As you saw in Part B, the vapor above the cyclohexane-acetone solution is composed of both cyclohexane vapor and acetone vapor. What mole fraction of the vapor above the solution, X(cy) vapor), is cyclohexane?

Are we supposed to guess at the data?

To determine the mole fraction of cyclohexane in the vapor above the solution, we need to know the mole fraction of cyclohexane in the liquid phase and the mole fraction of acetone in the liquid phase.

Let's assume that the mole fraction of cyclohexane in the liquid phase is represented by X(cy) liquid and the mole fraction of acetone in the liquid phase is represented by X(ac) liquid.

According to Raoult's law, the partial pressure of each component in the vapor phase is proportional to the mole fraction of that component in the liquid phase. Mathematically, this can be written as:

P(cy) vapor = X(cy) liquid * P(cy) pure
P(ac) vapor = X(ac) liquid * P(ac) pure

Where P(cy) vapor and P(ac) vapor are the partial pressures of cyclohexane and acetone in the vapor phase, respectively. P(cy) pure and P(ac) pure are the vapor pressures of pure cyclohexane and acetone, respectively.

Since the total pressure above the solution is the sum of the partial pressures of cyclohexane and acetone, we can write:

P(total) = P(cy) vapor + P(ac) vapor

Now, we can express the mole fraction of cyclohexane in the vapor phase as:

X(cy) vapor = P(cy) vapor / P(total)

Given the values of X(cy) liquid and X(ac) liquid in the solution, we can substitute them into the equations above and solve for X(cy) vapor.

To find the mole fraction of cyclohexane in the vapor above the cyclohexane-acetone solution, we need to know the mole fraction of cyclohexane in the liquid phase, X(cy) liquid, and the vapor pressure of both components, P(cy) and P(ac) respectively.

The mole fraction of cyclohexane in the vapor phase, X(cy) vapor, can be calculated using Raoult's law, which states that the vapor pressure of a component in an ideal solution is equal to the product of the mole fraction of that component in the liquid phase and its pure component vapor pressure.

Mathematically, Raoult's law can be expressed as:

P(cy) = X(cy) liquid * P(cy)°

Where P(cy) is the vapor pressure of cyclohexane in the solution, X(cy) liquid is the mole fraction of cyclohexane in the liquid phase, and P(cy)° is the vapor pressure of pure cyclohexane.

Similarly, for acetone:

P(ac) = X(ac) liquid * P(ac)°

To find the mole fraction of cyclohexane in the vapor phase, X(cy) vapor, we can rearrange the equation:

X(cy) vapor = P(cy) / (P(cy) + P(ac))

To calculate X(cy) vapor, we need to know the mole fraction of cyclohexane in the liquid phase, X(cy) liquid, and the vapor pressures of both components, P(cy) and P(ac).

Therefore, the answer to your question depends on the values of X(cy) liquid, P(cy), and P(ac) which are not provided in the given information.