Problem 21 - Chemistry: The Central Science

Question

(a) Is lattice energy usually endothermic or exothermic? (b) Write the chemical equation that represents the process of lattice energy for the case of \(\mathrm{NaCl}\). (c) Would you expect salts like \(\mathrm{NaCl}\), which have singly-charged ions, to have larger or smaller lattice energies compared to salts like \(\mathrm{CaO}\) which are composed of doubly-charged ions?

Step-by-Step Solution

Answer

Lattice energy is usually endothermic when breaking apart an ionic solid but exothermic when forming ionic solids from their gaseous ions. The chemical equation for the formation of NaCl with lattice energy is \[ \mathrm{Na^{+}(g)} + \mathrm{Cl^{-}(g)} \rightarrow \mathrm{NaCl(s)} + (-U_\mathrm{L}) \] Salts composed of doubly-charged ions, like CaO, would have larger lattice energies compared to salts with singly-charged ions like NaCl.

Step 1: Part (a): Lattice Energy - Endothermic or Exothermic?

Lattice energy is the amount of energy needed to break apart an ionic solid and separate it into its gaseous ions. Alternatively, it can be described as the energy released when an ionic solid forms from its gaseous ions. Since energy is required to break the ionic bonds in a solid, lattice energy is usually considered as an endothermic process. However, when ionic solids form from gaseous ions, the process is exothermic, as energy is released. So, lattice energy is usually endothermic when breaking apart an ionic solid but exothermic when forming ionic solids from their gaseous ions.

Step 2: Part (b): Lattice Energy Process for NaCl

We will write the chemical equation representing the process of lattice energy for NaCl. We will consider the exothermic process, where energy is released when NaCl solid is formed from its gaseous ions. 1. Start with the ions in the gaseous state: \(\mathrm{Na^{+}(g)}\) and \(\mathrm{Cl^{-}(g)}\). 2. Combine the ions to form a solid crystal lattice: \(\mathrm{NaCl(s)}\). 3. Include the lattice energy, represented by \(U_\mathrm{L}\), and note that it's negative since energy is released: \(-U_\mathrm{L}\). The chemical equation for the formation of NaCl with lattice energy is \[ \mathrm{Na^{+}(g)} + \mathrm{Cl^{-}(g)} \rightarrow \mathrm{NaCl(s)} + (-U_\mathrm{L}) \]

Step 3: Part (c): Lattice Energies Comparison for NaCl and CaO

Now we will compare the lattice energies of salts with singly-charged ions like NaCl and salts with doubly-charged ions like CaO. Lattice energy depends on the charges of the ions and the distances between them. It can be estimated using the following equation derived from Coulomb's Law: \(U_\mathrm{L} = k\frac{Q_1 Q_2}{r}\), where - \(U_\mathrm{L}\) = lattice energy, - \(k\) = proportionality constant, - \(Q_1\) and \(Q_2\) = charges of ions, and - \(r\) = distance between ions. From the equation, it's clear that higher charges on the ions result in higher lattice energies. Thus, salts composed of doubly-charged ions, like CaO, would have larger lattice energies compared to salts with singly-charged ions like NaCl.

Key Concepts

Ionic Solids

Ionic solids are a fascinating subject in chemistry. They are compounds made up of positively and negatively charged ions that are held together by strong electrostatic forces. These forces are the reason ionic solids maintain a structured, crystal lattice form. The arrangement of ions in this lattice is key to the properties of the solid.
- Ionic solids are typically hard and brittle, due to the strong forces holding the ions. - They have high melting and boiling points, because a lot of energy is needed to break the ionic bonds.
When discussing ionic solids, it's crucial to understand that they do not conduct electricity in solid form. However, when melted or dissolved in water, they become excellent conductors. This is because the ions are free to move and carry charge.

Gaseous Ions

Gaseous ions are ions that exist in the gas phase, distinct from the ions within an ionic solid. These ions can be either positive (cations) or negative (anions). The transition between gaseous ions and ionic solids is a key aspect in understanding lattice energy.
- In gaseous form, ions are free and not bound in a crystal structure. - The formation of an ionic solid from gaseous ions releases energy.
This release of energy is essential when discussing endothermic and exothermic processes, as it helps us understand why energy dynamics play a significant role in the formation and breakdown of these structures.

Coulomb's Law

Coulomb's Law is fundamental to understanding interactions between charged particles, like ions. This law helps explain the forces between ions in an ionic solid and consequently affects lattice energy.
Let's break down the key equation: \[ U_\mathrm{L} = k\frac{Q_1 Q_2}{r} \],where:

• \(U_\mathrm{L}\) is the lattice energy.
• \(k\) is a constant of proportionality.
• \(Q_1\) and \(Q_2\) represent the charges of the ions.
• \(r\) is the distance between the ions.

According to Coulomb's Law, lattice energy is directly dependent on the magnitude of the charges and inversely proportional to the distance between the ions. This means that the greater the charge of the ions, the stronger the forces holding them together, resulting in higher lattice energy.

Comparison of Lattice Energies

The comparison of lattice energies between different ionic compounds demonstrates how varying ion charges and distances influence strength and stability. More specifically, lattice energies vary based on:
- **The magnitude of ionic charges**: Ionic compounds with higher charges, such as those with doubly-charged ions, generally have larger lattice energies. For example, calcium oxide (CaO), which consists of doubly-charged ions, has more substantial lattice energy than sodium chloride (NaCl), with singly-charged ions.
- **The inter-ionic distance**: The smaller the distance between ions, the greater the lattice energy, as ions are more tightly held together.
This implies that salts such as CaO are more structurally robust than salts like NaCl due to the greater forces of attraction between their ions.

Charged Ions

Charged ions are the cornerstone of ionic compounds. These ions arise when atoms gain or lose electrons, resulting in a net charge. There are two types of charged ions:

• Cations: Positively charged ions, which have lost electrons.
• Anions: Negatively charged ions, which have gained electrons.

The interaction between cations and anions leads to the formation of ionic bonds. These charged ions are critical to lattice energy and have a direct influence on the strength of ionic solids.
Key Factors:
- The extent of ion charges significantly impacts lattice energy, with greater charges leading to higher lattice energy. - Understanding the behavior of charged ions helps us explain why certain compounds have thicker and more sturdy crystal lattices.