Problem 24 - Chemistry The Molecular Science

Question

Calculate the enthalpy of solution of \(\mathrm{CaBr}_{2}\) given that its lattice energy is \(-1984 \mathrm{~kJ} / \mathrm{mol}\) and the total enthalpy of hydration of its ions is \(-1827 \mathrm{~kJ} / \mathrm{mol}\).

Step-by-Step Solution

Answer

The enthalpy of solution of \(\mathrm{CaBr}_2\) is \(-3811\ \mathrm{kJ/mol}\).

Step 1: Understanding the Problem

We need to calculate the enthalpy of solution of \(\mathrm{CaBr}_2\). We are given the lattice energy, which is \(-1984 \, \mathrm{kJ/mol}\), and the total enthalpy of hydration of its ions, which is \(-1827 \, \mathrm{kJ/mol}\).

Step 2: Define Enthalpy of Solution Equation

The enthalpy of solution \(\Delta H_{\text{soln}}\) can be calculated using the relation: \[ \Delta H_{\text{soln}} = \Delta H_{\text{lattice}} + \Delta H_{\text{hydration}} \] where \(\Delta H_{\text{lattice}}\) is the lattice energy and \(\Delta H_{\text{hydration}}\) is the enthalpy of hydration.

Step 3: Substitute Values Into Equation

Plug the given values into the equation: \[ \Delta H_{\text{soln}} = (-1984 \, \mathrm{kJ/mol}) + (-1827 \, \mathrm{kJ/mol}) \]

Step 4: Calculate Enthalpy of Solution

Perform the addition: \[ \Delta H_{\text{soln}} = -1984 + (-1827) = -3811 \, \mathrm{kJ/mol} \]

Step 5: Interpret the Result

The negative sign indicates the solution process is exothermic, meaning the dissolution of \(\mathrm{CaBr}_2\) in water releases energy.

Key Concepts

Understanding Lattice Energy

Lattice energy is a measure of the strength of the forces holding the ions together in an ionic solid. It is defined as the amount of energy required to completely separate one mole of a solid ionic compound into its gaseous ions.
This energy is always given as a negative value because breaking bonds requires energy input. For example, \(\mathrm{CaBr_2}\) has a lattice energy of \(-1984\,\mathrm{kJ/mol}\), indicating a strong interaction between calcium and bromide ions.

The magnitude of lattice energy depends on the charge of the ions and the distance between them. Higher charges and smaller distances lead to larger lattice energies. In summary, it reflects the stability of the ionic compound. The larger its absolute value, the more stable the ionic compound.

Exploring Enthalpy of Hydration

The enthalpy of hydration refers to the energy change when one mole of gaseous ions dissolve in water to form hydrated ions. It is measured as a negative value, like in the case of \(-1827\,\mathrm{kJ/mol}\) for the hydration of ions from \(\mathrm{CaBr_2}\).
This process involves two main steps:

• The separation of water molecules to make room for the ions.
• The formation of ion-dipole interactions between the ion and water molecules.

Enthalpy of hydration is exothermic because energy is released when these interactions are formed.
The stronger the attraction between the water molecules and the ions, the more exothermic the hydration process. This is influenced by the size and charge of the ions.
In essence, it provides insight into how much energy is released when ions become surrounded by water molecules upon dissolution.

Exothermic Processes in Enthalpy of Solution

An exothermic process is one that releases energy into the surroundings, typically in the form of heat. In the context of the enthalpy of solution, this term describes the overall energy change when a solute dissolves in a solvent.
When \(\mathrm{CaBr_2}\) dissolves in water, the enthalpy of solution calculated is \(-3811\,\mathrm{kJ/mol}\), which is exothermic. Here's why:

• Negative lattice energy is overcome by a highly exothermic hydration process.
• The solution releases more energy than it consumes.

Exothermic processes are significant in many real-world applications, from chemical reactions in metabolic processes to heating packs.
For students, understanding whether a process is exothermic helps predict whether it will release or absorb energy, crucial for both practical and theoretical applications in chemistry.