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

Raoult's law is a theoretical model that applies to ideal solutions of two or more volatile components. It states that the partial vapor pressure of a component in a mixture is equal to the mole fraction of that component in the solution, multiplied by the vapor pressure of the pure component at the same temperature. Mathematically, this can be expressed as: $$ P_A = x_A P_A^* $$ Where \(P_A\) is the partial vapor pressure of component A in the mixture, \(x_A\) is the mole fraction of component A in the solution, and \(P_A^*\) is the vapor pressure of pure component A at the same temperature.

Deviations from Raoult's law occur when the solution exhibits non-ideal behavior, which means that the interactions between the molecules of the different components in the mixture are not the same as those in the pure components. There are two types of deviations from Raoult's law: positive and negative. Positive deviation: This occurs when the interaction between the molecules of the different components is weaker than the interaction between the molecules of the pure components. In this case, the partial vapor pressure of each component is higher than the one predicted by Raoult's law, which means that the solution has a higher volatility than expected from an ideal solution. Negative deviation: This occurs when the interaction between the molecules of the different components is stronger than the interaction between the molecules of the pure components. In this case, the partial vapor pressure of each component is lower than the one predicted by Raoult's law, which means that the solution has a lower volatility than expected from an ideal solution.

The enthalpy of solution, \(\Delta H_{\mathrm{soln}}\), is the heat absorbed or released when a solute is dissolved in a solvent to form a solution. When there are deviations from Raoult's law, the enthalpy of solution will not be equal to zero, as it would be in the case of an ideal solution. For a positive deviation from Raoult's law, the enthalpy of solution will be positive, which means that the process of dissolving the solute in the solvent is endothermic. This is because the weaker interaction between the different components requires more energy to overcome the stronger interaction between the molecules of the pure components. For a negative deviation from Raoult's law, the enthalpy of solution will be negative, which means that the process of dissolving the solute in the solvent is exothermic. This is because the stronger interaction between the different components releases more energy than needed to overcome the weaker interaction between the molecules of the pure components. In conclusion, the relationship between the enthalpy of solution, \(\Delta H_{\mathrm{soln}}\), and the deviations from Raoult's law can be summarized as follows: - For positive deviations from Raoult's law: \(\Delta H_{\mathrm{soln}} > 0\) - For negative deviations from Raoult's law: \(\Delta H_{\mathrm{soln}} < 0\)