Question

Given these data, calculate the enthalpy of hydration of \(\mathrm{I}^{-}\). Lattice energy of \(\mathrm{LiI}=-759 \mathrm{~kJ} / \mathrm{mol}\); enthalpy of solution of \(\mathrm{LiI}=-63.3 \mathrm{~kJ} / \mathrm{mol} ;\) hydration enthalpy of \(\mathrm{Li}^{+}=-558 \mathrm{~kJ} / \mathrm{mol}\).

Short answer

The enthalpy of hydration of \( \mathrm{I}^{-} \) is \( -264.3 \text{ kJ/mol} \).

Step-by-step solution

Understand the Components

To find the enthalpy of hydration of \( \mathrm{I}^{-} \), we need to know the lattice energy of \( \mathrm{LiI} \), the enthalpy of solution of \( \mathrm{LiI} \), and the hydration enthalpy of \( \mathrm{Li}^{+} \). These values are given as \( \Delta H_{\text{lattice}} = -759 \text{ kJ/mol} \), \( \Delta H_{\text{solution}} = -63.3 \text{ kJ/mol} \), and \( \Delta H_{\text{hydration, } \mathrm{Li}^{+}} = -558 \text{ kJ/mol} \) respectively.

Set up the Enthalpy of Solution Equation

The equation for the enthalpy of solution relates lattice energy and hydration enthalpies: \[ \Delta H_{\text{solution}} = \Delta H_{\text{hydration, } \mathrm{Li}^{+}} + \Delta H_{\text{hydration, } \mathrm{I}^{-}} - \Delta H_{\text{lattice}} \] Thus, the enthalpy of hydration for \( \mathrm{I}^{-} \) can be rearranged as: \[ \Delta H_{\text{hydration, } \mathrm{I}^{-}} = \Delta H_{\text{solution}} + \Delta H_{\text{lattice}} - \Delta H_{\text{hydration, } \mathrm{Li}^{+}} \]

Substitute the Known Values

Substitute the known values into the rearranged equation: \[ \Delta H_{\text{hydration, } \mathrm{I}^{-}} = (-63.3) + (-759) - (-558) \] This simplifies to: \[ \Delta H_{\text{hydration, } \mathrm{I}^{-}} = -63.3 - 759 + 558 \]

Perform the Calculation

Calculate each part: \[ -63.3 - 759 = -822.3 \] Then: \[ -822.3 + 558 = -264.3 \] The enthalpy of hydration of \( \mathrm{I}^{-} \) is thus \( -264.3 \text{ kJ/mol} \).

Key concepts

Lattice Energy

Lattice energy is a crucial concept in chemistry, especially when dealing with ionic compounds. It is defined as the energy required to separate one mole of an ionic solid into its gaseous ions. This energy reflects the strength of the force holding the ions together in the solid. A high lattice energy value implies that the ionic compound is very stable.Let's break it down:

• When ions are closely packed in a solid, they experience strong electrostatic forces of attraction.
• Lattice energy measures how much energy is needed to overcome these forces and pull the ions apart.
• It is usually a large negative value because energy is released when ions form a solid lattice from gaseous ions.

For example, in this exercise, lithium iodide (\(\text{LiI}\)) has a lattice energy of \(-759 \text{ kJ/mol}\), indicating a strong ionic bond between \(\text{Li}^+\) and \(\text{I}^-\). Understanding lattice energy helps in predicting the stability of ionic compounds and their solubility in water.

Enthalpy of Solution

Enthalpy of solution (\(\Delta H_{\text{solution}}\)) is a thermodynamic quantity that defines the heat change when a solute dissolves in a solvent to form a solution. This process can either absorb or release heat.When an ionic compound like lithium iodide (\(\text{LiI}\)) dissolves in water, several steps occur:

• The ionic lattice must first break to free the ions, an endothermic process requiring energy input.
• Then, the ions interact with water molecules, releasing energy as hydration occurs.

The enthalpy of solution is calculated by accounting for both the lattice energy and the hydration enthalpies of the ions involved. In simple terms:\[\Delta H_{\text{solution}} = \Delta H_{\text{hydration, Li}^+} + \Delta H_{\text{hydration, I}^-} - \Delta H_{\text{lattice}}\]In this exercise, the enthalpy of solution for \(\text{LiI}\) is given as \(-63.3 \text{ kJ/mol}\), which suggests slightly more energy is released in hydration compared to the energy required to break the lattice.

Hydration Enthalpy

Hydration enthalpy is the energy change when one mole of gaseous ions dissolves in water to form hydrated ions. Usually, it is a negative value because the process releases energy due to the attraction between ions and water molecules. Hydration enthalpy is critical in the process of an ionic compound dissolving.Here's what happens during hydration:

• Ions become surrounded by water molecules, stabilizing in solution.
• Energy is released as ions attract polar water molecules, resulting in an exothermic reaction.

For example, lithium ions (\(\text{Li}^+\)) have a hydration enthalpy of \(-558 \text{ kJ/mol}\). This means lithium ions release a significant amount of energy upon hydration. In this exercise, by knowing the enthalpy values for both \(\text{Li}^+\) and \(\text{I}^-\) ions, you can calculate the enthalpy of hydration for iodide ions (\(\text{I}^-\)), which results in \(-264.3 \text{ kJ/mol}\). This calculation highlights the energy dynamics during the dissolution process, an essential part of solution chemistry.