Answer :
To calculate the vapor composition of a solution, we can use Raoult's law, which states that the vapor pressure of a component in an ideal solution is directly proportional to its mole fraction in the liquid phase.
Let's assume that the mole fraction of acetone in the liquid phase is x_acetone and the mole fraction of cyclohexane is x_cyclohexane. According to Raoult's law, the partial pressure of acetone in the vapor phase, p_acetone, is given by p_acetone = p°acetone * x_acetone, where p°acetone is the vapor pressure of pure acetone.
Similarly, the partial pressure of cyclohexane in the vapor phase, p_cyclohexane, is given by p_cyclohexane = p°cyclohexane * x_cyclohexane, where p°cyclohexane is the vapor pressure of pure cyclohexane.
Since the total pressure above the solution is the sum of the partial pressures, we have: p_total = p_acetone + p_cyclohexane.
Now, let's solve the equations using the given values:
p°acetone = 229.5 torr
p°cyclohexane = 97.6 torr
We can rearrange the equations to find x_acetone and x_cyclohexane:
x_acetone = p_acetone / p°acetone
x_cyclohexane = p_cyclohexane / p°cyclohexane
Substituting the equations, we get:
x_acetone = (p°acetone * x_acetone) / p°acetone
x_cyclohexane = (p°cyclohexane * x_cyclohexane) / p°cyclohexane
Simplifying, we find:
x_acetone = x_acetone
x_cyclohexane = x_cyclohexane
Therefore, the mole fractions of acetone and cyclohexane in the vapor above the solution are the same as their mole fractionsin the liquid phase.
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