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# If ${{\text{P}}^0}_{\text{A}}$ and ${{\text{P}}^0}_{\text{B}}$ are 108 and 36 torr respectively . what will be mole fraction of A in vapour phase if B has mole fraction 0.5 in the solution?${\text{A}}{\text{. 0}}{\text{.25}} \\ {\text{B}}{\text{. 0}}{\text{.75}} \\ {\text{C}}{\text{. 0}}{\text{.60}} \\ {\text{D}}{\text{. 0}}{\text{.35}} \\$

Last updated date: 18th Sep 2024
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Hint: Here we have given mole fraction of B in the solution and from this we can find mole fraction of A in the solution by subtracting mole fraction of B from 1. We have to find a mole fraction of A in the vapour phase and that will be found using partial pressure concept and use of dalton’s law.

We have
${{\text{P}}^0}_{\text{A}}$ = 108 torr
${{\text{P}}^0}_{\text{B}}$ = 36 torr
Mole dfraction of B in solution = 0.5
Hence mole dfraction of A in the solution = 1 – 0.5 = 0.5
${p_T} = {P^0}_A{x_A} + {P^0}_B{x_B}$
Putting all the values we get,
${P_T} = 108 \times \dfrac{1}{2} + 36 \times \dfrac{1}{2} = 54 + 18 = 72$
Partial pressure with respect to A and B.
${P_A} = {P^0}_A{x_A} = 108 \times \dfrac{1}{2} = 54$
${P_B} = 18$
Now assume ${Y_A}$ be the mole dfraction of A in vapour phase
So according to dalton’s law
${P_A} = {Y_A} \times {P_T}$
Now putting all the values we get
$54 = {Y_A} \times 72 \\ {Y_A} = \dfrac{3}{4} = 0.75 \\$
Hence option B is the correct option.

Note: Whenever we get this type of question the key concept of solving is we have to understand the terms like in solution and in vapour phase and also remember how to find partial pressure because partial pressure has a great role in solving this type of question.