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 \(\mathrm{NaCl}\).

Short answer

The enthalpy of solution for one mole of solid NaCl is \(-1569 \mathrm{~kJ/mol}\), calculated using the thermodynamic equation: \(ΔH_{solution} = ΔH_{lattice} + ΔH_{hydration}\), where \(ΔH_{lattice} = -786 \mathrm{~kJ/mol}\) and \(ΔH_{hydration} = -783 \mathrm{~kJ/mol}\).

Step-by-step solution

Write down the given values

We know the given values of lattice energy and enthalpy of hydration: ΔH_lattice = -786 kJ/mol (for NaCl) ΔH_hydration = -783 kJ/mol (for 1 mole of Na+ and 1 mole of Cl- ions)

Use the thermodynamic equation

Now we will use the following equation to find the enthalpy of solution: ΔH_solution = ΔH_lattice + ΔH_hydration

Substitute the given values in the equation and calculate ΔH_solution

Substitute the given values in the equation: ΔH_solution = (-786 kJ/mol) + (-783 kJ/mol) Now, add the values: ΔH_solution = -1569 kJ/mol The enthalpy of solution for one mole of solid NaCl is -1569 kJ/mol.

Key concepts

Lattice Energy

Lattice energy is a crucial concept in understanding the formation of ionic compounds, such as sodium chloride (NaCl). It refers to the amount of energy released when one mole of a compound forms from its gaseous ions. In simpler terms, it's the energy that holds the ions together in the solid lattice structure.

For NaCl, the lattice energy is \(-786 \, \text{kJ/mol}. \) This negative value indicates that energy is released during the formation, confirming that the process is exothermic.

• Represents stability of the ionic compound
• Higher lattice energy means stronger attractions within the compound
• Negative value signifies exothermic process

This energy plays a significant role in determining the properties of the compound, like melting and boiling points. It's a key factor when calculating the enthalpy of solution.

Enthalpy of Hydration

The enthalpy of hydration refers to the energy change when one mole of gaseous ions dissolves in water, forming hydrated ions. It reflects the interaction between the ions and surrounding water molecules.

In the case of NaCl, the enthalpy of hydration is \(-783 \, \text{kJ/mol}. \) This reveals that the dissolution process involves energy release, as the ions are stabilized by water molecules.

• Measures energy change when ions dissolve in water
• Negative value indicates exothermic hydration
• Hydration involves ion-dipole interactions with water molecules

Enthalpy of hydration is vital for understanding solubility, as it gives insights into how well a compound can dissolve in water. This concept is essential to calculate the enthalpy of solution and predict the energy involved in dissolving NaCl.

NaCl

Sodium chloride, commonly known as table salt, is an essential compound for both chemical and biological processes. Made from sodium (Na) and chlorine (Cl), it's an ionic compound formed by the transfer of electrons from sodium to chlorine.

NaCl structure involves a cubic lattice, where each ion is surrounded by six oppositely charged ions, forming a stable arrangement. This results in significant lattice energy, contributing to its high melting point and solubility characteristics.

• Binary ionic compound
• Formed by electron transfer, creating Na⁺ and Cl^- ions
• Exists as a cubic crystal lattice

Understanding NaCl's formation, structure, and properties is crucial when studying lattice energy and enthalpy of hydration, as it directly influences the thermodynamics of solution processes.

Thermodynamic Equation

The thermodynamic equation linking lattice energy, enthalpy of hydration, and enthalpy of solution is central to solving problems involving ionic solutions. It allows us to quantify the total energy change when an ionic solid dissolves in water.

The equation is expressed as follows:\[\Delta H_\text{solution} = \Delta H_\text{lattice} + \Delta H_\text{hydration}\]This represents the total energy involved in dissolving 1 mole of NaCl, combining both the input of energy to break the lattice and the exothermic output from hydration.

Provides relationship between lattice energy and hydration

Calculates energy change when ionic compounds dissolve

Important for predicting solubility and reaction energetics

Understanding this equation helps us predict whether the dissolution process will be endothermic (absorbs energy) or exothermic (releases energy), which is critical for various chemical applications and processes.