Question

Which compound in each of the following pairs of ionic substances has the most negative lattice energy? Justify your answers. a. NaCl, KCl b. LiF, 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 negative lattice energy because Na is smaller than K. b. LiF has the most negative lattice energy because F is smaller than Cl. c. MgO has the most negative lattice energy because O2- is smaller than OH-. d. Fe(OH)3 has the most negative lattice energy due to its higher cation charge e. Na2O has the most negative lattice energy because O2- has a higher charge than Cl-. f. MgO has the most negative lattice energy due to both its ion charges and ion sizes.

Step-by-step solution

a. NaCl vs. KCl

Between NaCl and KCl, the charges on the ions are the same (+1 for Na and K, -1 for Cl), so the deciding factor will be the size of the ions. Na is smaller than K, so the Na+ ion and the Cl- ion will be closer together, therefore NaCl will have a more negative lattice energy.

b. LiF vs. LiCl

In this case, the cations are the same (Li+), so the deciding factor will be the size of the anions. F is smaller than Cl, so the force of attraction will be stronger in LiF. Thus, LiF will have a more negative lattice energy than LiCl.

c. \(\mathrm{Mg}(\mathrm{OH})_{2}\) vs. \(\mathrm{MgO}\)

For these compounds, the cations are the same (Mg2+), as well as the magnitude of the anions charges(-2 in both cases). However, the size of the anions differs. O2- is smaller than the OH- anion, so MgO has a more negative lattice energy than \(\mathrm{Mg}(\mathrm{OH})_{2}\).

d. \(\mathrm{Fe}(\mathrm{OH})_{2}\) vs. \(\mathrm{Fe}(\mathrm{OH})_{3}\)

In this case, the cations are Fe(II) in \(\mathrm{Fe}(\mathrm{OH})_{2}\) and Fe(III) in \(\mathrm{Fe}(\mathrm{OH})_{3}\). So, there is a difference in charge between the two compounds. The cation with a higher charge (Fe(III)) will lead to a more negative lattice energy, so \(\mathrm{Fe}(\mathrm{OH})_{3}\) will have the most negative lattice energy.

e. \(\mathrm{NaCl}\) vs. \(\mathrm{Na}_{2} \mathrm{O}\)

These compounds have the same cation (Na+), so the deciding factor will be the charges of the anions. O2- has a higher anion charge than Cl-, and as a result, \(\mathrm{Na}_{2} \mathrm{O}\) will have the most negative lattice energy.

f. \(\mathrm{MgO}\) vs. \(\mathrm{BaS}\)

For this pair, we need to look at both the cation and anion properties. Mg2+ has a higher charge than Ba2+, and O2- has a higher charge than S2-. However, Mg2+ is smaller than Ba2+ and O2- is smaller than S2-. Due to both the charge and size of the ions, MgO has a more negative lattice energy than BaS.

Key concepts

Ionic Compounds

Ionic compounds are made up of ions held together by strong forces called ionic bonds. These ions are typically formed when elements transfer electrons to achieve a full outer shell, resulting in positively charged cations and negatively charged anions. This transfer creates a strong electrostatic attraction between the oppositely charged ions.

The strength of the ionic bond—and consequently the lattice energy of the compound—depends significantly on several factors, including the sizes and charges of the involved ions. Ionic compounds tend to form crystalline solids at room temperature with high melting points due to the significant energy required to overcome the ionic bonds.

They are generally soluble in water, and when dissolved or melted, they can conduct electricity due to the mobility of their free ions. Understanding the nature of ionic compounds is crucial in determining their properties and behavior in different conditions.

Ion Charge

Ion charge plays a crucial role in determining the lattice energy of ionic compounds. The charge of an ion is the result of losing or gaining electrons, leading to positively charged cations or negatively charged anions. The greater the magnitude of the charge on the ions, the stronger the electrostatic forces of attraction between them.

This concept is encapsulated by Coulomb's Law, which states that the force of attraction between two ions increases with the product of their charges. Therefore, compounds composed of ions with higher charges will generally exhibit more negative lattice energies, which indicates stronger ionic bonds. For example, a 2+ cation and a 2- anion will create a stronger attraction than a 1+ cation and 1- anion, all else being equal.

Ultimately, understanding ion charge is essential for predicting the stability and strength of the ionic bonds in a compound.

Ion Size

Ion size, or ionic radius, is another key factor affecting the lattice energy of ionic compounds. Generally, smaller ions allow the nuclei of the ions to be closer together, resulting in a stronger electrostatic attraction and thus, more negative lattice energy.

When comparing two ionic compounds with similar charges, the compound with smaller ions will typically have a more negative lattice energy. For instance, smaller ions can pack more tightly together in the crystal lattice, reducing the distance between oppositely charged ions and intensifying the force of attraction.

This rule holds true even when different anions or cations are involved, as long as the charge remains unchanged. Understanding how ion size influences lattice energy can help predict the properties of ionic compounds in various chemical contexts.

Cation and Anion Comparison

When comparing cations and anions in ionic compounds, both the size and charge of these ions must be considered to determine factors like lattice energy. Cations are typically smaller than their neutral atoms, as they lose electrons and the electron cloud contracts. Anions, however, gain electrons and are usually larger than their neutral counterparts.

In comparisons where the charges are equivalent, the smaller ion will lead to a stronger electrostatic attraction. As shown in certain compound pairs, differences in ion size can significantly affect the compound's overall stability and energy properties, as seen with comparisons such as NaCl vs. KCl or LiF vs. LiCl.

Ultimately, understanding the dynamics between cations and anions, including how their sizes and charges influence the interactions within the crystal lattice, is essential for anyone studying the binding forces and dissolution properties of ionic compounds.