Question

Silver nitrate has a lattice energy of \(-820 \mathrm{~kJ} / \mathrm{mol}\) and a heat of solution of \(22.6 \mathrm{~kJ} / \mathrm{mol}\). Calculate the heat of hydration for silver nitrate.

Short answer

The heat of hydration for silver nitrate is 842.6 kJ/mol.

Step-by-step solution

Understanding the Problem

The heat of hydration can be calculated by finding the difference between the heat of solution and the lattice energy for a compound. For silver nitrate, these values are given.

Calculation of Heat of Hydration

The heat of hydration (ΔH_{hydration}) is given by the formula: ΔH_{hydration} = ΔH_{solution} + ΔH_{lattice}. Here, ΔH_{solution} is the heat of solution and ΔH_{lattice} is the lattice energy. Since lattice energy is the energy required to separate a mole of a solid ionic compound into its constituent ions in gas phase, it is a positive value when absorbed (endothermic process), but we are considering the reverse (exothermic) process, so we take its value as negative in the heat of hydration calculation.

Compute the Heat of Hydration

Using the provided values, ΔH_{hydration} = 22.6 ΔH_{solution} - (-820 ΔH_{lattice}).

Substitute the Values

Substitute the given numbers into the formula to find ΔH_{hydration}: ΔH_{hydration} = 22.6 kJ/mol + 820 kJ/mol.

Calculate the Result

Perform the arithmetic to find the heat of hydration: ΔH_{hydration} = 22.6 kJ/mol + 820 kJ/mol = 842.6 kJ/mol.

Key concepts

Lattice Energy

Lattice energy plays a crucial role in understanding ionic compounds and their properties. It is defined as the amount of energy released when one mole of an ionic crystalline compound is formed from its gaseous ions. In more simple terms, it's the 'glue' that holds the ions together in a crystal lattice.

Consider it as a measure of the strength of the bonds between the ions. The higher the lattice energy, the stronger the forces that bind the ions, and consequently, the more stable the compound. This concept is important especially when we look at why some compounds have higher melting points and why some dissolve more readily in water than others.

Relevance to Hydration

When an ionic compound dissolves in water, the lattice energy must be overcome to separate the ions. This process requires energy and is crucial to understanding the overall heat changes that occur during the dissolution of ionic compounds.

Heat of Solution

The heat of solution, also known as the enthalpy of solution, is the enthalpy change associated with dissolving a substance in a solvent. This value can be either endothermic (positive, absorbing heat) or exothermic (negative, releasing heat).

When an ionic compound dissolves, the process involves breaking apart the lattice and hydrating the ions. The heat of solution is influenced by both the lattice energy and the hydration energy of the ions. The balance between these two energies determines whether the process will overall absorb or release heat.

Understanding with Example

In the context of our example, the silver nitrate has a given heat of solution of 22.6 kJ/mol, which means that when this compound dissolves, this energy is involved in overcoming the lattice energy and in stabilizing the ions in solution.

Enthalpy Change

Enthalpy change represents the heat change in a system at constant pressure, which in chemical reactions is an essential part of understanding energy transfer. This concept is especially important in reactions that involve breaking and making bonds, such as the dissolution of ionic compounds.

The enthalpy change can be categorized based on the type of reaction, such as formation, combustion, or hydration. The sign of enthalpy change indicates whether a reaction is exothermic (negative sign, releases heat) or endothermic (positive sign, absorbs heat).

Calculating Heat of Hydration

As illustrated in the given exercise, the heat of hydration can be calculated from the enthalpy change of the solution and the lattice energy. By understanding these individual enthalpy changes, students can determine the overall energy involved when a substance like silver nitrate hydrates, which in the given example amounted to 842.6 kJ/mol.