Two liquids X and Y form an ideal solution. The mixture has a vapour pressure of 400 mm at 300 K when mixed in the molar ratio of 1:1 and a vapour pressure of 350 mm when mixed in the molar ratio of 1:2 at the same temperature. The vapour pressures of the two pure liquids X and Y respectively are

Question

Two liquids X and Y form an ideal solution. The mixture has a vapour pressure of 400 mm at 300 K when mixed in the molar ratio of 1:1 and a vapour pressure of 350 mm when mixed in the molar ratio of 1:2 at the same temperature. The vapour pressures of the two pure liquids X and Y respectively are (A) 250 mm, 550 mm (B) 350 mm, 450 mm (C) 350 mm, 700 mm (D) 500 mm, 500 mm

Tardigrade Admin · Accepted Answer

In 1st case, When two liquids X and Y are mixed in the molar ratio

1 : 1

.
Moles of

X = 1

Moles of

Y = 1

Mole fraction of

X (χ_{X}) = \frac{1}{2}

Mole fraction of

Y (χ_{Y}) = \frac{1}{2}

We know that

P = P_{X}^{o} χ_{X} + p_{Y}^{o} χ_{y}

(P = total pressure of mixture)

400 = \frac{1}{2} p_{X}^{o} + \frac{1}{2} p_{Y}^{o}

400 \times 2 = p_{X}^{o} + p_{Y}^{o}

.. (i)
For case

I I^{n d},

When liquids are mixed in the molar ratio of

1 : 2

Moles of

X = 1

Moles of

Y = 2

Mole fraction of

X (χ_{X}) = \frac{1}{3}

Mole fraction of

Y (χ_{Y}) = \frac{2}{3}

P = p_{X}^{o} χ_{X} + P_{Y}^{o} χ_{Y}

350 = \frac{1}{3} p_{X}^{o} + \frac{2}{3} P_{Y}^{o}

350 \times 3 = p_{X}^{o} + 2 P_{Y}^{o}

...(ii)
From Eqs (i) and (ii), we get

p_{X}^{o} = 550 mm

P_{Y}^{o} = 250 mm

$250 mm, 550 mm$

$350 mm, 450 mm$

$350 mm, 700 mm$

$500 mm, 500 mm$

$550 mm, 250 mm$

Q. Two liquids X and Y form an ideal solution. The mixture has a vapour pressure of 400mm at 300K when mixed in the molar ratio of 1:1 and a vapour pressure of 350mm when mixed in the molar ratio of 1:2 at the same temperature. The vapour pressures of the two pure liquids X and Y respectively are

250mm,550mm

350mm,450mm

350mm,700mm

500mm,500mm

550mm,250mm

$250 mm, 550 mm$

$350 mm, 450 mm$

$350 mm, 700 mm$

$500 mm, 500 mm$

$550 mm, 250 mm$