Question

Specify which compound in each of the following pairs of ionic compounds should have the higher lattice energy: (a) AlN or \(\mathrm{CaO},\) (b) \(\mathrm{NaF}\) or \(\mathrm{CsF},\) (c) \(\mathrm{MgCl}_{2}\) or \(\mathrm{MgF}_{2}\). Explain your choice.

Short answer

AlN, NaF, and MgF2 have higher lattice energies due to higher charges or smaller ion sizes.

Step-by-step solution

Understanding Lattice Energy

Lattice energy refers to the energy released when ions in the gaseous state combine to form an ionic solid. It is influenced by the charge and size of the ions involved. Higher charges and smaller ion sizes typically result in higher lattice energies because the electrostatic forces between the ions are stronger.

Comparing AlN and CaO

AlN consists of Al (3+) and N (3-), while CaO consists of Ca (2+) and O (2-). Since AlN has ions with higher charges, it will have a higher lattice energy compared to CaO.

Comparing NaF and CsF

Both NaF and CsF have ions with the same charges, Na (1+) with F (1-) and Cs (1+) with F (1-). However, Cs is larger than Na, making NaF have a higher lattice energy since smaller ions lead to stronger attractions.

Comparing MgCl2 and MgF2

MgCl2 contains Mg (2+) with Cl ions, while MgF2 has Mg (2+) with F ions. Though the cation charge is the same, F is smaller than Cl, thus MgF2 will have a higher lattice energy as the smaller ion leads to a greater attraction between ions.

Key concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons between each other. This transfer creates ions: atoms or molecules that carry an electric charge. Typically, an ionic compound forms between a metal, which loses electrons to become a positively charged ion (cation), and a non-metal, which gains those electrons to become a negatively charged ion (anion).

The structure of ionic compounds is often a lattice. This lattice is a repeating pattern of ions that extends in three dimensions. The strength of the ionic bonds in these compounds depends on several factors, including ion charges and sizes, which affect their physical properties like melting point and solubility.

Electrostatic Forces

Electrostatic forces are the glue that holds ionic compounds together. These forces are the result of attractions between oppositely charged ions and repulsions between similarly charged ions.

The strength of electrostatic forces is influenced by the magnitude of the charges and the distance between the ions. Positively and negatively charged ions attract each other, and the force of this attraction is what we call electrostatic force. Since like charges repel each other, maintaining a structured lattice requires a careful balance.

In the context of lattice energy, strong electrostatic forces suggest a higher amount of energy needed to separate the ions. This directly relates to the lattice energy, as stronger forces translate into a more stable and, thus, higher energy lattice.

Ion Size

The size of an ion, or its ionic radius, plays a crucial role in determining the properties of an ionic compound. Generally, smaller ions can get closer to each other in a lattice, increasing the electrostatic forces between them.

For example, between sodium fluoride (\(\text{NaF}\)) and cesium fluoride (\(\text{CsF}\)), sodium ions, being smaller, allow for closer packing in the crystal lattice than the larger cesium ions. This closer packing translates into stronger attractive forces and in turn, a higher lattice energy.

As a general rule, the smaller the ion, the higher the lattice energy due to the decrease in distance between oppositely charged ions, which strengthens the electrostatic attractions.

Ion Charge

Ion charge is another critical factor affecting lattice energy. The charge of an ion is determined by how many electrons have been lost or gained. Ions with higher charges create stronger electrostatic attractions, leading to higher lattice energies.

In comparing magnets, for example, a stronger magnet creates a stronger pull. Similarly, ionic compounds with highly charged ions have stronger attractions.

For instance, comparing aluminum nitride (\(\text{AlN}\)) with calcium oxide (\(\text{CaO}\)), the ions in AlN have charges of 3+ and 3-, whereas in CaO they are 2+ and 2-. As a result, AlN possesses a higher lattice energy due to these stronger charges, resulting in more robust binding within the lattice structure.