Question

Which compound in each of the following pairs of ionic substances has the most exothermic lattice energy? Justify your answers. a. \(\mathrm{NaCl}, \mathrm{KCl}\) b. \(\mathrm{LiF}, \mathrm{LiCl}\) c. \(\mathrm{Mg}(\mathrm{OH})_{2}, \mathrm{MgO}\) d. \(\mathrm{Fe}(\mathrm{OH})_{2}, \mathrm{Fe}(\mathrm{OH})_{3}\) e. \(\mathrm{NaCl}, \mathrm{Na}_{2} \mathrm{O}\) f. \(\mathrm{MgO}, \mathrm{BaS}\)

Short answer

a. NaCl has the most exothermic lattice energy because it has a smaller atomic radius than KCl. b. LiF has the most exothermic lattice energy due to the smaller atomic radius of F compared to Cl. c. MgO has the most exothermic lattice energy as it has ions with higher charges compared to Mg(OH)₂. d. Fe(OH)₃ has the most exothermic lattice energy due to the higher positive charge on the Fe ion compared to Fe(OH)₂. e. Na₂O has the most exothermic lattice energy because it has a higher charge on the O ion compared to NaCl. f. MgO has the most exothermic lattice energy since it has smaller atomic radii for Mg and O compared to Ba and S in BaS.

Step-by-step solution

Compare NaCl and KCl

In NaCl, Na has a charge of +1, and Cl has a charge of -1. In KCl, K also has a charge of +1, and Cl has a charge of -1. The charges are identical between the two compounds, so we will compare the distances between ions. Sodium (Na) has a smaller atomic radius than potassium (K), hence NaCl will have shorter distances between its ions, leading to a more exothermic lattice energy. Thus, NaCl has the most exothermic lattice energy.

Compare LiF and LiCl

In LiF, Li has a charge of +1, whereas F has a charge of -1. In LiCl, Li has a charge of +1, and Cl has a charge of -1. The charges in both compounds are identical. However, fluorine (F) has a smaller atomic radius than chlorine (Cl), hence LiF will have shorter distances between its ions, leading to a more exothermic lattice energy. Thus, LiF has the most exothermic lattice energy.

Compare Mg(OH)₂ and MgO

In Mg(OH)₂, Mg has a charge of +2, while OH has a charge of -1. In MgO, Mg has a charge of +2, and O has a charge of -2. Since MgO has ions with higher charges, their interactions will be stronger, leading to a more exothermic lattice energy. Thus, MgO has the most exothermic lattice energy.

Compare Fe(OH)₂ and Fe(OH)₃

In Fe(OH)₂, Fe has a charge of +2, and OH has a charge of -1. In Fe(OH)₃, Fe has a charge of +3, and OH has a charge of -1. Fe(OH)₃ has a higher positive charge on the Fe ion, leading to stronger interactions and a more exothermic lattice energy. Thus, Fe(OH)₃ has the most exothermic lattice energy.

Compare NaCl and Na₂O

In NaCl, Na has a charge of +1, and Cl has a charge of -1. In Na₂O, Na has a charge of +1, and O has a charge of -2. Na₂O has a higher charge on the O ion, which will lead to stronger interactions and a more exothermic lattice energy. Thus, Na₂O has the most exothermic lattice energy.

Compare MgO and BaS

In MgO, Mg has a charge of +2, and O has a charge of -2. In BaS, Ba has a charge of +2, and S has a charge of -2. The charges are identical between the two compounds, so we must compare the distances between ions. Magnesium (Mg) and oxygen (O) both have smaller atomic radii than barium (Ba) and sulfur (S), respectively. Hence, MgO will have shorter distances between its ions, leading to a more exothermic lattice energy. Thus, MgO has the most exothermic lattice energy.

Key concepts

Ionic Substances

Ionic substances are compounds formed by the chemical bonding between metals and nonmetals, where electrons are transferred from one atom to another, resulting in the formation of oppositely charged ions. This transfer of electrons leads to the creation of positive ions (cations) and negative ions (anions). Once formed, these ions arrange themselves in a highly ordered structure known as a lattice. The strength of the bond in these lattices is significant because it influences properties such as melting point, boiling point, and hardness.

The energy released when the ions bond to form the lattice is referred to as lattice energy, and it is always exothermic. That means the process of forming an ionic solid from its ions gives off energy. Lattice energy is an important factor in determining the stability and solubility of ionic substances. In general, the greater the lattice energy, the more stable the ionic compound is.

Atomic Radius

The atomic radius of an element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding cloud of electrons. When examining lattice energy, atomic radius plays a crucial role.

As atomic radius decreases, ions can get closer together, and the electrostatic attraction between them increases, leading to higher lattice energy. This is why in compounds where the charges are the same, the one with the smaller atomic radius will generally have a more exothermic lattice energy, as seen in the comparison between NaCl and KCl in the original exercise.

Ion Charge

The charge of an ion significantly influences the strength of the electrostatic forces that hold the ionic lattice together. The greater the charge, the stronger the force of attraction between the ions.

This means that for ionic compounds with similar atom sizes or if comparing atoms of the same element but with different charges, the compound with ions that have higher charges will typically have a more exothermic lattice energy. This explains why MgO, which includes a divalent cation and anion (Mg^2+ and O^2−), has a more exothermic lattice energy compared to Mg(OH)₂ or any other compound with ions of lower charges.