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Question:
If $ \chi_{1} $ and $ \chi_{2} $ represent the mole fractions of a component $ A $ in the vapour phase and liquid mixture respectively, and $ p^{\circ}_{A} $ and $ p^{\circ}_{B} $
represent vapour pres sines of pure A and pure B, then total vapour pressure of liquid mixture is
If $ \chi_{1} $ and $ \chi_{2} $ represent the mole fractions of a component $ A $ in the vapour phase and liquid mixture respectively, and $ p^{\circ}_{A} $ and $ p^{\circ}_{B} $
represent vapour pres sines of pure A and pure B, then total vapour pressure of liquid mixture is
Updated On: Jun 23, 2023
- $ \frac{\rho^{\circ}_{A}\chi_{1}}{\chi_{2}} $
- $ \frac{\rho^{\circ}_{A}\chi_{2}}{\chi_{1}} $
- $ \frac{\rho^{\circ}_{B}\chi_{1}}{\chi_{2}} $
- $ \frac{\rho^{\circ}_{B}\chi_{2}}{\chi_{1}} $
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The Correct Option is B
Solution and Explanation
Mole fraction in the vapour phase $\left(\chi_{1}\right)=\frac{p_{A}}{p_{total}}$
But, $P_{A}\times\chi_{A}\times p_{A}^{\circ}=\chi_{2}p_{A}^{\circ}$
or $ \chi_{1}\times p_{A}^{\circ} \left(as \chi_{A}=\chi_{1}\right)$
$\therefore \chi_{1}=\frac{\chi_{2}p_{A}^{\circ}}{p_{total}}$
or $p_{total}=\frac{p^{\circ}_{A}\chi_{2}}{\chi_{1}}$
But, $P_{A}\times\chi_{A}\times p_{A}^{\circ}=\chi_{2}p_{A}^{\circ}$
or $ \chi_{1}\times p_{A}^{\circ} \left(as \chi_{A}=\chi_{1}\right)$
$\therefore \chi_{1}=\frac{\chi_{2}p_{A}^{\circ}}{p_{total}}$
or $p_{total}=\frac{p^{\circ}_{A}\chi_{2}}{\chi_{1}}$
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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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