How does \(\Delta H_{\text {soln }}\) relate to deviations from Raoult's law? Explain.

Raoult's law states that in an ideal mixture of volatile components, the partial vapor pressure of a component is equal to the product of the mole fraction of that component in the mixture and its vapor pressure in the pure state. Mathematically, it can be expressed as: \[ P_A = x_A P^*_A \] where \(P_A\) = partial vapor pressure of component A in the mixture, \(x_A\) = mole fraction of A in the solution, \(P^*_A\) = vapor pressure of pure A.

Deviations from Raoult's law mainly arise due to the non-ideal behavior of mixtures as a result of differences in molecular interactions between the components (such as molecular size, polarity, or hydrogen bonding). Negative deviation: If attractive interactions between A-B are stronger than those in component A (A-A) and component B (B-B), vapor pressure is lowered, and the system exhibits a negative deviation from Raoult's law. Positive deviation: If attractive interactions between A-B are weaker than those in component A (A-A) and component B (B-B), vapor pressure is higher, and the system exhibits a positive deviation from Raoult's law.

The enthalpy change (∆H_soln) is the heat absorbed or released when a solute dissolves in a solvent. It represents the interactions between the solute and solvent particles. The relationship between ∆H_soln and deviations from Raoult's law can be described as follows: 1. If ∆H_soln = 0, it indicates that the bonds formed between the solute and solvent are equal to the energy consumed in breaking their respective bonds. This results in ideal behavior, and the solution will obey Raoult's law. 2. If ∆H_soln > 0, it implies that the energy required to break the interactions between the solute and solvent particles is more significant than the energy released by the formation of new solute-solvent bonds. This implies weaker A-B interactions which leads to a positive deviation from Raoult's law. 3. If ∆H_soln < 0, it implies that the energy released by forming bonds between solute-solvent molecules is more considerable than the energy needed to break their bonds. This indicates stronger A-B interactions, and the solution will show a negative deviation from Raoult's law. In summary, deviations from Raoult's law are related to the enthalpy change of the solution, which reflects the strength of interactions between the solute and solvent molecules. If ∆H_soln is positive, the solution will have a positive deviation from Raoult's law, while if ∆H_soln is negative, the solution will show a negative deviation.