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P_A and P_B are the vapour pressure of pure liquid components, A and B, respectively of an ideal binary solution. If x_A represents the mole fraction of component A, the total pressure of the solution will be

1. P_A + x_A (P_B - P_A)
2. P_B + x_A (P_A - P_B)
3. P_B + x_A (P_B - P_A)
4. P_B + x_A (P_A - P_B)

Correct answer: P_B + x_A (P_A - P_B)

Solution

The total pressure of an ideal binary solution is given by Raoult's law: P_total = P_A * x_A + P_B * x_B. Substituting x_B = 1 - x_A, the equation simplifies to P_total = P_B + x_A (P_A - P_B).

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