Problem 22 - Chemistry: The Central Science in SI Units, Global Edition

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-Br ionic interactions. (d) \(\mathrm{KBr}\) has a high molar mass compared to other salts like \(\mathrm{NaCl}\)

Step-by-Step Solution

Answer

Choice (c) The enthalpy of mixing must be small compared to the enthalpies for breaking up water-water interactions and K-Br ionic interactions.

Step 1: Answer Choice (a) Analysis

Potassium salts being always soluble in water doesn't explain how \(\mathrm{KBr}\) dissolves with positive enthalpy, so we can eliminate this choice.

Step 2: Answer Choice (b) Analysis

The entropy of mixing refers to the increase in disorder when two substances mix. An unfavorable entropy of mixing would suggest that the dissolution process is less likely to occur, so this statement does not provide a good explanation.

Step 3: Answer Choice (c) Analysis

This statement suggests that the enthalpy of mixing is small compared to the enthalpies required to break water-water and K-Br ion interactions. If this is true, then the overall enthalpy change could still be positive, but small enough for the dissolution to occur due to other factors (e.g. entropy change). This statement could provide a good explanation.

Step 4: Answer Choice (d) Analysis

The high molar mass of \(\mathrm{KBr}\) compared to salts like \(\mathrm{NaCl}\) doesn't provide an explanation for its solubility in water with positive enthalpy of solution. This statement can be disregarded. From the analysis of each statement, it is clear that the best explanation for the given behavior of \(\mathrm{KBr}\) is provided by:

Step 5: Final Answer

Choice (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 property that describes how much of a solute can dissolve in a solvent at a given temperature. This process depends on interactions between entities involved, which includes solvent-solvent, solute-solute, and solute-solvent interactions.
For \( ext{KBr}\), its solubility in water can be understood by analyzing these interactions. Even though the enthalpy of solution is positive, it still dissolves relatively well. This indicates that the driving forces for solubility are more than just the enthalpy change.
Primarily, what contributes significantly to \( ext{KBr}\)'s solubility in water, despite its positive enthalpy change, is the strong ion-dipole interactions formed between \( ext{K}^+\) and \( ext{Br}^-\) ions and water molecules. Such interactions can overpower the energy required to break existing bonds in the pure solute and solvent.

Entropy of Mixing

Entropy of mixing is a thermodynamic concept referring to the increase in disorder or randomness when two substances are combined. When \( ext{KBr}\) dissolves in water, the entropy change (\( \Delta S \)) is often positive.
This favorable entropy change is due to the increased randomness as ion distribution becomes uniform throughout the solution rather than clustered in a solid state. However, if this entropy change were unfavorable, it would counteract the solubility, making dissolution less viable.
The entropy of mixing in this case is significant enough to help favor the process of solubilization, despite a positive enthalpy change. It plays a crucial role in compensating for the energy needed to overcome the cohesive forces within pure substances.

Water-Water Interactions

Water molecules are known for their strong hydrogen bonding capabilities, forming highly cohesive networks. This binding within water must be disrupted to allow solute particles like \( ext{K}^+\) and \( ext{Br}^-\) ions to disperse in the water.
The energy required to break these water-water interactions contributes to the positive enthalpy of solution observed when dissolving \( ext{KBr}\) in water. However, it’s not just the breaking of these bonds; the formation of new interactions between water and ions (ion-dipole interactions) is also important.
While breaking water-water interactions increases the energy requirement, creating new solute-solvent interactions helps in balancing the energy scale, along with the entropic contributions to the process.