Comprehension

Raoult’s law for volatile liquids states that the partial vapour pressure of each component in the solution is directly proportional to its mole fraction, whereas for a non-volatile solute, it states that the vapour pressure of a solution of a non-volatile solute is equal to the vapour pressure of the pure solvent at that temperature multiplied by its mole fraction.

Two liquids A and B are mixed with each other to form a solution, the vapour phase consists of both components of the solution. Once the components in the solution have reached equilibrium, the total vapour pressure of the solution can be determined by combining Raoult’s law with Dalton’s law of partial pressures.

If a non-volatile solute B is dissolved into a solvent A to form a solution, the vapour pressure of the solution will be lower than that of the pure solvent.

The solutions which obey Raoult’s law over the entire range of concentration are ideal solutions, whereas the solutions for which vapour pressure is either higher or lower than that predicted by Raoult’s law are called non-ideal solutions.

Non-ideal solutions are identified by determining the strength of the intermolecular forces between the different molecules in that particular solution. They can either show positive or negative deviation from Raoult’s law depending on whether the A – B interactions in solution are stronger or weaker than A – A and B – B interactions.

Question: 1

20 mL of a liquid A was mixed with 20 mL of liquid B. The volume of resulting solution was found to be less than 40 mL. What do you conclude from the above data?

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Negative deviation implies stronger A–B interactions, causing decrease in volume and vapour pressure.
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Solution and Explanation

Step 1: When two liquids A and B are mixed, if the resulting volume is less than the sum of their individual volumes, it indicates that the intermolecular forces between A and B are stronger than those between A–A and B–B.
Step 2: This causes the molecules to come closer, leading to volume contraction.
Conclusion: The solution exhibits negative deviation from Raoult’s Law.
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Question: 2

Which of the following show positive deviation from Raoult’s law?
Carbon disulphide and Acetone;
Phenol and Aniline;
Ethanol and Acetone

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Positive deviation = weaker intermolecular attractions, leading to higher vapour pressure and volume expansion.
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Solution and Explanation

Step 1: Positive deviation from Raoult’s law occurs when A–B interactions are weaker than A–A and B–B interactions.
Step 2: This results in:
- Increased escaping tendency of molecules,
- Increased vapour pressure,
- Volume expansion.
Step 3: In the given options, Carbon disulphide and Acetone form a non-ideal solution with weak intermolecular forces, leading to positive deviation.
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Question: 3

The vapour pressure of a solution of glucose in water is 750 mm Hg at 100°C. Calculate the mole fraction of solute.
(Vapour pressure of water at 373 K = 760 mm Hg)

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Use \( P = P^0 \times X \) to calculate mole fraction. Always subtract to find solute’s mole fraction: \( X_B = 1 - X_A \).
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Solution and Explanation

Step 1: According to Raoult’s law:

\[ P_{\text{solution}} = P^0_{\text{solvent}} \times X_{\text{solvent}} \]

Step 2: Let \( X_{\text{solute}} = x \), then:

\[ X_{\text{solvent}} = 1 - x \]

Step 3: Given:

\[ \begin{align*} P_{\text{solution}} &= 750 \, \text{mm Hg} \\ P^0_{\text{solvent}} &= 760 \, \text{mm Hg} \end{align*} \]

Step 4:

\[ \begin{align*} 750 &= 760(1 - x) \Rightarrow \frac{750}{760} = 1 - x \\ x &= 1 - \frac{750}{760} = \frac{10}{760} = 0.0132 \end{align*} \]

Conclusion: Mole fraction of glucose = 0.0132

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