Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If and are the mole fraction of A and B in solution while and are the mole fraction of A and B in vapour pha

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Q.
Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If $x_{A}$ and $x_{B}$ are the mole fraction of A and B in solution while $y_{A}$ and $y_{B}$ are the mole fraction of A and B in vapour phase then: [2025]

1 $\frac{x_{A}}{x_{B}} < \frac{y_{A}}{y_{B}}$

2 $\frac{x_{A}}{x_{B}} = \frac{y_{A}}{y_{B}}$

3 $\frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$

4 $(x_{A} - y_{A}) < (x_{B} - y_{B})$

Ans.
(3)

$\frac{y_{A}}{y_{B}} = \frac{P_{A}^{°} x_{A}}{P_{B}^{°} x_{B}}$

$\frac{y_{A}}{y_{B}} = \frac{350 x_{A}}{750 x_{B}}$

$\frac{x_{A}}{x_{B}} = \frac{750 y_{A}}{350 y_{B}}$

$Thus \frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$

Solution

1 $\frac{x_{A}}{x_{B}} < \frac{y_{A}}{y_{B}}$

2 $\frac{x_{A}}{x_{B}} = \frac{y_{A}}{y_{B}}$

3 $\frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$

4 $(x_{A} - y_{A}) < (x_{B} - y_{B})$

Ans.
(3)

$\frac{y_{A}}{y_{B}} = \frac{P_{A}^{°} x_{A}}{P_{B}^{°} x_{B}}$

$\frac{y_{A}}{y_{B}} = \frac{350 x_{A}}{750 x_{B}}$

$\frac{x_{A}}{x_{B}} = \frac{750 y_{A}}{350 y_{B}}$

$Thus \frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$

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Solution

Q. Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If xA and xB are the mole fraction of A and B in solution while yA and yB are the mole fraction of A and B in vapour phase then: [2025]

1 xAxB<yAyB

2 xAxB=yAyB

3 xAxB>yAyB

4 (xA-yA)<(xB-yB)

Ans. (3) yAyB=PA°xAPB°xB yAyB=350xA750xB xAxB=750yA350yB Thus xAxB>yAyB

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1 $\frac{x_{A}}{x_{B}} < \frac{y_{A}}{y_{B}}$

2 $\frac{x_{A}}{x_{B}} = \frac{y_{A}}{y_{B}}$

3 $\frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$

4 $(x_{A} - y_{A}) < (x_{B} - y_{B})$

Ans.
(3)

$\frac{y_{A}}{y_{B}} = \frac{P_{A}^{°} x_{A}}{P_{B}^{°} x_{B}}$

$\frac{y_{A}}{y_{B}} = \frac{350 x_{A}}{750 x_{B}}$

$\frac{x_{A}}{x_{B}} = \frac{750 y_{A}}{350 y_{B}}$

$Thus \frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$