Question

The lattice energy of \(\mathrm{NaCl}\) is \(-786 \mathrm{kJ} / \mathrm{mol},\) and the enthalpy of hydration of 1 mole of gaseous 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 kJ/mol, calculated using the formula: Enthalpy of solution = Lattice energy + Enthalpy of hydration, and plugging in the given values: -786 kJ/mol for lattice energy and -783 kJ/mol for enthalpy of hydration.

Step-by-step solution

Identify the given values

We have been given the lattice energy of NaCl (-786 kJ/mol) and the enthalpy of hydration of 1 mole of gaseous Na^+ and Cl^- ions (-783 kJ/mol).

Use the formula for enthalpy of solution

The formula for the enthalpy of solution is: Enthalpy of solution = Lattice energy + Enthalpy of hydration

Insert the given values into the formula

Now, we need to plug the given values into the formula: Enthalpy of solution = -786 kJ/mol + (-783 kJ/mol)

Calculate the enthalpy of solution

Perform the calculation: Enthalpy of solution = -1569 kJ/mol So, the enthalpy of solution per mole of solid NaCl is -1569 kJ/mol.

Key concepts

Lattice Energy

Lattice energy is an essential concept when discussing ionic compounds. It refers to the energy required to separate one mole of an ionic solid into its gaseous ions. Imagine it as the glue that holds the ions together in a solid. When ionic bonds are formed, energy is released. This is because ions are coming together to form a more stable, lower-energy structure.

• High Lattice Energy: Indicates a strong ionic bond, requiring more energy to break.
• Low Lattice Energy: Indicates a weaker bond, which is easier to break apart.

In the context of \mathrm{NaCl}, the lattice energy is \(-786 \, \mathrm{kJ/mol}\). It tells us that a considerable amount of energy must be supplied to the system to overcome this stability and separate it into gaseous ions. The lattice energy directly influences the enthalpy of the solution, as breaking these bonds is an integral part of the solution process.

Enthalpy of Hydration

Enthalpy of hydration is the energy change when one mole of ions dissolves in a large amount of water to form a solution. It's similar to lattice energy but works in the opposite way:

• Exothermic Process: When hydrating ions release energy, the process is exothermic, meaning it releases heat.
• Hydration: The amount of energy released depends on the size and charge of the ions. Smaller, highly charged ions release more energy upon hydration.

For \mathrm{NaCl}, the enthalpy of hydration for sodium and chloride ions is \(-783 \, \mathrm{kJ/mol}\). This indicates the energy released when these ions become surrounded by water molecules, stabilizing in solution. In enthalpy calculations for solutions, you combine the lattice energy with the enthalpy of hydration to understand how the process affects the temperature of the system. Here, it helps in understanding if the solution process is endothermic (absorbs heat) or exothermic (releases heat).

Thermochemistry

Thermochemistry involves the study of heat energy changes accompanying chemical reactions. It is a subset of thermodynamics and provides insight into how energy changes in a system.A key aspect of thermochemistry includes calculating the enthalpy changes that occur during reactions or processes, such as:

• Enthalpy of Reaction: Change in heat content during a chemical reaction at constant pressure.
• Enthalpy of Solution: Important in determining how dissolving substances affect energy—either absorbing or releasing heat.

In the exercise involving \mathrm{NaCl}, understanding thermochemistry helps predict whether the dissolution process will warm up or cool down the surrounding environment.By calculating the enthalpy of solution, you determine the process is exothermic (like in our example with \(-1569 \, \mathrm{kJ/mol}\)). Thus, it releases heat, helping us predict the effects on the surroundings and influence on solution making.