A solution has a 1:4 mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at 20°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
- 0.178
- 0.278
- 0.378
- 0.478
The Correct Option is D
Solution and Explanation
Pentane solution mole fraction =\(\frac{1}{1}\) + 4 = \(\frac{1}{5}\)
Hexane solution mole fraction = \(\frac{4}{1}\) + 4 = \(\frac{4}{5}\)
Total pressure of the solution, Ps = Xp POp + XH PHO = \(\frac{1}{5}\) \(\times\) 440 mm Hg + \(\frac{4}{5}\) \(\times\)120 mm Hg = 184 mm Hg The amount of pentane in the vapour phase is expressed as \(\frac{x_pp^0_p}{p_s}\) = \(\frac{88}{184}\) =0.478.
Therefore, the correct option is (D): 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.