Problem 40 - Chemistry An Atoms First Approach

Question

a. Use the following data to calculate the enthalpy of hydration for calcium chloride and calcium iodide. $$\begin{array}{|llc|} \hline & \text { Lattice Energy } & \Delta H_{\text {soln }} \\ \hline \mathrm{CaCl}_{2}(s) & -2247 \mathrm{kJ} / \mathrm{mol} & -46 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{Cal}_{2}(s) & -2059 \mathrm{kJ} / \mathrm{mol} & -104 \mathrm{kJ} / \mathrm{mol} \\ \hline \end{array}$$ b. Based on your answers to part a, which ion, \(\mathrm{Cl}^{-}\) or \(\mathrm{I}^{-}\), is more strongly attracted to water?

Step-by-Step Solution

Answer

The enthalpy of hydration for calcium chloride is \(2201 \ \text{kJ/mol}\) and for calcium iodide is \(1955 \ \text{kJ/mol}\). Since the enthalpy of hydration of calcium chloride is higher, the Cl- ion is more strongly attracted to water than the I- ion.

Step 1: Understand the enthalpy of hydration formula

The enthalpy of hydration is the change in enthalpy when one mole of a substance is dissolved in water to form an infinitely dilute solution. The enthalpy of hydration can be calculated as follows: \[ \Delta H_{\text{hyd}} = \Delta H_{\text{soln}} - \Delta H_{\text{lattice}} \]

Step 2: Calculate the enthalpy of hydration for calcium chloride

Now let's calculate the enthalpy of hydration for calcium chloride using the given values: \[ \begin{aligned} \Delta H_{\text{hyd CaCl}_2} &= \Delta H_{\text{soln CaCl}_2} - \Delta H_{\text{lattice CaCl}_2} \\ &= (-46 \ \text{kJ/mol}) - (-2247 \ \text{kJ/mol}) \\ &= 2201 \ \text{kJ/mol} \end{aligned} \]

Step 3: Calculate the enthalpy of hydration for calcium iodide

Now let's calculate the enthalpy of hydration for calcium iodide using the given values: \[ \begin{aligned} \Delta H_{\text{hyd CaI}_2} &= \Delta H_{\text{soln CaI}_2} - \Delta H_{\text{lattice CaI}_2} \\ &= (-104 \ \text{kJ/mol}) - (-2059 \ \text{kJ/mol}) \\ &= 1955 \ \text{kJ/mol} \end{aligned} \]

Step 4: Determine which ion, Cl- or I-, is more strongly attracted to water

Based on the enthalpy of hydration values calculated in steps 2 and 3, we can now compare the ions. The enthalpy of hydration of calcium chloride is higher than that of calcium iodide: \(2201 \ \text{kJ/mol} > 1955 \ \text{kJ/mol}\). This means that the Cl- ion is more strongly attracted to water molecules than the I- ion due to the higher negative enthalpy associated with the process.

Key Concepts

Understanding Lattice Energy

Lattice energy is a concept crucial for understanding why compounds dissolve in water. It is defined as the energy required to separate one mole of an ionic solid into gaseous ions. Imagine lattice energy as the glue holding ions together in a solid lattice structure. High lattice energy means that the bonds are strong, and separating the ions will require more energy. For instance, calcium chloride has a lattice energy of -2247 kJ/mol, indicating the energy needed to break apart its ions in a solid state. By understanding lattice energy, we can grasp why some ionic compounds dissolve more easily than others based on their lattice energy values.

Exploring calcium chloride

Calcium chloride (CaCl extsubscript{2}) is a common ionic compound with many uses, including in de-icing roads. It is composed of calcium ions (Ca extsuperscript{2+}) and chloride ions (Cl extsuperscript{-}). The high lattice energy of calcium chloride suggests that its ions are strongly bonded in the lattice structure. Despite this, calcium chloride dissolves in water, producing a significant enthalpic change because of the highly exothermic hydration of its ions. This process is what accounts for its practical uses, as the release of energy contributes to its efficacy in lowering the freezing point of water and melting ice.

Understanding calcium iodide

Calcium iodide (CaI extsubscript{2}) is another ionic compound, similar to calcium chloride, but with iodine ions (I extsuperscript{-}) instead of chloride ions. Its lattice energy is -2059 kJ/mol, which is lower than that of calcium chloride. This lower lattice energy translates to weaker ionic bonds in the crystal structure as compared to calcium chloride. As a result, less energy is required to dissolve it in water. However, its enthalpy of hydration is also substantial, indicating a large release of energy when calcium iodide is dissolved in water, contributing to its stability in aqueous solutions.

Ion attraction to water

Ions have different levels of attraction to water, a property influenced by their charge density and size. Chloride ions (Cl extsuperscript{-}) have a stronger attraction to water molecules than iodide ions (I extsuperscript{-}) due to their smaller size and higher charge density. This enhanced attraction is reflected in the more negative enthalpy of hydration for calcium chloride versus calcium iodide. Water molecules are polar, with a slight positive charge on hydrogen atoms and a slight negative charge on oxygen atoms. When chloride ions are introduced, the water molecules orient themselves to maximize electrostatic interactions, creating a more stable, hydrated ion. These interactions make chloride ions more favorable when dissolving in water, evident from how they influence the enthalpy of hydration.