Consider the formation of a solution of aqueous potassium chloride. Write the thermochemical equations for (a) the conversion of solid KCl into its gaseous ions and (b) the subsequent formation of the solution by hydration of the ions. The lattice energy of \(\mathrm{KCl}\) is \(-715 \mathrm{~kJ} \mathrm{~mol}^{-1}\), and the hydration energy of the ions is \(-686 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Calculate the enthalpy of solution of \(\mathrm{KCl}\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\)

When dealing with chemical processes, understanding the energy changes that occur is crucial. Thermochemical equations provide this insight by combining chemical equations with the heat flow that accompanies the reactions. These equations are a form of bookkeeping for the energy involved in chemical transformations.

For example, in the dissolution of potassium chloride (KCl), we consider two main steps: the breaking of the solid ionic lattice, which requires energy (endothermic), and the stabilization of ions in solution by hydration, which releases energy (exothermic). The sum of these energy changes, represented by the respective thermochemical equations, gives us the enthalpy of solution, reflecting whether the overall process absorbs or releases heat.

Hydration energy is the amount of energy released when ions are surrounded by water molecules and thus stabilized in a solution. The energy is released because of the strong attractions between ions and the polar water molecules.

This interaction is crucial in determining how substances dissolve in water. A higher hydration energy means that the water molecules more effectively stabilize the ions, which can lead to more favorable dissolution. In the case of potassium chloride, the hydration energy is -686 kJ/mol, highlighting an exothermic process in which the system releases energy to its surroundings.

Lattice energy is the energy required to break apart the ionic lattice of a crystalline solid into its gaseous ions. This energy is directly related to the strength of the electrostatic forces between the ions in the lattice. The stronger these forces, the higher the lattice energy will be, and consequently, the more energy it will require to break the lattice apart.

For KCl, the lattice energy is +715 kJ/mol, an indicator of the energy required to disrupt the orderly array of potassium and chloride ions and convert them into gaseous ions. Lattice energy is a fundamental concept in understanding why some salts dissolve more easily in water than others, as it provides a measure of the solid's stability.

The process of dissolving KCl in water is a complex one, involving several energy changes. Initially, solid KCl must overcome its lattice energy to separate into potassium and chloride ions in the gaseous state. Once these ions are gaseous, they interact with water through hydration, an exothermic process that releases energy.

These interactions, endothermic lattice disruption followed by exothermic hydration, combine to determine the overall enthalpy of solution. For KCl, the enthalpy of solution can be calculated by adding the lattice energy and hydration energy, leading to a slightly positive value of +29 kJ/mol. This indicates that, overall, the dissolution of KCl in water requires a small input of energy from the surroundings to occur.