Question

The lattice energy of \(\mathrm{NaCl}\) is \(-786 \mathrm{kJ} / \mathrm{mol}\), and the enthalpy of hydration of 1 mole of gaseous \(\mathrm{Na}^{+}\) and 1 mole of gaseous \(\mathrm{Cl}^{-}\) ions is \(-783 \mathrm{kJ} / \mathrm{mol} .\) Calculate the enthalpy of solution per mole of solid NaCl.

Short answer

The enthalpy of solution per mole of solid NaCl is \(-1569 \mathrm{kJ/mol}\).

Step-by-step solution

Dissolution Process

The dissolution of NaCl can be thought of as a multi-step process: 1. Break the lattice structure of NaCl, which involves the lattice energy. 2. Hydrate the separated Na⁺ and Cl⁻ ions, which involves the enthalpy of hydration. Step 2: Apply Hess's law to calculate the enthalpy of solution

Hess's Law

Hess's law states that the total enthalpy change of a reaction is independent of the pathway and depends only on the initial and final states. We can use this law to calculate the enthalpy of dissolution by adding the enthalpy changes for the steps described above. Enthalpy change for the dissolution process = Lattice energy + Enthalpy of hydration Step 3: Calculate the enthalpy of solution

Enthalpy of Solution Calculation

Using the given values, we can now calculate the enthalpy of solution for NaCl: Enthalpy of solution = -786 kJ/mol (lattice energy) + (-783 kJ/mol) (enthalpy of hydration) Enthalpy of solution = -786 kJ/mol - 783 kJ/mol = -1569 kJ/mol The enthalpy of solution per mole of solid NaCl is -1569 kJ/mol.

Key concepts

Lattice Energy

The concept of lattice energy is crucial when discussing ionic compounds. It represents the energy released when ions combine to form a crystalline lattice from their gaseous state, or conversely, the energy required to separate ions from the solid lattice to individual gaseous ions. In the case of sodium chloride (NaCl), the lattice energy is particularly high due to the strong electrostatic attraction between the oppositely charged Na⁺ and Cl^- ions.

Considering its definition, the lattice energy is always a negative value, meaning it is exothermic when forming the crystal lattice. This energy plays a key role in the dissolution process of ionic substances since it needs to be overcome to dissolve the salt. The greater the lattice energy, the more stable the ionic crystal, and the more energy is required to break it apart into individual ions.

Enthalpy of Hydration

Once the ionic lattice is broken apart, the individual ions are surrounded by water molecules. This process is called hydration, and the heat change associated with it is known as the enthalpy of hydration. It is also an exothermic process, as water molecules stabilize the ions through ion-dipole interactions, releasing energy.

The enthalpy of hydration for sodium and chloride ions has a high negative value, indicating that a large amount of energy is released when water molecules surround these ions. This process contributes to how easily a salt like NaCl can dissolve in water, as the released energy helps to compensate for the energy required to disrupt the ionic lattice.

Hess's Law

Hess's law is a powerful tool in thermodynamics that helps us understand the energy changes during chemical reactions. It states that the total change in enthalpy for a chemical reaction is the same regardless of the number of steps or the pathway taken from reactants to products. This means the enthalpy change is a state function, dependent only on the initial and final states, and not the specific route taken.

Using Hess's law allows us to calculate the enthalpy changes for reactions that may be difficult to measure directly. By breaking the reaction down into simpler steps for which the enthalpy changes are known, and then summing these values, we can determine the overall enthalpy change. This method is particularly useful in the context of the enthalpy of solution, which involves several steps - breaking the lattice and hydrating the ions.

Dissolution Process

The dissolution process entails dissolving a solute into a solvent to form a solution. For ionic compounds like NaCl, this process can be seen as a series of steps. First, the ionic lattice structure is broken, and then the individual ions are stabilized in the solvent through hydration. The energy changes for both these steps need to be considered to understand the overall enthalpy of solution.

The dissolution is spontaneous if the overall enthalpy change is negative, indicating that the process is exothermic. In practice, factors such as temperature and the solvent's polarity also influence how easily a solute will dissolve. Understanding the dissolution process and the related energetics helps us predict the solubility of various substances and manage reactions in a range of scientific and industrial applications.