Problem 38 - Chemistry A Molecular Approach

Question

Use the data to calculate the heats of hydration of lithium chloride and sodium chloride. Which of the two cations, lithium or sodium, has stronger ion-dipole interactions with water? Why? $$ \begin{array}{lcc} \text { Compound } & \text { Lattice Energy (kJ/mol) } & \Delta H_{\text {soln }}(\mathrm{kJ} / \mathrm{mol}) \\ \hline \mathrm{LiCl} & -834 & -37.0 \\ \hline \mathrm{NaCl} & -769 & +3.88 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The heat of hydration for LiCl is 797 kJ/mol and for NaCl is 772.88 kJ/mol. Lithium has stronger ion-dipole interactions with water as it has a higher heat of hydration.

Step 1: Understand the Concepts

The heat of hydration is the heat change when 1 mole of gaseous ions dissolve in enough water to form an infinitely dilute solution. The enthalpy of solution (ΔH_{soln}) is the change in enthalpy when one mole of a substance dissolves in water to form an infinitely dilute solution. Both the lattice energy and the heat of hydration are related to the enthalpy of solution through the Born-Haber cycle.

Step 2: Apply the Born-Haber Cycle

According to the Born-Haber cycle, the enthalpy of solution (ΔH_{soln}) can be calculated from the lattice energy and the heat of hydration by the following equation: ΔH_{soln} = ΔH_{hydration} + Lattice Energy. To find the heat of hydration (ΔH_{hydration}), this equation needs to be rearranged to solve for ΔH_{hydration}: ΔH_{hydration} = ΔH_{soln} - Lattice Energy.

Step 3: Calculate the Heat of Hydration for LiCl

Substitute the given values into the equation for LiCl: ΔH_{hydration, LiCl} = ΔH_{soln, LiCl} - Lattice Energy_{LiCl} = -37.0 kJ/mol - (-834 kJ/mol) = 797 kJ/mol.

Step 4: Calculate the Heat of Hydration for NaCl

Substitute the given values into the equation for NaCl: ΔH_{hydration, NaCl} = ΔH_{soln, NaCl} - Lattice Energy_{NaCl} = 3.88 kJ/mol - (-769 kJ/mol) = 772.88 kJ/mol.

Step 5: Compare the Heats of Hydration

Compare the calculated heat of hydration for LiCl and NaCl to determine which cation has stronger ion-dipole interactions with water. The larger the heat of hydration (more negative), the stronger the ion-dipole interactions.

Step 6: Conclusion

Because ΔH_{hydration, LiCl} is greater than ΔH_{hydration, NaCl}, lithium cations have stronger ion-dipole interactions with water compared to sodium cations.

Key Concepts

Lattice Energy

Lattice energy is the amount of energy released when ions are combined to form a crystalline lattice. It essentially reflects the strength of the ionic bonds within a crystalline solid. A higher lattice energy implies a more stable ionic compound and more energy is required to separate the ions.

In the context of our exercise, lithium chloride (LiCl) has a higher lattice energy (-834 kJ/mol) compared to sodium chloride (NaCl) with -769 kJ/mol. This suggests that the ionic bonds in LiCl are stronger, indicating more energy is released when these ions come together to form the lattice structure.

Enthalpy of Solution

The enthalpy of solution, or \(\Delta H_{soln}\), is the heat change associated with dissolving a solute in a solvent to create a solution. When the enthalpy of solution is negative, it suggests that the dissolution process is exothermic, i.e., heat is released. Conversely, a positive enthalpy of solution indicates that the process is endothermic, requiring heat input.

In the given problem, LiCl has an \(\Delta H_{soln}\) of -37.0 kJ/mol, which means it releases heat when dissolving, whereas NaCl has a positive \(\Delta H_{soln}\) of +3.88 kJ/mol, suggesting it absorbs heat from the surroundings to dissolve.

Born-Haber Cycle

The Born-Haber cycle is a hypothetical series of steps that represents the formation of an ionic compound from its constituent elements in their standard states. It is employed to relate lattice energy with other thermodynamic quantities and is invaluable for understanding the energetics of crystal formation.

For our exercise, we can use the Born-Haber cycle to find the heat of hydration by rearranging the relationship between \(\Delta H_{soln}\), lattice energy, and the heat of hydration (\(\Delta H_{hydration}\)). This method allows us to dissect the dissolution process into comprehensible parts, making it easier to analyze and compare the energetics of different ionic substances.

Ion-Dipole Interactions

Ion-dipole interactions are forces of attraction between an ion and the partial charges on a polar molecule, like water. These interactions are crucial in the process of dissolving ionic compounds in water because they help stabilize the ions in the solution.

The heat of hydration is indicative of the strength of these interactions. A higher (more negative) heat of hydration implies that more energy is released when the ion is surrounded by water molecules, pointing to stronger ion-dipole interactions. From our calculations, LiCl has a higher heat of hydration compared to NaCl, which leads to the conclusion that lithium cations form stronger ion-dipole interactions in solution than sodium cations.