5 moles of liquid X and 10 moles of liquid Y make a solution having a vapour pressure of 70 torr. The vapour pressures of pure X and Y are 63 torr and 78 torr respectively. Which of the following is true regarding the described solution?

CONCEPT:

Vapour Pressure and Deviations from Raoult's Law

• Raoult's Law states that the partial vapour pressure of a component in a solution is proportional to its mole fraction and the vapour pressure of the pure component.
• The total vapour pressure of an ideal solution can be calculated using:

  P_total = x_XP^o_X + x_YP^o_Y

  • Where x_X and x_Y are the mole fractions of components X and Y.
  • P^o_X and P^o_Y are the vapour pressures of pure components X and Y respectively.
• If the actual total vapour pressure deviates from the ideal total vapour pressure:
  • Positive deviation occurs when the actual vapour pressure is higher than expected (weaker intermolecular forces).
  • Negative deviation occurs when the actual vapour pressure is lower than expected (stronger intermolecular forces).

EXPLANATION:

• Mole fractions:
  • Total moles = 5 + 10 = 15
  • x_X = 5/15 = 1/3, x_Y = 10/15 = 2/3
• Ideal total vapour pressure (using Raoult's Law):
  • P_ideal = x_XP^o_X + x_YP^o_Y
  • = (1/3)(63) + (2/3)(78)
  • = 21 + 52
  • = 73 torr
• Actual total vapour pressure = 70 torr
• Ideal total vapour pressure = 73 torr

Since the actual pressure is lower than the ideal pressure, the solution exhibits a negative deviation from Raoult's Law.

Therefore, the solution shows negative deviation.