Question

\(\mathrm{KBr}\) is relatively soluble in water, yet its enthalpy of solution is \(+19.8 \mathrm{kJ} / \mathrm{mol} .\) Which of the following statements provides the best explanation for this behavior? (a) Potassium salts are always soluble in water. (b) The entropy of mixing must be unfavorable. (c) The enthalpy of mixing must be small compared to the enthalpies for breaking up water-water interactions and K-Brionic interactions. (d) KBr has a high molar mass compared to other salts like NaCl.

Short answer

The best explanation for KBr's behavior with positive enthalpy of solution while being soluble in water is given by statement (c): The enthalpy of mixing must be small compared to the enthalpies for breaking up water-water interactions and K-Br ionic interactions.

Step-by-step solution

Statement (a) explanation

Potassium salts are always soluble in water. This statement does not provide any explanation for the enthalpy of solution being positive (+19.8 kJ/mol). It only states KBr's solubility properties.

Statement (b) explanation

The entropy of mixing must be unfavorable. Entropy is a measure of disorder in a system. The dissolution process generally results in an increase in the disorder of the system due to mixing. This statement is contradictory since KBr is soluble in water, which indicates that the entropy of mixing must be favorable, not unfavorable.

Statement (c) explanation

The enthalpy of mixing must be small compared to the enthalpies for breaking up water-water interactions and K-Br ionic interactions. Enthalpy of solution is the sum of: 1. Enthalpy for breaking up water-water interactions (enthalpy of hydration for water). 2. Enthalpy for breaking up K-Br ionic interactions (lattice enthalpy). 3. Enthalpy for forming new interactions between water molecules and solute ions (enthalpy of hydration for solute ions). A positive enthalpy of solution means that the process is endothermic, which means it absorbs energy from its surroundings. This statement suggests that the favorable enthalpy of mixing is relatively small compared to the endothermic processes of breaking up water-water and K-Br ionic interactions. Therefore, the overall enthalpy of solution is positive. This statement provides a reasonable explanation for the behavior of KBr with a positive enthalpy of solution.

Statement (d) explanation

KBr has a high molar mass compared to other salts like NaCl. This statement doesn't directly explain the connection between KBr's solubility in water and its positive enthalpy of solution. Molar mass doesn't necessarily correlate with solubility or enthalpy of solution.

Conclusion

The best explanation for KBr's behavior with positive enthalpy of solution while being soluble in water is given by statement (c): The enthalpy of mixing must be small compared to the enthalpies for breaking up water-water interactions and K-Br ionic interactions.

Key concepts

Solubility

Solubility is a key property in chemistry, describing how much of a solute can dissolve in a solvent at a given temperature. When a salt like potassium bromide (KBr) dissolves in water, it breaks into its ions (K\(^+\) and Br\(^-\)). This process involves an interplay of energies, including those needed to break bonds.
On a molecular level, solubility depends on the compatibility of the interactions between water molecules and the ions from the solute. If these new interactions are energetically favorable, more of the solute tends to dissolve. However, even if these interactions are not overwhelmingly stronger, solubility can still be positive if entropy considerations come into play.
Several factors affect solubility:

• Temperature: Higher temperatures can increase solubility for many salts.
• Nature of the solute and solvent: "Like dissolves like" is a general rule, indicating that polar solvents like water are good at dissolving ionic compounds.
• Presence of other substances: Sometimes, other ions or compounds in solution can increase or decrease solubility.

Ionic Interactions

Ionic interactions occur when opposite charges attract each other, such as in salts. In the case of KBr, strong ionic interactions exist between the potassium (K\(^+\)) and bromide (Br\(^-\)) ions.
These ionic bonds are initially strong in the solid state, requiring energy to break. Known as lattice enthalpy, this energy must be overcome for the salt to dissolve in water. The energy introduced during the process comes from the new attractions formed between the ions and water molecules.
The dissolution of KBr involves several energy steps:

• Breaking K-Br ionic bonds (endothermic process requiring energy).
• Breaking water's hydrogen bonding structure to make room for ions (also endothermic).
• Forming new attractions between K\(^+\), Br\(^-\), and water molecules (exothermic).

Despite the positive enthalpy of the dissolution process, ionic interactions with water still stabilize ions and aid dissolution.

Entropy

Entropy is a measure of disorder or randomness in a system. In thermodynamics, systems naturally progress toward a state of higher entropy.
When KBr dissolves in water, its crystalline structure breaks down, leading to greater freedom of movement for ions. This transition results in an increase in entropy, or more disorder. The initial mixing of water molecules and the KBr compound might result in some structured interactions, but overall, the process boosts entropy.
Key aspects of entropy in the dissolution process:

• The breakdown of a solid structure into individual ions adds randomness.
• Solvent molecules like water become more disordered as they surround and interact with ions.
• Increased entropy can help drive dissolution even when enthalpy changes might not be highly favorable.

It is important to consider both enthalpy and entropy in understanding solubility, especially in cases where the enthalpy of solution is positive but a substance is still soluble.