Question

The entropy change when a solution forms can be expressed by the term \(\Delta S^{\circ}\) soln. . When an ion dissolves and water molecules are ordered around it, the ordering would be expected to make a negative contribution to \(\Delta S_{\text {soln. }}^{\circ}\). An ion that has more charge density will have a greater hydration effect, or ordering of water molecules. Based on this information, which of the following compounds will have the most negative \(\Delta S_{\text {soln }}^{\circ}\) ? A. \(\mathrm{KCl}\) B. \(\mathrm{LiF}\) C. \(\mathrm{CaS}\) D. \(\mathrm{NaCl}\)

Short answer

C. \(\text{CaS}\)

Step-by-step solution

- Understand the Relationship Between Charge Density and Entropy Change

The problem states that an ion with more charge density will have a greater hydration effect and thus a greater ordering of water molecules around it. This increases negative contributions to \(\Delta S_{\text{soln}}^{\circ}\).

- Identify the Charge Density

Charge density depends on both the charge of the ion and the size of the ion. Higher charge and smaller size result in higher charge density.

- Determine Ion Charges and Sizes

Review the charges and approximate sizes of the ions:- \(\text{K}^{+}\): +1 charge, large size- \(\text{Cl}^{-}\): -1 charge, large size- \(\text{Li}^{+}\): +1 charge, small size- \(\text{F}^{-}\): -1 charge, small size- \(\text{Ca}^{2+}\): +2 charge, medium size- \(\text{S}^{2-}\): -2 charge, medium size- \(\text{Na}^{+}\): +1 charge, medium size

- Compare Charge Densities

Evaluate the charge density for each compound by considering both the cation and anion in each pair:- \(\text{KCl}\): Moderate charge density- \(\text{LiF}\): Higher charge density due to both ions having small size- \(\text{CaS}\): Highest charge density due to high charges (2+ and 2-) and relatively smaller sizes- \(\text{NaCl}\): Moderate charge density

- Determine the Most Negative \(\Delta S_{\text{soln}}^{\circ}\)

The compound with the highest charge density will have the most negative \(\Delta S_{\text{soln}}^{\circ}\). Based on the comparison, \(\text{CaS}\) has the highest charge density due to its 2+ and 2- charges.

Key concepts

Charge Density

Charge density is a measure of the charge of an ion relative to its size. It helps us understand how strongly an ion can attract other molecules or ions. The equation for charge density is \( \text{Charge Density} = \frac{\text{Charge}}{\text{Volume}} \). However, in simpler terms for ionic compounds, we consider the charge and the size of the ion. Higher charge and smaller size result in higher charge density.

This concept is key because it influences how ions interact with water molecules when they dissolve. For example, ions with higher charge density create a stronger electric field, pulling water molecules closer and more orderly around them.
The result is a more negative entropy change (\( \Delta S_{\text{soln.}} \)) when the solution forms because the water molecules become more ordered.

Hydration Effect

When an ion dissolves in water, it attracts water molecules, a process called hydration. The extent of this hydration or ordering of water molecules depends on the ion's charge density.
Higher charge density means a stronger charge attracts more water molecules closer, causing more structuring or ordering of the water around the ion.

This structuring can be visualized as a sort of 'shell' of water molecules that form around the ion. This shell of ordered water molecules is energetically favorable for stabilizing the ion in solution, but it also makes the system more ordered.
Hence, ions with higher charge density have a greater hydration effect, leading to a greater decrease in entropy (\( \Delta S_{\text{soln.}} \)) when they dissolve.

Entropy Change (\( \Delta S_{\text{soln.}} \))

Entropy change (\( \Delta S_{\text{soln.}} \)) in solution formation is a measure of the disorder or randomness in the system. When an ionic compound dissolves, two main factors affect the entropy change:

• Disruption of the ionic lattice (increases entropy)
• Hydration and ordering of water molecules around ions (decreases entropy)

For ions with high charge density, the hydration effect is strong, leading to a significant ordering of water molecules. This process decreases the overall entropy of the system, resulting in a more negative \( \Delta S_{\text{soln.}} \).

In the given exercise, \ \( \text{CaS} \) has the highest charge density due to the 2+ and 2- charges of its ions. This results in the most significant ordering of water molecules and therefore the most negative \( \Delta S_{\text{soln.}} \). Understanding this helps predict the behavior of different ionic compounds in solution, crucial for many applications in chemistry and material science.