Question

The lattice energy \(^{*}\) of Nal is \(-686 \mathrm{kJ} / \mathrm{mol}\), and the enthalpy of hydration is \(-694 \mathrm{kJ} / \mathrm{mol} .\) Calculate the enthalpy of solution per mole of solid NaI. Describe the process to which this enthalpy change applies.

Short answer

The enthalpy of solution for NaI can be calculated using the given lattice energy (-686 kJ/mol) and enthalpy of hydration (-694 kJ/mol) with the formula: Enthalpy of solution = Lattice energy + Enthalpy of hydration. Plugging in the values, the enthalpy of solution is -1380 kJ/mol, indicating an exothermic process of dissolving one mole of solid NaI in water.

Step-by-step solution

Identify the known values

: We are given the lattice energy for NaI, which is -686 kJ/mol, and the enthalpy of hydration, which is -694 kJ/mol.

Write the equation to calculate the enthalpy of solution

: The enthalpy of solution can be calculated using the following equation: Enthalpy of solution = Lattice energy + Enthalpy of hydration

Plug in the known values and solve the equation

: Now, we'll input the given values into the equation and solve for the enthalpy of solution: Enthalpy of solution = (-686 kJ/mol) + (-694 kJ/mol) Enthalpy of solution = -1380 kJ/mol

Describe the process to which this enthalpy change applies

: The enthalpy change of -1380 kJ/mol applies to the process of dissolving one mole of solid NaI in water. This value is the overall energy change that occurs when the NaI lattice structure is broken, and the ions (Na+ and I-) are hydrated, with water molecules surrounding them in an aqueous solution. The negative value of the enthalpy of solution indicates that this is an exothermic process, releasing energy in the form of heat.

Key concepts

Lattice Energy

Lattice energy is a measure of the strength of the forces between the ions in an ionic solid. Imagine it as the ‘glue’ holding the lattice together. For a compound like sodium iodide (NaI), the lattice structure is comprised of alternating positive (Na+) and negative (I-) ions.
To dissolve the compound in water, this strong ionic lattice must first be broken apart, which requires energy. In the NaI example, the lattice energy is given as -686 kJ/mol. Since this value is negative, it indicates that energy is released when the lattice forms. Conversely, breaking the lattice apart would require the same amount of energy but in a positive form.
Understanding lattice energy is crucial because it helps predict the solubility of a compound, its melting point, and its overall stability. The higher the lattice energy, the more stable the compound and the more energy is required to break it down.

Enthalpy of Hydration

The enthalpy of hydration refers to the energy change when gaseous ions dissolve in water and become surrounded by water molecules. It is a good indicator of how each ion interacts with water.
In the case of NaI dissolving, both sodium (Na+) and iodide (I-) ions are being hydrated. The given value, -694 kJ/mol, means that more energy is released when these ions interact with water than was used to break the ionic lattice. This is because forming new ion-water attractions can be highly exothermic, as water molecules stabilize the ions.
As an additional perspective, the strength of ion-water interactions can vary depending on the size and charge of the ions. Smaller and more highly charged ions tend to have larger enthalpies of hydration. This balancing act between breaking the lattice and hydrating the ions is what governs the solubility of substances.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the energy changes during chemical reactions. In every chemical process, energy is either absorbed or released, which correlates with changes in enthalpy—one of the main components of thermochemistry.
When discussing the dissolution of an ionic compound, thermochemistry revolves around the enthalpy changes during the breaking of the ionic lattice and the subsequent hydration of the ions. By analyzing these enthalpy changes, we can determine if the process will be endothermic (absorbing heat) or exothermic (releasing heat).
Thermochemical calculations often involve Hess’s Law, which states that the total enthalpy change for a reaction is the same, no matter how it is achieved. This principle allows us to use provided enthalpy values, such as lattice energy and enthalpy of hydration, to determine the overall enthalpy of solution.

Exothermic Process

An exothermic process is one that releases energy to the surrounding environment, usually in the form of heat.
Dissolving NaI in water, as seen in the given exercise, is an exothermic process because the overall enthalpy change (-1380 kJ/mol) is negative. This tells us that more energy is released by forming new bonds during hydration than is used to break the ionic lattice. Thus, the solution and the surroundings get warmer during this dissolution.
Recognizing an exothermic process is important for various applications. In industrial settings, exothermic reactions can be harnessed to produce heat for other purposes, while, in a biological context, they play a role in cellular energy production. Awareness of energy changes is also necessary for making predictions about reaction spontaneity and safety implications.