Problem 39 - Chemistry A Molecular Approach

Question

Lithium iodide has a lattice energy of \(-7.3 \times 10^{2} \mathrm{~kJ} / \mathrm{mol}\) and a heat of hydration of \(-793 \mathrm{~kJ} / \mathrm{mol}\). Find the heat of solution for lithium iodide and determine how much heat is evolved or absorbed when \(15.0 \mathrm{~g}\) of lithium iodide completely dissolves in water.

Step-by-Step Solution

Answer

-1523 kJ/mol is the heat of solution for lithium iodide, and for 15.0 g, the heat evolved is calculated to be \( -1523 \,\text{kJ/mol} \times \frac{15.0 \,\text{g}}{133.84 \,\text{g/mol}} = -170.82 \,\text{kJ} \).

Step 1: Calculate the Heat of Solution

The heat of solution can be found by adding the lattice energy and the heat of hydration. Use the formula: Heat of Solution = Lattice Energy + Heat of Hydration. So, for Lithium Iodide, the Heat of Solution = \( -7.3 \times 10^{2} \,\text{kJ/mol} \) + \( -793 \,\text{kJ/mol} \).

Step 2: Determine the Heat Evolved

To find the Heat of Solution, perform the addition: \( -7.3 \times 10^{2} \,\text{kJ/mol} \) + \( -793 \,\text{kJ/mol} \) = \( -730 \,\text{kJ/mol} \) + \( -793 \,\text{kJ/mol} \) = \( -1523 \,\text{kJ/mol} \). This is the amount of heat evolved per mole when lithium iodide dissolves in water.

Step 3: Calculate Moles of Lithium Iodide

Given that mass is 15.0 g, calculate the number of moles using the molar mass of lithium iodide (LiI), which is \(\text{Li} (6.94 \,\text{g/mol}) + \text{I} (126.9 \,\text{g/mol}) = 133.84 \,\text{g/mol}\). The number of moles \(n\) is given by \(n = \frac{mass}{molar \hspace{2pt} mass} = \frac{15.0 \,\text{g}}{133.84 \,\text{g/mol}}\).

Step 4: Calculate the Heat Evolved for the Given Mass

Multiply the Heat of Solution per mole by the number of moles to find the total heat evolved: Total Heat Evolved = Heat of Solution per mole \times Moles of Lithium Iodide = \( -1523 \,\text{kJ/mol} \times \frac{15.0 \,\text{g}}{133.84 \,\text{g/mol}} \).

Key Concepts

Lattice Energy

Lattice energy refers to the amount of energy that is required to separate a mole of an ionic compound into its constituent ions in gaseous form. This energy is indicative of the strength of the bonds holding the ions together in the solid state. A higher lattice energy means a stronger attraction between the ions, resulting in a more stable ionic compound. In the context of dissolving ionic substances in water, the lattice energy must be overcome for the ions to disperse and interact with the water molecules.

For example, lithium iodide (LiI) has a lattice energy of \( -7.3 \times 10^{2} \mathrm{~kJ} / \mathrm{mol} \), signifying that this amount of energy is released when gaseous Li and I ions come together to form the solid compound. Conversely, this same amount of energy must be absorbed to break apart LiI back into gaseous ions. Understanding lattice energy is pivotal for comprehending how ionic compounds like LiI dissolve in water.

Heat of Hydration

Heat of hydration is the amount of heat energy released when one mole of ions interacts with water molecules to form hydrated ions. When ionic compounds dissolve in water, their ions are surrounded by water molecules, a process that typically releases energy. This energy release is due to the attractive forces between the water's polar molecules and the ions.

In our exercise, lithium iodide has a heat of hydration of \( -793 \mathrm{~kJ} / \mathrm{mol} \). This negative sign indicates that the process is exothermic; energy is released into the surroundings as heat. Consequently, the attraction between the water molecules and lithium and iodide ions in the solution causes the overall temperature of the solution to increase.

Enthalpy Change

Enthalpy change, in the study of chemistry, relates to the heat exchange with the surroundings at constant pressure. It's a measure of the total heat content of a system and can be expressed as the sum of internal energy plus the product of pressure and volume. For reactions occurring in solution, the enthalpy change is associated with either the absorption or release of heat, which corresponds to endothermic or exothermic processes, respectively.

In the given exercise, the enthalpy change when dissolving lithium iodide in water is calculated by adding the lattice energy and the heat of hydration. With both values being negative, it indicates that the overall process of LiI dissolving is exothermic; the system releases heat to the environment. For instance, when 15.0 grams of LiI dissolve, the enthalpy change tells us how much heat, in kJ, is evolved. This is practically important, as it determines whether a solution will heat up or cool down during dissolution, which can impact various chemical processes and applications.