Which of the following is incorrect for the given graph?

\(\Delta V_{mix} = positive\)

The correct answer is option 2. \(\Delta V_{mix} = positive\).

Raoult’s Law states that for an ideal solution, the partial vapor pressure of each component (\(P_A\)) is proportional to its mole fraction (\(X_A\)):

\(P_A = P_A^o X_A \)

where \(P_A^o\) is the vapor pressure of the pure component A.

Deviations from Raoult’s Law can be classified into two types:

i. Positive Deviations: When the vapor pressure of the solution is higher than predicted by Raoult’s Law.

ii. Negative Deviations: When the vapor pressure of the solution is lower than predicted by Raoult’s Law.

From the given graph it is clear that the graph is for negative deviation.

Characteristics of Negative Deviations

Mixing Volume (\(\Delta V_{mix}\))

Negative Deviations: When a solution shows negative deviations from Raoult's Law, the actual volume of the mixture is less than the sum of the volumes of the pure components. This happens because the intermolecular forces between different components are stronger than those in the pure substances. This stronger interaction results in a more compact arrangement of molecules, thus a decrease in volume.

\(\Delta V_{mix} = V_{solution} - (V_A^o + V_B^o) \)

For negative deviations, \(\Delta V_{mix}\) is negative.

Enthalpy of Mixing (\(\Delta H_{mix}\))

Negative Deviations: The enthalpy of mixing is negative because the mixing process is exothermic. This means that heat is released when the components mix. The release of heat indicates that the interactions between different molecules in the solution are stronger than the interactions between the molecules of the pure components.

\(\Delta H_{mix} = H_{solution} - (H_A^o + H_B^o) \)

For negative deviations, \(\Delta H_{mix}\) is negative.

Vapor Pressure (\(P_A\))

Negative Deviations: In solutions showing negative deviations, the actual vapor pressure of the component is lower than the value predicted by Raoult’s Law. This occurs because the intermolecular interactions in the solution are stronger, reducing the tendency of molecules to escape into the vapor phase.

\(P_A < P_A^o X_A \)

Evaluating Each Statement

1. \(\Delta V_{mix} = \text{negative}\)

Correct: For negative deviations, the mixing volume is indeed less than the sum of the volumes of the pure components. Hence, \(\Delta V_{mix}\) is negative

2. \(\Delta V_{mix} = \text{positive}\)

Incorrect: Positive \(\Delta V_{mix}\) occurs with positive deviations from Raoult's Law, not negative deviations. For negative deviations, \(\Delta V_{mix}\) should be negative.

3. \(\Delta H_{mix} = \text{negative}\)

Correct: For negative deviations, the mixing process is exothermic, leading to a negative \(\Delta H_{mix}\).

4. \(P_A < P_A^o X_A\)

Correct: For negative deviations, the actual vapor pressure is less than the value predicted by Raoult’s Law, indicating that \(P_A < P_A^o X_A\).Conclusion

The statement that is incorrect for negative deviations from Raoult's law is: 2. \(\Delta V_{mix} = \text{positive}\)

In negative deviations, \(\Delta V_{mix}\) is negative, not positive.