Problem 43 - Chemistry A Molecular Approach

Question

Explain the trend in the lattice energies of the alkaline earth metal oxides. MISSED THIS? Read Section 10.4 $$ \begin{array}{lc} \text { Metal Oxide } & \text { Lattice Energy (k } \mathrm{J} / \mathrm{mol} \text { ) } \\ \hline \mathrm{MgO} & -3795 \\ \hline \mathrm{CaO} & -3414 \\ \hline \mathrm{SrO} & -3217 \\ \hline \mathrm{BaO} & -3029 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The lattice energies of the alkaline earth metal oxides decrease from MgO to BaO, due to the increase in ionic radius and decrease in charge density of the metal ions as one moves down the group.

Step 1: Understanding Lattice Energy

Lattice energy is the energy released when cations and anions combine to form an ionic compound. A higher lattice energy indicates a stronger force of attraction between the ions, resulting in a more stable compound.

Step 2: Identifying the Trend

Upon examining the given lattice energies for the alkaline earth metal oxides, we see a decrease as we move down the group: MgO has the highest lattice energy, followed by CaO, SrO, and BaO has the lowest.

Step 3: Explaining the Trend with Ionic Radii

The trend in the lattice energies can be explained by the increase in ionic radii as we move down the group. A larger ionic radius means the outer electrons are further from the nucleus, which leads to weaker attraction between the cation and anion, thus lower lattice energy.

Step 4: Considering Charge Density

Charge density, which is the charge over the volume of the ion, also decreases down the group. Smaller ions with higher charge densities will have stronger electrostatic attractions with the opposite ion, producing higher lattice energies.

Key Concepts

Ionic Compound Formation

Understanding the formation of ionic compounds is essential when studying chemistry. An ionic compound is made up of positively charged ions, called cations, and negatively charged ions, known as anions. These ions are held together by the strong electrostatic forces of attraction, which arise due to their opposite charges.

For example, when an alkaline earth metal reacts with oxygen, the metal loses electrons to form cations while oxygen gains electrons to become an oxide anion. The resulting compound, such as MgO or CaO, is held together by this ionic bond. The strength of the bond and thus, the stability of the compound, can be quantified through a property called lattice energy.

For students, recognizing that the formation of these compounds involves electron transfer and subsequent attraction between ions lays the groundwork for understanding their properties, including lattice energies.

Trend in Lattice Energy

Lattice energy plays a pivotal role in illustrating the stability of ionic compounds. It is the energy released when one mole of an ionic crystalline compound is formed from its gaseous ions. When looking at the lattice energies of alkaline earth metal oxides, there's a clear trend observed: as we move down the group in the periodic table, the lattice energies decrease.

This is visible with the values given, such as MgO at -3795 kJ/mol leading down to BaO at -3029 kJ/mol. The reason behind this trend involves the size and charge of the ions involved, two factors that significantly influence the strength of the ionic bonds within the compounds. A higher lattice energy indicates a stronger ionic bond, translating to a more stable compound.

Ionic Radii Influence on Lattice Energy

The size of an ion, or its ionic radius, is a key factor affecting lattice energy. As the ionic radius increases, the distance between the nucleus of the cation and the outer electrons of the anion increases, which often results in a weaker force of attraction between the ions.

In the case of alkaline earth metal oxides, going from MgO to BaO, the metals' ionic radii increase due to the addition of electron shells as we move down the group. Thus, the outer electrons of the oxide ions are further from the metal cations, leading to a reduction in lattice energy. This principle helps students understand why MgO, with the smallest cation among the given examples, has the highest lattice energy.

Charge Density and Lattice Energy

Charge density is the measure of the charge of an ion relative to its volume. High charge density means a greater charge per unit volume, which typically results in a stronger electrostatic pull between oppositely charged ions and, consequently, a higher lattice energy.

For alkaline earth metals, the cations have a +2 charge, but as we move down the group from Mg to Ba, the size of the cations increases, leading to a decrease in charge density. The smaller Mg²⁺ ion has a higher charge density compared to the larger Ba²⁺ ion. Therefore, the force of attraction between the Mg²⁺ ion and O^2- ion is greater than that between Ba²⁺ and O^2-, making MgO's lattice energy the highest among the alkaline earth metal oxides listed.

Students can visualize this concept by thinking of charge density as the 'concentration' of electrical charge over the space an ion occupies. A 'concentrated' charge interacts more intensely with its surroundings, which is why compounds like MgO exhibit greater lattice energies.