Problem 22 - Chemistry The Molecular Science

Question

The lattice energy of \(\mathrm{CaCl}_{2}\) is \(-2258 \mathrm{~kJ} / \mathrm{mol}\), and the total enthalpy of hydration of its ions is \(-2175 \mathrm{~kJ} / \mathrm{mol}\). Determine whether the process of dissolving \(\mathrm{CaCl}_{2}\) in water is endothermic or exothermic.

Step-by-Step Solution

Answer

The dissolution of \( \mathrm{CaCl}_{2} \) is exothermic.

Step 1: Identify Given Values

First, identify the given values in the problem: The lattice energy of \( \mathrm{CaCl}_{2} \) is \( -2258 \ \mathrm{kJ/mol} \) and the enthalpy of hydration of the ions is \( -2175 \ \mathrm{kJ/mol} \).

Step 2: Understand Additional Concepts

Recall that the solution process of an ionic compound involves overcoming the lattice energy (usually endothermic when described as positive) and the enthalpy of hydration (exothermic). The net enthalpy change determines whether the process is exothermic or endothermic.

Step 3: Calculate ΔH Solution

The enthalpy change of the solution, \( \Delta H_{\text{solution}} \), can be calculated using the formula: \( \Delta H_{\text{solution}} = \text{Lattice Energy} + \text{Enthalpy of Hydration} \).

Step 4: Substitute Given Values

Substitute the given values into the formula: \( \Delta H_{\text{solution}} = (-2258 \ \mathrm{kJ/mol}) + (-2175 \ \mathrm{kJ/mol}) \).

Step 5: Compute the Solution Enthalpy

Calculate the enthalpy: \( \Delta H_{\text{solution}} = -2258 + (-2175) \), resulting in \( \Delta H_{\text{solution}} = -4433 \ \mathrm{kJ/mol} \).

Step 6: Determine Endothermic or Exothermic

Since the resultant \( \Delta H_{\text{solution}} \) is negative, the dissolution process is exothermic, meaning it releases heat into the surroundings.

Key Concepts

Enthalpy of Hydration

The enthalpy of hydration is a crucial concept in chemistry, particularly when discussing the solvation process of ionic compounds in water. Fundamentally, it refers to the energy change when one mole of ions dissolves in water, resulting in hydrated ions. This process often involves the interaction between ions from the solute and polar water molecules. Here, water molecules act as a medium to stabilize the ions by surrounding them in what is known as the hydration shell.

The enthalpy of hydration is usually an exothermic process. This implies that it releases energy, as the energy required to break the ion-ion interactions in the lattice is less than the energy released when ions interact with water molecules. So, when you dissolve an ionic compound like calcium chloride ( CaCl_2 ) in water, you're essentially harvesting the energy released during this hydration process. It's this release of energy that contributes to the decrease in the system's enthalpy and controls whether the overall dissolution is an exothermic or endothermic process.

Exothermic Process

An exothermic process is one that releases energy to the surroundings, typically in the form of heat. This is a common occurrence in many chemical reactions and physical changes, including the dissolution of some substances. The energy released usually translates to an increase in temperature of the solution or the immediate environment. For example, if you dissolve calcium chloride ( CaCl_2 ) in water, as we calculated, the net energy change ( ∆H_{solution} ) is negative (-4433 kJ/mol).

Because the value is negative, it signifies that the dissolution process is exothermic. The system has released more energy than it absorbed. This is akin to seeing smoke rise from a campfire, though in this case it's heat energy emerging from the interaction between hydrated ions and water molecules. Understanding exothermic processes helps in predicting how a reaction impacts its environment, and in turn, can be crucial in designing chemical processes or reactions that are either energy neutral or controlled for specific purposes.

Endothermic vs Exothermic

The distinction between endothermic and exothermic reactions is fundamental in understanding chemical processes. Endothermic processes absorb energy from their surroundings, resulting in a positive change in enthalpy ( ∆H ). These reactions often require added energy to proceed, as they involve breaking stronger bonds than those formed in the products, or they may require energy to be forced into the system.

On the other hand, exothermic reactions release energy. For exothermic reactions, the change in enthalpy is negative because the energy required to break the initial bonds is less than the energy released when new bonds are formed. It's like turning off an electric heater—the energy (heat) disperses to the surroundings.

In practical terms, understanding whether a process is endothermic or exothermic can influence how you approach a reaction. This knowledge helps predict the feasibility of reactions and the conditions required for reactions to occur efficiently. For example, knowing that dissolving calcium chloride is an exothermic process allows chemists to use it in applications as a de-icer or a desiccant, as it helps release heat and warm even in cold environments.