Question

(a) Discuss the factors that contribute towards KCl being a readily soluble salt \(\left(35 \text { g per } 100 \text { g } \mathrm{H}_{2} \mathrm{O} \text { at } 298 \mathrm{K}\right)\) (b) Develop your answer to part (a) by using the following data: \(\Delta_{\text {hyd }} H^{\circ}\left(\mathrm{K}^{+}, \mathrm{g}\right)=-330 \mathrm{kJ} \mathrm{mol}^{-1}\) \(\Delta_{\mathrm{hyd}} H^{0}\left(\mathrm{Cl}^{-}, \mathrm{g}\right)=-370 \mathrm{kJ} \mathrm{mol}^{-1}\) \(\Delta_{\text {latticc }} H^{\circ}(\mathrm{KCl}, \mathrm{s})=-715 \mathrm{kJ} \mathrm{mol}^{-1}\)

Short answer

KCl's solubility arises from the nearly balanced lattice and hydration energy values, making it readily soluble in water.

Step-by-step solution

Understanding Solubility

Solubility of salts depends on the balance between lattice energy and hydration energy. Lattice energy is the energy needed to break apart the ions in a solid compound, whereas hydration energy is the energy released when ions are surrounded by water molecules. If the hydration energy is greater than lattice energy, the salt is more likely to dissolve.

Calculating Total Energy Change

We need to compare the hydration energies of the ions and the lattice energy of KCl. The process involves the dissolution of 1 mol of KCl into its ions and the subsequent hydration of these ions. The given values are \(\Delta_{\text{hyd}} H^{\circ}(\text{K}^+, \text{g}) = -330 \, \text{kJ/mol}\), \(\Delta_{\text{hyd}} H^{\circ}(\text{Cl}^-, \text{g}) = -370 \, \text{kJ/mol}\), and \(\Delta_{\text{lattice}} H^{\circ}(\text{KCl}, \text{s}) = -715 \, \text{kJ/mol}\). The total hydration energy is \(-330 + (-370) = -700 \, \text{kJ/mol}\).

Analyzing Energy Balance

Compare the total hydration energy (-700 kJ/mol) with the lattice energy (-715 kJ/mol). The lattice energy is slightly greater than the hydration energy; however, the difference is small, showing that the dissolution process is still favorable. The small difference indicates that ion attractions in KCl are reasonably balanced by hydration forces, making KCl soluble.

Conclusion

The factors contributing to KCl's solubility are mainly derived from its energetic balance. The relatively close magnitude of the lattice and hydration energies described shows that KCl is capable of dissolving fairly well in water due to the favorable formation of ion-water interactions ensuring solubility.

Key concepts

Lattice Energy

Lattice energy is a fundamental concept to understand why ionic compounds like KCl behave the way they do in terms of solubility. It refers to the energy required to separate the ions in an ionic solid to an infinite distance apart. Essentially, it's about breaking the ionic bonds that hold the solid structure together.

For potassium chloride (KCl), the lattice energy is given as \[\Delta_{\text{lattice}} H^{\circ}(\text{KCl}, \text{s}) = -715 \, \text{kJ/mol}\]This negative sign indicates that energy is released when the ions come together to form the solid compound, meaning it is a highly exothermic process. To dissolve KCl in water, this lattice energy must be overcome.

• High lattice energy implies strong ionic bonds and less solubility since more energy is required to dissociate the ions.
• Conversely, lower lattice energy suggests weaker ionic bonds and therefore, potentially greater solubility if other factors are favorable.

Despite KCl's considerable lattice energy, its solubility in water can be explained by comparing it with other energies, specifically, hydration energy.

Hydration Energy

Hydration energy plays a crucial role in the solubility of salts. It represents the energy released when ions interact with water molecules, forming hydrated ions, which helps in dissolving the salt.

For KCl, we have the hydration energy values:\[\Delta_{\text{hyd}} H^{\circ}(\text{K}^+, \text{g}) = -330 \, \text{kJ/mol}\]\[\Delta_{\text{hyd}} H^{\circ}(\text{Cl}^-, \text{g}) = -370 \, \text{kJ/mol}\]The total hydration energy is calculated as:\[-330 + (-370) = -700 \, \text{kJ/mol}\]

When ions from KCl dissolve in water, they are surrounded by water molecules, and energy is released during the formation of these new ion-water interactions. The hydration energy is slightly less negative than the lattice energy but close enough to allow the dissolution of KCl.

• The substantial negative hydration energy indicates that the formation of these interactions compensates for the energy required to break the lattice bonds.
• This closes the energy gap, making it energetically feasible for KCl to dissolve in water.

Hydration energy essentially shows the favorability of ion-water compared to ion-ion interactions, which enhances salt solubility.

Thermodynamics of Solubility

The thermodynamics of solubility encompasses both lattice and hydration energy, dictating whether a salt like KCl will dissolve in water. Solubility is an interplay of these energetic changes when a salt transitions from solid to aqueous ions.

When evaluating the solubility of KCl, we look at the balance between its lattice energy and hydration energy. The slight disparity between these energies proposes a near balance:

• Lattice energy of -715 kJ/mol needs to be compensated by hydration energy during dissolution.
• The total hydration energy is -700 kJ/mol, which, despite being slightly lower, suggests a feasible dissolution process.

This energy balance is key in understanding why KCl is soluble in water. It shows that even if the lattice energy is slightly greater than the hydration energy, other driving forces and entropic factors make dissolution favorable.

Overall, when considering the thermodynamics of KCl solubility:

• Close energy values mean that the combination of enthalpy and entropy changes favors dissolving.
• Energy balance aligns with thermodynamic principles, suggesting that KCl readily dissolves due to favorable energetic conditions at standard room temperature.

It’s not just the energy values alone but the broader thermodynamic context, including temperature and entropy, that decide the extent of solubility.