Problem 22 - Chemistry: The Central Science

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?

Step-by-Step Solution

Answer

The high solubility of \(\mathrm{KBr}\) in water, despite its endothermic enthalpy of solution (\(ΔH = +198\, \mathrm{kJ/mol}\)), can be explained by the significant increase in entropy (disorder) that occurs as the \(\mathrm{KBr}\) dissociates into its component ions. This increase in entropy, along with the strong ion-dipole attractions between the \(\mathrm{KBr}\) ions and water molecules, offset the positive enthalpy change and make the overall Gibbs Free Energy (ΔG) favorable for \(\mathrm{KBr}\) to dissolve spontaneously in water, resulting in high solubility.

Step 1: Understanding Enthalpy and Entropy

The solubility of a substance depends not only on the enthalpy change but also the entropy change. Enthalpy change, denoted by ΔH, is a measure of energy absorbed or released during a process. A positive ΔH indicates an endothermic process (energy is absorbed), while a negative ΔH indicates an exothermic process (energy is released). Entropy, denoted by ΔS, is a measure of the degree of disorder in a system. An increase in entropy means an increase in disorder, while a decrease in entropy means a decrease in disorder.

Step 2: Recall Gibbs Free Energy

The Gibbs Free Energy (ΔG) is the main factor that determines whether a process is spontaneous or not. It is calculated using the formula: \[ΔG = ΔH - TΔS\] Where ΔG is Gibbs Free Energy, ΔH is the Enthalpy change, T is the temperature in Kelvin, and ΔS is the Entropy change. A process is spontaneous if ΔG is negative, non-spontaneous if ΔG is positive.

Step 3: Enthalpy Change of KBr in Water

We are given that the enthalpy change (ΔH) of \(\mathrm{KBr}\) in water is about \(+198\, \mathrm{kJ/mol}\), which means the process is endothermic, and energy is absorbed when KBr dissolves in water. At first glance, this may lead us to believe that the solubility should be low because the process requires energy input.

Step 4: Entropy Change of KBr in Water

When KBr dissolves in water, it breaks into its component ions - \(K^+\) and \(Br^-\). This increases the number of particles in the solution, leading to an increase in disorder or entropy (ΔS). Entropy is an important factor in determining solubility, and the increase in entropy can help offset the positive enthalpy change, making the overall process more favorable.

Step 5: Explaining High Solubility

The high solubility of KBr in water can be explained by the fact that the increase in entropy outweighs the endothermic enthalpy change. This means that although energy is absorbed when KBr dissolves in water, the resulting increase in disorder (entropy) is significant enough to make the overall process (Gibbs Free Energy) favorable, resulting in a high solubility. Additionally, the strong ion-dipole attractions between the KBr ions and the water molecules further contribute to the solubility.