Question:
A solution has a $1: 4$ mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at $20^{\circ} C$ are $440 \,mm$ of $Hg$ for pentane and $120 \,mm$ of $Hg$ for hexane. The mole fraction of pentane in the vapour phase would be
A solution has a $1: 4$ mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at $20^{\circ} C$ are $440 \,mm$ of $Hg$ for pentane and $120 \,mm$ of $Hg$ for hexane. The mole fraction of pentane in the vapour phase would be
Updated On: Jun 23, 2023
- 0.549
- 0.2
- 0.786
- 0.478
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The Correct Option is D
Solution and Explanation
Total vapour pressure of mixture
$=$ (Mole fraction of pentane $\times$ VP of pentane) $+$ (Mole fraction of hexane $\times$ VP of hexane)
= VP of pentane in mixture $+$ VP of hexane in mixture.
$=\left(\frac{1}{5} \times 440+\frac{4}{5} \times 120\right)=184 \,mm$
$\because$ VP of Pentane in mixture.
$=$ VP of mixture $\times$ mole fraction of pentane in vapour phase
$88=184 \times$ mole fraction of pentane in vapour phase
$\therefore$ Mole fraction of pentane in vapour phase
$=\frac{88}{184}=0.478$
$=$ (Mole fraction of pentane $\times$ VP of pentane) $+$ (Mole fraction of hexane $\times$ VP of hexane)
= VP of pentane in mixture $+$ VP of hexane in mixture.
$=\left(\frac{1}{5} \times 440+\frac{4}{5} \times 120\right)=184 \,mm$
$\because$ VP of Pentane in mixture.
$=$ VP of mixture $\times$ mole fraction of pentane in vapour phase
$88=184 \times$ mole fraction of pentane in vapour phase
$\therefore$ Mole fraction of pentane in vapour phase
$=\frac{88}{184}=0.478$
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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.