Question:
The vapour pressures of pure liquids $A$ and $B$ are $400$ and $600\, mmHg$, respectively at $298\,K$. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid $B$ is $0.5$ in the mixture. The vapour pressure of the final solution, the mole fraction of components $A$ and $B$ in vapour phase, respectively are -
The vapour pressures of pure liquids $A$ and $B$ are $400$ and $600\, mmHg$, respectively at $298\,K$. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid $B$ is $0.5$ in the mixture. The vapour pressure of the final solution, the mole fraction of components $A$ and $B$ in vapour phase, respectively are -
Updated On: Sep 14, 2024
- 500 mmHg, 0.5, 0.5
- 450 mmHg, 0.4, 0.6
- 450 mmHg, 0.5, 0.5
- 500 mmHg, 0.4, 0.6
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The Correct Option is D
Solution and Explanation
$P_{\text {total }}=X_{A} . P_{A}^{0}+X_{B} \cdot P_{B}^{0}=0.5 \times 400+0.5 \times 600$
$=500 mmHg$
Now, mole fraction of A in vapour,
$Y _{ A }=\frac{ P _{ A }}{ P _{\text {total }}}=\frac{0.5 \times 400}{500}=0.4$
and mole fraction of $B$ in vapour, $Y _{ B }=1-0.4=0.6$
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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.