Question

Two liquids X and Y form an ideal solution. At 300 K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm of Hg. At the same temperature, 1 mol of Y is further added to this solution, vapour pressure of the solution increases by 10 mm of Hg. Vapour pressure( in mm of Hg) of X and Y in their pure states will be respectively.
(A) 200 and 300
(B) 300 and 400
(C) 400 and 600
(D) 500 and 600

Answer 1

Hint: It is important to understand the relation between the vapour pressure of the ideal solution and the concentration of individual liquids in the solution. Based on this you can find a relation between the two quantities and thus calculate the vapor pressure of the liquids in pure state.

Complete step-by-step answer:
Vapour pressure can be defined as a measure of the tendency of a material to change into the gaseous or vapour state. In addition to that, it is seen that the vapour pressure increases with temperature. Raoult's law states that the vapour pressure of a component of a homogenous mixture (liquid and liquid) is equal to the product of mole fraction of that component and its vapour pressure in pure form. Thus, the total vapour pressure becomes,
$\text{P = }{{\text{x}}_{\text{x}}}\text{P}_{\text{x}}^{\text{0}}\text{ + }{{\text{x}}_{\text{y}}}\text{P}_{\text{y}}^{\text{0}}$
We will substitute the values obtained from the first solution.
$550=\left( \dfrac{1}{1+3} \right)\text{P}_{\text{x}}^{\text{0}}\text{ + }\left( \dfrac{3}{1+3} \right)\text{P}_{\text{y}}^{\text{0}}$
$560=\left( \dfrac{1}{1+4} \right)\text{P}_{\text{x}}^{\text{0}}\text{ + }\left( \dfrac{4}{1+4} \right)\text{P}_{\text{y}}^{\text{0}}$
On solving the above two equations for vapour pressure in pure form, we get,
$\text{P}_{\text{x}}^{\text{0}}$ = 400 mm of Hg
$\text{P}_{\text{y}}^{\text{0}}$ = 600 mm of Hg

Therefore, the correct answer is option (C).

Note: It is important to know that not all binary homogeneous mixtures tend to form an ideal solution. For example, mixture of heptane and hexane form an ideal solution. However, on the other hand, a mixture of water and acetone show deviation from Raoult's law and thus the above formula cannot be applied to this binary mixture.