Problem 61 - Introductory Chemistry Atoms First

Question

Consider an ionic solid dissolving in a liquid. Suppose the energy released as solute-solvent interactions take place is substantially less than the energy required to break up the lattice and to make room in the solvent. Would the solid be very soluble in this liquid? Explain your answer fully.

Step-by-Step Solution

Answer

In conclusion, the ionic solid would not be very soluble in the given liquid due to a positive enthalpy of solution (∆H_sol) arising from the substantially lower solvation energy (∆H_solvation) compared to the lattice energy (∆H_lattice). This indicates an endothermic and energetically unfavourable dissolution process.

Step 1: Understand the energy changes during dissolution of ionic solids

Ionic solids dissolve in a liquid through the breaking of ionic lattice to form separated ions, which then form a solution through solute-solvent interactions. Energy changes in two main ways during this process: 1. Lattice energy is required to break the ionic lattice into separated ions. 2. Solvation energy is the energy released as a result of solute-solvent interactions.

Step 2: Define the relationship between solvation energy, lattice energy, and the enthalpy of solution

The enthalpy of solution (∆H_sol) represents the overall energy change during the dissolution process. It's the sum of the lattice energy (∆H_lattice) and the solvation energy (∆H_solvation): ∆H_sol = ∆H_lattice + ∆H_solvation If ∆H_sol is negative (exothermic), it implies that the dissolution process is energetically favourable, leading to a more soluble ionic solid. If ∆H_sol is positive (endothermic), it implies that the dissolution process is energetically unfavourable, leading to a less soluble ionic solid.

Step 3: Analyze the given information about energy changes

The information provided states that the solvation energy (∆H_solvation) is substantially less than the lattice energy (∆H_lattice). In other words: ∆H_solvation << ∆H_lattice This implies that the energy released by solute-solvent interactions is not sufficient to overcome the energy required to break the ionic lattice.

Step 4: Determine the solubility of the ionic solid

Recall the relationship between the enthalpy of solution, lattice energy, and solvation energy: ∆H_sol = ∆H_lattice + ∆H_solvation Given that ∆H_solvation is substantially less than ∆H_lattice, it follows that the enthalpy of solution (∆H_sol) will be positive, indicating an endothermic process. Since the dissolution process is energetically unfavourable, the ionic solid will not be very soluble in the given liquid.

Step 5: Conclude the explanation

In conclusion, an ionic solid with a substantially lower solvation energy compared to its lattice energy would have a positive enthalpy of solution (∆H_sol), making the dissolution process endothermic and energetically unfavourable. Therefore, the solid would not be very soluble in the given liquid.

Key Concepts

Lattice Energy

Lattice energy is a fundamental concept when discussing the dissolution of ionic solids. It refers to the energy required to break the ionic bonds in a solid to separate its ions. Think of lattice energy as the glue holding the ions together tightly in a structured, repeating pattern known as a lattice. Stronger ionic bonds mean higher lattice energy, which suggests more energy is needed to dismantle the structure. The strength of lattice energy depends on:

• The charge of the ions: Higher charges often lead to stronger attractions and higher lattice energies.
• The size of the ions: Smaller ions are more strongly attracted to each other, resulting in higher lattice energies.

Understanding lattice energy helps predict how much energy will be needed to dissolve a solid. If the lattice energy is significant, a substantial amount of energy must be supplied to overcome these strong ionic interactions.

Solvation Energy

Solvation energy, also known as hydration energy when water is the solvent, is crucial in the dissolution process. It is the energy released when solute particles interact with solvent molecules. During dissolution, ions from the solute become surrounded by solvent molecules, forming a solvation shell. The interaction between the ions and the solvent molecules releases energy, which can help offset the energy cost from breaking the lattice. Several factors influence solvation energy:

• Polarity of the solvent: Polar solvents, such as water, often provide greater solvation energy due to stronger dipole interactions with ions.
• Size and charge of ions: Smaller and highly charged ions typically experience stronger interactions, leading to greater solvation energy.

When determining solubility, it's important to compare solvation energy to lattice energy. High solvation energy can provide the required energy to disrupt the lattice, promoting solubility.

Solubility

Solubility is the ability of a solute to dissolve in a solvent, forming a homogeneous mixture. It is a pivotal concept when examining how ionic solids dissolve. We determine solubility by assessing the enthalpy of solution, which is affected by both lattice and solvation energies. If the energy released during solvation exceeds the energy required to overcome the lattice energy, the solution process is favorable, indicating good solubility. Factors influencing solubility include:

• Temperature: Generally, higher temperatures increase solubility of solids.
• Nature of solute and solvent: "Like dissolves like" is a good rule; polar solutes dissolve well in polar solvents.

The relationship between solubility, lattice energy, and solvation energy is crucial. If solvation energy is insufficient compared to lattice energy, dissolution becomes endothermic, resulting in low solubility. Understanding these energy shifts helps predict solubility and guide decisions in practical scenarios.