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At $25 ° C,$ the total pressure of an ideal solution obtained by mixing 3 moles of A and 2 moles of B, is $184$ torr. What is the vapour pressure (in torr) of pure B at the same temperature (vapour pressure of pure A, at 25°C, is 200 torr)

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180

100

160

answer is B.

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Detailed Solution

$P = P_{A} + P_{B} = x_{A} p_{A}^{\circ} + x_{B} p_{B}^{\circ}$

where $P =$ total pressure, $p =$ partial pressure,

$p^{\circ} =$ vapour pressure, $x =$ mole fraction

or $184 = \frac{3}{5} \times 200 + \frac{2}{5} \times p_{B}^{o} or 184 = 120 + \frac{2}{5} p_{B}^{o}$

or $p_{B}^{\circ} = 160 torr$ .

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