Name: Raoult's Law
Uploaded: 2019-07-19
Duration: 3 min 24 s
Description: Raoult's law is a chemical law that states that the vapour pressure of a solution is dependent on the mole fraction of a solute added to the solution. Learn...

Question

The vapour pressure of pure benzene is

22 mm of Hg

and that of pure toluene is

75 mm of Hg

at

20 ° C

. What is the composition of the solution of these two components that have a vapour pressure of

50 mm of Hg

at this temperature? What is the composition of vapour in equilibrium with this solution?

Accepted Answer

Given, the vapour pressure of pure benzene, $P_{ben}^{\circ} = 22 mm of Hg$

Vapour pressure of pure toluene,

$P_{tol}^{\circ} = 75 mm of Hg$

Total vapour pressure, $P_{total} = 50 mm of Hg$

According to Raoult's law,

$P_{total} = P_{ben}^{\circ} . x_{ben} + P_{tol}^{\circ} . x_{tol} (As we know sum of mole fractions of all components is 1) x_{ben} + x_{tol} = 1 or x_{tol} = 1 - x_{ben}) P_{total} = P_{ben}^{\circ} . x_{ben} + P_{tol}^{\circ} . (1 - x_{ben}) 50 = 22 . x_{ben} + 75 . (1 - x_{ben})$

$x_{ben} = 0.47 x_{tol} = 1 - x_{ben} = 1 - 0.47 = 0.53$

Hence, the mole fraction of benzene and toluene in solution is $0.47$ and $0.53$ , respectively. This is the composition of the solution.

Now, the composition in the vapour phase:-

Mole fraction of benzene in the vapour phase, $x_{ben}^{v} = \frac{Partial pressure of benzene}{Total vapour pressure} = \frac{P_{ben}^{\circ} \times x_{ben}}{P_{total}} = \frac{22 \times 0.47}{50} = 0.20$

Mole fraction of toluene in the vapour phase, $x_{tol}^{v} = \frac{Partial pressure of toluene}{Total vapour pressure} = \frac{P_{tol}^{\circ} \times x_{tol}}{P_{total}} = \frac{75 \times 0.53}{50} = 0.80 or x_{ben}^{v} + x_{tol}^{v} = 1 0.20 + x_{tol}^{v} = 1 x_{tol}^{v} = 1 - 0.20 = 0.80$

So, the mole fraction of benzene and toluene in the vapour phase is $0.20$ and $0.80$ , respectively. This is the composition in the vapour phase.

Important Questions on Dilute Solution and Colligative Properties

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The vapour pressure of pure benzene is 22 mm of Hg and that of pure toluene is 75 mm of Hg at 20° C. What is the composition of the solution of these two components that have a vapour pressure of 50 mm of Hg at this temperature? What is the composition of vapour in equilibrium with this solution?

Important Questions on Dilute Solution and Colligative Properties

Learn and Prepare for any exam you want !