Question

The enthalpy of solution of \(\mathrm{KBr}\) in water is about \(+198 \mathrm{~kJ} / \mathrm{mol}\). Nevertheless, the solubility of \(\mathrm{KBr}\) in water is relatively high. Why does the solution process occur even though it is endothermic?

Short answer

The dissolution of KBr in water is endothermic with an enthalpy change of +198 kJ/mol. However, the process occurs due to the significant increase in entropy upon dissolution, resulting in a thermodynamically spontaneous process. Although the lattice enthalpy (energy required to break the ionic lattice) is greater than the hydration enthalpy (energy released due to ion-dipole interactions), the difference is not too large. It is the increase in entropy, representing the disorder and randomness in the system, that compensates for the positive enthalpy change. Consequently, the Gibbs free energy change (∆G), which combines enthalpy (∆H) and entropy (∆S) through the equation ∆G = ∆H - T∆S, remains negative, leading to a spontaneous dissolution process.

Step-by-step solution

Understand the enthalpy change of the solution process

The dissolution of an ionic compound in water generally involves three main steps: 1. Breaking the ionic lattice of the solute (lattice enthalpy). 2. Breaking the hydrogen bonds in water (enthalpy of water). 3. Forming solvation shells around the ions (hydration enthalpy). The overall enthalpy of the solution process is the sum of the enthalpy changes in all three steps. For KBr, the overall enthalpy change is given as +198 kJ/mol, which is endothermic (positive enthalpy change).

Consider the role of lattice enthalpy and hydration enthalpy

Since the dissolution process of KBr is endothermic, the lattice enthalpy (energy required to break the ionic lattice of KBr) must be greater than the hydration enthalpy (energy released due to the formation of solvation shells around the ions). However, the hydration enthalpy of both K+ and Br- ions is significantly high, as they get surrounded by water molecules and form strong ion-dipole interactions. The difference between the lattice enthalpy and the hydration enthalpy is not too large in this case, which makes the dissolution of KBr in water favorable.

Evaluate the role of entropy in the dissolution process

Entropy (the measure of disorder or randomness) also plays a significant role in the dissolution process. When KBr dissolves in water, it releases K+ and Br- ions that are randomly surrounded by water molecules. The breaking of the ionic lattice, as well as the hydration of the ions, increases the entropy of the system. The increase in entropy makes the process thermodynamically spontaneous (favorable).

Combining enthalpy and entropy to understand the dissolution process

In the dissolution process of KBr in water, even though the enthalpy change is endothermic, the increase in entropy overcomes the positive enthalpy change, making the process thermodynamically favorable. The overall Gibbs free energy change (∆G), which takes into account both enthalpy (∆H) and entropy (∆S), must be negative for a process to be spontaneous. Given by the equation: \[∆G = ∆H - T∆S\] where T is the temperature in Kelvin. In the case of KBr dissolution in water, the entropy term, T∆S, compensates for the positive enthalpy change, resulting in a negative Gibbs free energy change and a spontaneous dissolution process. In conclusion, the dissolution process of KBr in water occurs despite being endothermic due to the significant increase in entropy that compensates for the positive enthalpy change.

Key concepts

Lattice Enthalpy

Lattice enthalpy is a vital concept when studying the dissolution of ionic compounds like potassium bromide (KBr) in water. It represents the energy needed to break the bonds that hold the ions in the crystal lattice structure when the solid compound turns into its gaseous ionic components. In simpler terms, it's like the 'strength' of the ionic crystal.

For KBr, breaking apart the lattice to produce separate K+ and Br- ions requires a considerable amount of energy. This energy cost is one reason why you might think KBr won't dissolve easily. However, the high lattice enthalpy does not tell the whole story of solubility. It is actually the balance between this energy and other enthalpies involved in the solution process that determines if a compound is soluble or not.

In the case of KBr, the high solubility despite its positive enthalpy of solution hints that other factors like hydration enthalpy, which we'll look at next, significantly shape the overall process.

Hydration Enthalpy

Hydration enthalpy is another piece of the puzzle in understanding why substances like KBr dissolve in water. After you have separated the ions from their lattice structure, they interact with water molecules. The hydration enthalpy is the energy change when water molecules cluster around these free ions, forming a 'solvation shell'.

The hydration enthalpy is usually exothermic, meaning it releases energy, because new attractions between the water molecules and the ions (ion-dipole interactions) are formed. These new interactions are quite stable and release more energy as heat. For KBr, both potassium (K+) and bromide (Br-) ions have a strong affinity for water molecules, resulting in a significant release of energy when they become hydrated.

This release of energy helps balance out the high energy demand needed to break the lattice structure, contributing to the feasibility of KBr dissolving in water, despite an overall endothermic reaction.

Entropy and Dissolution

Let's talk about a term that may sound scientific yet is highly relevant to the process of dissolution—entropy. Entropy basically measures the level of disorder or randomness in a system. In most natural processes, entropy tends to increase.

In the context of KBr dissolving in water, entropy plays a superhero role. When the solid KBr dissolves, the ions that were once ordered within a rigid lattice become dispersed in the water, assuming random positions. This dispersal results in a major increase in disorder—hence, a significant increase in entropy.

This entropy boost often has enough 'oomph' to drive the dissolution process forward, even if the enthalpy changes suggest it shouldn't happen. In essence, the preference of nature for disorder helps solid substances like KBr dissolve in water, adding another layer of understanding to the complexity of dissolve.

Gibbs Free Energy

Finally, let's unite the concepts of enthalpy, entropy, and temperature to look at the dissolution process from the perspective of Gibbs free energy. This quantity, denoted as ∆G, provides the bottom line on whether a process will occur spontaneously.

Gibbs free energy considers both the heat content (enthalpy) and the disorder (entropy) in the system and is expressed by the formula: \[∆G = ∆H - T∆S\], where ∆H is the change in enthalpy, ∆S is the change in entropy, and T is the temperature in Kelvin. A negative ∆G indicates a spontaneous process.

In the case of KBr, despite the endothermic reaction (positive ∆H), the large increase in entropy (∆S) when multiplied by the temperature (T) becomes significant enough to make ∆G negative. Essentially, it's the combination of these factors that determines the spontaneity of dissolution. To put it simply, nature 'prefers' a process that frees up heat or increases disorder. For KBr, it's the increase in disorder—or entropy—that encourages its dissolution in water, despite the related energy costs.