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

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P_B + x_A(P_A – P_B)

P_A + x_A(P_A – P_B)

P_B + x_A(P_B – P_A)

P_A + x_A(P_B – P_A)

answer is D.

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Detailed Solution

Given , P_A= V.P of pure liq. A

P_B= V.P of pure liq. B

X_A = M.F of A in liq. mix

X_B = M.F of B in liq. mix

According to Raoult's law,

$\begin{array}{l} {P_{tot}} = {P_A}{X_A} + {P_B}{X_B}\\ \,\,\,\,\,\,\,\,\, = {P_A}{X_A} + {P_B}(1 - {X_A})\,\,\\ \,\,\,\,\,\,\,\,\, = {P_A}{X_A} + {P_B} - {P_B}{X_A}\\ \,\,\,\,\,\,\,\,\,\, = {P_B} + {X_A}({P_A} - {P_B}) \end{array}$

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