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Question:
Vapour pressure of pure benzene is $119$ torr and that of toluene is $37.0$ torr at the same temperature. Mole fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of toluene $0.50$, will be :
Vapour pressure of pure benzene is $119$ torr and that of toluene is $37.0$ torr at the same temperature. Mole fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of toluene $0.50$, will be :
Updated On: Jan 15, 2024
- $0.137$
- $0.237$
- $0.435$
- $0.205$
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The Correct Option is B
Solution and Explanation
$P_{A}=P^{0}_{A}\times x_{A}=$ total pressure $\times y_{A}$
$P_{B}=P^{0}_{B}\times x_{B}=$ total pressure $\times y_{B}$
where $x$ and $y$ represents mole fraction in liquid and vapour phase respectively.
$\frac{P^{0}_{B}x^{0}_{B}}{P^{0}_{A}x_{A}}=\frac{y_{B}}{y_{A}} ; \frac{P^{0}_{B}\left(1-x_{A}\right)}{P^{0}_{A}x_{A}}=\frac{1-y_{A}}{y_{A}}$
on putting values $\frac{119\left(1-0.50\right)}{37\times0.50}=\frac{1-y_{A}}{y_{A}}$
on solving $y_{A} = 0.237$
$P_{B}=P^{0}_{B}\times x_{B}=$ total pressure $\times y_{B}$
where $x$ and $y$ represents mole fraction in liquid and vapour phase respectively.
$\frac{P^{0}_{B}x^{0}_{B}}{P^{0}_{A}x_{A}}=\frac{y_{B}}{y_{A}} ; \frac{P^{0}_{B}\left(1-x_{A}\right)}{P^{0}_{A}x_{A}}=\frac{1-y_{A}}{y_{A}}$
on putting values $\frac{119\left(1-0.50\right)}{37\times0.50}=\frac{1-y_{A}}{y_{A}}$
on solving $y_{A} = 0.237$
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.
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