Question

An ionic compound has a highly negative \(\Delta H_{\text {soln }}\) in water. Would you expect it to be very soluble or nearly insoluble in water? Explain in terms of enthalpy and entropy changes.

Short answer

The compound is expected to be very soluble in water because the highly negative \( \Delta H_{\text{soln}} \) makes the dissolution process spontaneous.

Step-by-step solution

- Understand the Problem

We are asked to determine whether a compound with a highly negative \( \Delta H_{\text{soln}} \) (enthalpy change of solution) would be very soluble or nearly insoluble in water. We need to use the concepts of enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) to explain our reasoning.

- Review Enthalpy Change of Solution

\( \Delta H_{\text{soln}} \) represents the enthalpy change when an ionic compound dissolves in water. A highly negative \( \Delta H_{\text{soln}} \) means the process releases a large amount of energy, making it exothermic.

- Assess Entropy Change

When an ionic compound dissolves in water, the system’s disorder usually increases, leading to a positive entropy change (\( \Delta S \)). This is because the ions become more dispersed when they are solvated by water molecules.

- Apply Gibbs Free Energy Equation

Use the Gibbs Free Energy equation \( \Delta G = \Delta H - T \Delta S \). For a process to be spontaneous (favorable), \( \Delta G \) must be negative. Since \( \Delta H_{\text{soln}} \) is highly negative and \( \Delta S \) is positive, \( \Delta G \) will be negative.

- Conclusion on Solubility

Because the Gibbs Free Energy change (\( \Delta G \)) is negative (indicating a spontaneous process) with a highly negative \( \Delta H_{\text{soln}} \), the compound is expected to be very soluble in water.

Key concepts

enthalpy change of solution

The enthalpy change of solution, denoted as \( \Delta H_{\text{soln}} \), represents the amount of energy absorbed or released when an ionic compound dissolves in water. A highly negative \( \Delta H_{\text{soln}} \) indicates that the process releases a significant amount of energy, making it exothermic.
This energy release is due to the strong attractions between the ions and water molecules, known as solvation or hydration energy.
Key points to remember:

• An exothermic reaction (\( \Delta H_{\text{soln}} \) is negative) releases energy.
• This release of energy often drives the dissolution process, making exothermic reactions generally more favorable.
  

By understanding this concept, we can infer that a highly negative \( \Delta H_{\text{soln}} \) suggests the ionic compound will dissolve readily in water since it releases a substantial amount of energy, favoring the dissolution process.

entropy change

Entropy change, represented as \( \Delta S \), refers to the change in disorder or randomness of a system during a process. When an ionic compound dissolves in water, the ions are separated and spread out among the water molecules, increasing the system's disorder.
This increase in disorder leads to a positive \( \Delta S \).
Important aspects of entropy change include:

• A positive entropy change (\( \Delta S \)) indicates increased disorder.
• An increase in randomness typically contributes to making the dissolution process more favorable.

As the entropy increases when the ionic compound dissolves, this contributes positively to the solubility of the compound in water. Therefore, the dissolution process generally becomes more energetically favorable as \( \Delta S \) becomes more positive.

Gibbs Free Energy

Gibbs Free Energy, \( \Delta G \), is a thermodynamic quantity used to determine whether a process is spontaneous. It combines enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) changes with temperature (T) in the equation: \[ \Delta G = \Delta H - T \Delta S \]
For a process to be spontaneous, \( \Delta G \) must be negative.
Key points to consider with Gibbs Free Energy:

• A negative \( \Delta G \) indicates a spontaneous and thermodynamically favorable process.
• When \( \Delta H \) is highly negative and \( \Delta S \) is positive, \( \Delta G \) is more likely to be negative.

With a highly negative \( \Delta H_{\text{soln}} \) and a positive \( \Delta S \), the calculated \( \Delta G \) is negative, leading to a spontaneous dissolution process. Therefore, the ionic compound is expected to be very soluble in water, as evidenced by the negative Gibbs Free Energy change.