Potassium nitrate dissolves readily in water, and its enthalpy of solution is \(+34.9 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\). (a) Does the enthalpy of solution favor the dissolving process? (b) Is the entropy change of the system likely to be positive or negative when the salt dissolves? (c) Is the entropy change of the system primarily a result of changes in positional disorder or thermal disorder? (d) Is the entropy change of the surroundings primarily a result of changes in positional disorder or thermal disorder? (e) What is the driving force for the dissolution of \(\mathrm{KNO}_{3}\) ?

The concept of entropy change is at the heart of understanding why substances like potassium nitrate dissolve in water. Entropy is a measure of the disorder in a system. When a solid dissolves, it breaks apart into its component ions or molecules and becomes dispersed in the solvent. This breakup and dispersal lead to an increase in the disorder of the system, hence an increase in entropy.

During the dissolution process, entropy tends to increase because the number of possible ways to arrange the particles increases significantly when a solid dissolves. In the case of potassium nitrate, when it dissolves in water, the K+ and NO3- ions that were once held in a rigid lattice structure can now move around freely in the solution, creating a multitude of new arrangements and thus a significant amount of entropy. This increased disorder in the system is a favorable change and contributes to the spontaneity of the dissolving process, despite the endothermic nature of the enthalpy of solution.

To grasp the dissolution process of an ionic compound like potassium nitrate (KNO3), we must comprehend two main aspects: the enthalpy and entropy changes associated with the process. Enthalpy of solution relates to the heat absorbed or released when a solute dissolves in a solvent. Since the enthalpy of solution for KNO3 is +34.9 kJ/mol, the dissolution is endothermic; it absorbs heat.

However, the dissolution of a compound also involves the aforementioned entropy change. Even though the process absorbs heat and is not energetically favored (based on enthalpy alone), the substantial increase in disorder (entropy) can drive the process to occur spontaneously. It’s the combination of these two factors, enthalpy and entropy, that determines the overall favorability of the dissolution process. The dissolution process is also governed by the solvent-solute interactions which can be a crucial factor in facilitating or opposing the process.

When discussing entropy change related to dissolution, positional disorder plays a key role. Positional disorder refers to the arrangement of particles within a system, and when a solute like KNO3 dissolves, the positional disorder increases significantly. The ions of KNO3 which were once in a fixed position within the crystalline solid can now move freely in the solution.

This increase in positional disorder upon dissolution implies that there are far more ways to arrange the ions in a solution than there were in the solid form. This diversity in particle arrangement contributes to the overall entropy increase. The solid state is highly ordered with particles in a fixed position, but dissolution results in a scattered, less organized system. It’s this transformation from order to disorder that encapsulates the concept of positional disorder and highlights why entropy generally increases during the dissolution process.