Question

Two liquids A and B are mixed in such a proportion that they form an ideal solution whose total vapor pressure is exactly three times that of the partial pressure of A. If \( P_A^\circ \) and \( P_B^\circ \) are the vapor pressures of pure A and B respectively, then the total vapor pressure of the solution is given by

• A. \( \frac{P_A^\circ P_B^\circ}{2} + P_A^\circ + P_B^\circ \)
• B. \( 3P_A^\circ + P_B^\circ \)
• C. \( \frac{P_A^\circ}{2} + P_B^\circ \)
• D. \( P_A^\circ + 2P_B^\circ \)
• E. More data needed to solve the problem
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Hint:

Raoult’s Law helps in calculating the vapor pressures of components in an ideal solution. Make sure to consider the mole fractions and partial pressures for each component.

Answer 1

The Correct Option is B

For an ideal solution, the total vapor pressure is given by Raoult’s Law: \[ P_{\text{total}} = X_A P_A^\circ + X_B P_B^\circ \] Given that the total pressure is 3 times the partial pressure of A, we have: \[ P_{\text{total}} = 3P_A^\circ + P_B^\circ \] Thus, the total vapor pressure is \( 3P_A^\circ + P_B^\circ \), matching option (b).