Question

The vapour pressure of the solution of two liquids \(\mathrm{A}\left(\mathrm{p}^{\circ}=80 \mathrm{~mm}\right)\) and \(\mathrm{B}\left(\mathrm{p}^{\circ}=120 \mathrm{~mm}\right)\) is found to be \(100 \mathrm{~mm}\) when \(\mathrm{x}_{\mathrm{A}}=0.4\). The result shows that : (1) solution exhibits ideal behaviour (2) \(\Delta \mathrm{H}_{\text {solution }}<0\) (3) solution shows negative deviations (4) solution will show positive deviations for lower concentration and negative deviations for higher concentrations.

Short answer

The correct answers are (2) \( \Delta H_{solution} <0 \) and (3) solution shows negative deviations.

Step-by-step solution

Understand Raoult's Law

Raoult's Law states that the partial vapor pressure of each component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction: \[ P_{\text{solution}} = x_A P_A^\text{pure} + x_B P_B^\text{pure} \]

Calculate Expected Vapour Pressure

Using Raoult's Law, calculate the expected vapour pressure for the solution if it behaves ideally. Given:- \( x_A = 0.4 \)- \( x_B = 1 - x_A = 0.6 \)- \( P_A^\text{pure} = 80 \text{ mm Hg} \)- \( P_B^\text{pure} = 120 \text{ mm Hg} \)Substitute these values into Raoult's Law:\[ P_{\text{ideal}} = (0.4 \times 80) + (0.6 \times 120) \]\[ P_{\text{ideal}} = 32 + 72 = 104 \text{ mm Hg} \]

Compare with Given Vapour Pressure

The given vapour pressure of the solution is 100 mm Hg, which is less than the calculated ideal vapour pressure of 104 mm Hg.

Determine the Type of Deviation

Since the actual vapour pressure (100 mm Hg) is lower than the ideal vapour pressure (104 mm Hg), the solution shows negative deviations from Raoult's Law.

Analyze the Result

The solution shows negative deviations, implying that the intermolecular forces in the solution are stronger than those in the pure components. Stronger interactions can also mean an exothermic dissolution process, where \( \Delta H_{solution} \) is less than zero.

Final Answer

Based on the analysis, the correct answers are:(2) \( \Delta H_{solution} <0 \)(3) solution shows negative deviations

Key concepts

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature. In a mixture, Raoult's Law helps us understand how the vapor pressure of each component affects the overall vapor pressure of the solution.
Using Raoult's Law, the total vapor pressure of an ideal solution is calculated as the sum of the partial pressures of each component. This is given by: \text{ Raoult's Law formula: } \(P_{\text{solution}} = x_A \times P_A^{\text{pure}} + x_B \times P_B^{\text{pure}}\) Where: *\(x_A\)* and \(x_B\) are the mole fractions of components A and B, respectively. *\(P_A^{\text{pure}}\)* and \(P_B^{\text{pure}}\) are the vapor pressures of the pure components A and B.

Ideal Solution

An ideal solution is a mixture of liquids that obeys Raoult's Law throughout its entire range of concentrations. In ideal solutions, the total vapor pressure is simply the sum of the contributions from each component, which is dependent on their respective mole fractions. Ideal solutions form with no change in enthalpy (\(\text{ΔH}_{\text{solution}} = 0\)) and no volume change upon mixing.
Characteristics of an ideal solution include: *It follows Raoult's Law perfectly.* *The intermolecular forces between unlike molecules are equivalent to those between like molecules.* *It shows no heat absorption or evolution when the components are mixed.* In our exercise, the calculated ideal vapor pressure was 104 mm Hg, but the actual vapor pressure was found to be 100 mm Hg, indicating a deviation from ideality.

Negative Deviation

Negative deviation from Raoult's Law occurs when the observed vapor pressure of a solution is lower than the expected vapor pressure calculated for an ideal solution. This happens because the intermolecular forces between the different components in the solution are stronger than those between the molecules in the pure components. Consequently, fewer molecules escape into the vapor phase, lowering the vapor pressure.
Negative deviation indicates: *Stronger attractive forces between different molecules compared to like molecules* *A lower evaporation rate than expected for an ideal solution* *The total vapor pressure is lower than the sum of the partial pressures anticipated in an ideal solution* This type of deviation is evident in our problem where the solution's vapor pressure (100 mm Hg) is less than the calculated ideal vapor pressure (104 mm Hg).

Intermolecular Forces

Intermolecular forces are the forces that mediate interaction between molecules, including forces of attraction or repulsion which act between molecules and other types of neighboring particles. They include: *Van der Waals forces (London dispersion forces)* *Dipole-dipole interactions* *Hydrogen bonds*
In a solution exhibiting negative deviation, the intermolecular forces between the different molecules (A and B) are stronger than the forces in the pure components. This increased attraction reduces the number of molecules escaping to the vapor phase, resulting in a lower vapor pressure. The stronger these interactions, the more noticeable the deviation from ideal behavior.

Exothermic Dissolution

An exothermic dissolution process is characterized by the release of heat when a solute dissolves in a solvent. In such a process, the enthalpy change of the solution \(\text{ΔH}_{\text{solution}}\) is negative. This happens because the new interactions between solute and solvent molecules are stronger than those in the separate components. The energy released in forming these stronger interactions is greater than the energy required to break the initial interactions.
Key points about exothermic dissolution include: *The solution releases heat, causing the temperature to rise* *The process has \(\text{ΔH}_{\text{solution}} < 0\)* *It supports the presence of strong intermolecular forces in the solution* In our exercise, the solution shows negative deviation and is likely to have an exothermic dissolution process, affirming that \(\text{ΔH}_{\text{solution}} < 0\).