Problem 22 - Chemistry The Central Science In Si Units

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

Statement (c) best explains it: small enthalpy of mixing compared to breaking initial interactions.

Step 1: Understand Enthalpy of Solution

The enthalpy of solution (98solution) of +19.8 kJ/mol indicates that dissolving KBr in water is an endothermic process. Energy is absorbed, suggesting that the formation of new interactions between KBr and water may not entirely compensate for the energy required to break the existing interactions (water-water and ionic K-Br bonds).

Step 2: Analyzing the Solubility Implication

The problem states that KBr is relatively soluble, which implies that despite the positive enthalpy change, the dissolution process is still favorable. This can usually be attributed to a favorable entropy change (98mixing).

Step 3: Consider Entropy Contribution

Even though the process absorbs heat, increasing the disorder in the system when KBr dissolves in water (forming a mixture instead of distinct components) increases entropy, which can drive the process to be spontaneous according to Gibbs Free Energy (97G = 9fl8 - T97S).

Step 4: Evaluate Each Option

- (a) Potassium salts generally dissolve well, but this neither explains the positive enthalpy nor addresses the entropy. - (b) A favorable entropy of mixing is typically the driving force for solubility when 9fl8 is positive, not unfavorable entropy. - (c) Suggests that the enthalpy of mixing (new interactions) is small compared to breaking the old interactions, aligning with a +19.8 kJ/mol 9fl8 as not significantly offsetting the cost of interaction breaking. - (d) High molar mass affects the amount of interactions per unit of mass, not directly explaining solubility or enthalpy in this context.

Step 5: Conclusion

Option (c) is the best explanation. The enthalpy of breaking the original bonds in water and KBr is not sufficiently offset by the new interactions formed between KBr and water, leading to a positive enthalpy of solution. However, the solubility suggests that there is a favorable entropy change that still allows the dissolution process to occur.

Key Concepts

Entropy of Mixing

The concept of entropy of mixing is central to understanding why substances dissolve. Entropy is a measure of disorder or randomness in a system. When \(\mathrm{KBr}\) dissolves in water, there is a significant increase in entropy. This is because the ordered structure of the ionic solid breaks apart, allowing the ions to spread throughout the solvent.
This increase in randomness is what we refer to as the entropy of mixing. It's often favorable, meaning it can drive a process even if it requires energy input, as seen with \(\mathrm{KBr}\).
The dissolution brings about higher entropy, off-setting the positive enthalpy of solution.

• Disorder is amplified: The ions disrupt the structure of water, leading to a greater number of microstates.
• Spontaneity is possible: Although energy is absorbed, the entropy component can make the overall process spontaneous due to the Gibbs Free Energy equation.

Solubility

Solubility refers to the ability of a substance (solute) to dissolve in a solvent. In the case of \(\mathrm{KBr}\), its solubility in water is influenced by several factors. Despite the endothermic nature of the process (absorbing heat), \(\mathrm{KBr}\) is still relatively soluble. This is largely due to the increase in entropy discussed earlier.
The phenomenon is counterintuitive; usually, substances with positive enthalpies of solution are less soluble at lower temperatures because heat is required to dissolve them.
However, the entropy term can dominate the solution process, making \(\mathrm{KBr}\) dissolve effectively even under these conditions.

• Positive entropy change increases solubility by enhancing disorder.
• Gibbs Free Energy: The relationship \( \Delta G = \Delta H - T \Delta S \) helps explain the balance between enthalpy and entropy that dictates whether \(\mathrm{KBr}\) will dissolve.

Endothermic Process

An endothermic process is one where heat is absorbed from the surroundings. Dissolution of \(\mathrm{KBr}\) in water showcases this. The measured enthalpy of solution is \( +19.8 ext{ kJ/mol} \), indicating that more energy is required to break bonds than is released in forming new ones.
The dissociation involves breaking water-water hydrogen bonds and ionic bonds in \(\mathrm{KBr}\). If these energy costs aren't fully offset by forming water-ion interactions, the enthalpy remains positive, a sign of an endothermic reaction.
Still, the dissolution process occurs because the increase in entropy overcomes the positive enthalpy.

• Heat absorption is notedthrough the endothermic nature but doesn't prevent solubility.
• Compensated by entropy: The resulting increase in entropy compensates for the endothermicity, making the process spontaneous overall.