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A solution is composed of 1.60 mol cyclohexane ([tex]P^\circ_{\text{cy}} = 97.6 \text{ torr}[/tex]) and 2.90 mol acetone ([tex]P^\circ_{\text{ac}} = 229.5 \text{ torr}[/tex]). What is the total vapor pressure [tex]P_{\text{total}}[/tex] above this solution?

Answer :

Final answer:

To find the total vapor pressure (Ptotal) above a solution, calculate the mole fraction of each component and then find the product of the mole fraction and the pure component's vapor pressure. Sum these partial pressures to obtain Ptotal.

Explanation:

To calculate the total vapor pressure (Ptotal) above the solution of cyclohexane and acetone, we apply Raoult's Law, which states that the partial vapor pressure of each component of an ideal solution is equal to the product of the mole fraction (X) of that component in the liquid phase and the vapor pressure of the pure component (P°).

The mole fractions for cyclohexane (Xcy) and acetone (Xac) are calculated by dividing the number of moles of each component by the total number of moles in the solution:

  • Xcy = moles of cyclohexane / total moles = 1.60 / (1.60 + 2.90) = 0.3556
  • Xac = moles of acetone / total moles = 2.90 / (1.60 + 2.90) = 0.6444

Then we calculate the partial vapor pressures of each component using their respective mole fractions:

  • Pcy = Xcy × P°cy = 0.3556 × 97.6 torr
  • Pac = Xac × P°ac = 0.6444 × 229.5 torr

Finally, we sum the partial vapor pressures to obtain the total vapor pressure:

Ptotal = Pcy + Pac = (0.3556 × 97.6 torr) + (0.6444 × 229.5 torr)

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