Question

The lattice energy* of Nal is \(-686 \mathrm{kJ} / \mathrm{mol}\) , and the enthalpy of hydration is \(-694 \mathrm{kJ} / \mathrm{mol}\) . Calculate the enthalpy of solution per mole of solid Nal. Describe the process to which this enthalpy change applies.

Short answer

The enthalpy of solution for solid NaI can be calculated using the equation: Enthalpy of Solution (ES) = Lattice energy (LE) + Enthalpy of hydration (HH). Substituting the given values, we find that ES = -686 kJ/mol + (-694 kJ/mol) = -1380 kJ/mol. This negative enthalpy change corresponds to an exothermic dissolution process in which solid NaI readily dissolves in water, as the formation of new ion-water interactions is energetically more favorable than maintaining the ionic lattice in the solid state.

Step-by-step solution

1. Identify the given values

: Lattice energy (LE) of NaI = -686 kJ/mol Enthalpy of hydration (HH) of NaI = -694 kJ/mol

2. Write down the equation for enthalpy of solution (ES)

: Enthalpy of Solution (ES) = Lattice energy (LE) + Enthalpy of hydration (HH)

3. Substitute the given values into the equation

: ES = (-686 kJ/mol) + (-694 kJ/mol)

4. Calculate the enthalpy of solution

: ES = -686 - 694 ES = -1380 kJ/mol

5. Describe the process to which the enthalpy change applies

: The calculated enthalpy change (-1380 kJ/mol) corresponds to the enthalpy of solution for solid NaI. This process involves the dissolution of one mole of solid NaI in a large amount of water. The enthalpy of solution is the sum of the energy required to break the ionic lattice in the solid (lattice energy) and the energy released when new interactions are formed between the ions and water molecules (enthalpy of hydration). In this case, the overall enthalpy change is negative, indicating that the dissolution process is exothermic and releases energy. The formation of new ion-water interactions is more energetically favorable than maintaining the ionic lattice in the solid state, and thus NaI dissolves readily in water.

Key concepts

Lattice Energy

Lattice energy is a crucial concept in understanding the energetics of ionic compounds. It is the energy required to separate one mole of an ionic solid into its gaseous ions. This is essentially the energy stored in the ionic bonds holding the compound together.
For example, in the case of NaI (sodium iodide), the lattice energy is \(-686 \text{kJ/mol}\).
When you break the ionic bonds to transform the compound into ions, this energy is absorbed from the surroundings, making the process endothermic.

Factors Affecting Lattice Energy

• -Ion Charge: The higher the charge on the ions, the greater the lattice energy. This is because the force of attraction between ions is stronger.
• -Ion Size: Smaller ions tend to have higher lattice energy because their charges are closer together, which increases the strength of their attraction.

The lattice energy is critical because it provides insight into the stability and strength of an ionic compound's structure.

Enthalpy of Hydration

The enthalpy of hydration is the energy change that occurs when one mole of gaseous ions dissolve in water to form a solution.
This process involves the interaction between water molecules and the ions, which stabilizes the ions in the solution and releases energy termed as the enthalpy of hydration.

Importance of Enthalpy of Hydration

Understanding enthalpy of hydration is vital because:

• It helps predict the solubility of compounds.
• It gives an indication of how strongly the ions will interact with water molecules.

For sodium iodide (NaI), the enthalpy of hydration is \(-694 \text{kJ/mol}\).
This indicates that when the ions are hydrated, a significant amount of energy is released, which contributes to the dissolution process.

Dissolution Process

The dissolution process is the sequence of steps that occur when a solid ionic compound dissolves in water. It involves the interplay of both lattice energy and enthalpy of hydration.
For NaI, the dissolution process involves the following steps:

• Breaking apart the ionic lattice, which requires energy (lattice energy).
• Hydrating the ions, which releases energy as water molecules interact with the ions (enthalpy of hydration).

The total enthalpy change for the dissolution, termed the enthalpy of solution, is the sum of these two energy changes. For NaI, it is calculated as:\[\text{Enthalpy of Solution} = \text{Lattice Energy} + \text{Enthalpy of Hydration} = -1380 \text{kJ/mol}\]This negative enthalpy value indicates that the dissolution of NaI is exothermic, releasing energy into the surroundings. The favorable release of energy when ions interact with water means NaI readily dissolves in water, explaining its high solubility. Understanding the dissolution process allows chemists to predict and manipulate the solubility and energetics of different ionic compounds.