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 ______.

Options

• 250 mm, 550 mm

• 350 mm, 450 mm

• 350 mm, 700 mm

• 550 mm, 250 mm

Answer 1

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 550 mm, 250 mm.

Explanation:

Molar ratio of 1 : 1 means x_x = x_Y = 0.5

`"P"_"total"` = x_xp_x° + x_Yp_Y°

or p_x° + p_Y° = 800       ...(i)

Molar ratio of 1 : 2 means, x_x = `1/3`, X_Y = `2/3`

`therefore 350 = 1/3 "p"_"x"° + 2/3 "p"_"Y"°`

or p_x° + 2 p_Y° = 1050   ...(ii)

Eqn (ii) - Eqn (i) gives p_Y° = 250 mm

Putting in (i), we get p_x° = 550 mm