyclohexane in the vapor = 0.333

To find the total vapor pressure above the solution, we need to calculate the partial pressures of cyclohexane and acetone in the vapor phase and then sum them.

Step 1: Calculate the partial pressure of cyclohexane in the vapor phase.

The partial pressure of cyclohexane is the product of its mole fraction in the vapor phase and the vapor pressure of pure cyclohexane:

Partial pressure of cyclohexane = mole fraction of cyclohexane in the vapor * vapor pressure of cyclohexane = 0.333 * 97.6 torr = 32.51 torr

Step 2: Calculate the partial pressure of acetone in the vapor phase.

The partial pressure of acetone is the product of its mole fraction in the vapor phase and the vapor pressure of pure acetone:

Partial pressure of acetone = mole fraction of acetone in the vapor * vapor pressure of acetone = (1 - mole fraction of cyclohexane in the vapor) * vapor pressure of acetone = (1 - 0.333) * 229.5 torr = 152.83 torr

Step 3: Calculate the total vapor pressure above the solution.

The total vapor pressure above the solution is the sum of the partial pressures of cyclohexane and acetone:

Total vapor pressure = partial pressure of cyclohexane + partial pressure of acetone = 32.51 torr + 152.83 torr = 185.34 torr

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