Question

Rationalize the following lattice energy values: $$ \begin{array}{|lc|} \hline & \text { Lattice Energy } \\ \text { Compound } & (\mathrm{kJ} / \mathrm{mol}) \\ \hline \mathrm{CaSe} & -2862 \\ \mathrm{Na}_{2} \mathrm{Se} & -2130 \\ \mathrm{CaTe} & -2721 \\ \mathrm{Na}_{2} \mathrm{Te} & -2095 \\ \hline \end{array} $$

Short answer

The given lattice energy values for the compounds can be rationalized based on the differences in ionic radii and charges of the constituent ions. Calcium compounds (CaSe and CaTe) have higher lattice energies than sodium compounds (Na₂Se and Na₂Te) due to the greater charge of Ca²⁺ ions compared to Na⁺ ions. Additionally, compounds containing the larger anion (Te²⁻) have lower lattice energies compared to those with the smaller anion (Se²⁻), as the greater interionic distance reduces the electrostatic attraction between the ions.

Step-by-step solution

Recognize the type of ionic bonds in the compounds

The given compounds have the following elements: - Ca (Calcium): A group 2 element (alkaline earth metal; metal; charge: +2) - Na (Sodium): A group 1 element (alkali metal; metal; charge: +1) - Se (Selenium): A group 16 element (chalcogen; non-metal; charge: -2) - Te (Tellurium): A group 16 element (chalcogen; non-metal; charge: -2)

Understand Lattice energy

The lattice energy of an ionic compound measures the amount of energy required to break one mole of the compound into its constituent ions in the gaseous state or the energy released when the ions come together to form the ionic compound. Lattice energy increases with the increasing charge on the ions and decreases with increasing ionic radii.

Analyze the similar compounds

There are two pairs of similar compounds: CaSe and CaTe, and Na₂Se and Na₂Te. In both pairs, the metal is the same, while the non-metal is different. The difference between Selenium and Tellurium is their atomic size. As both are in the same group, but Tellurium is below Selenium, Te has a larger atomic radius than Se.

Compare Lattice energies within pairs

We can now compare the lattice energies within each pair: - CaSe (-2862 kJ/mol) and CaTe (-2721 kJ/mol): As both share the same metal ion (Ca²⁺), the difference in lattice energy is mainly due to the different size of the anions (Se²⁻ and Te²⁻). Since the Te²⁻ ion is larger than the Se²⁻ ion, the lattice energy of CaTe is lower than that of CaSe. - Na₂Se (-2130 kJ/mol) and Na₂Te (-2095 kJ/mol): Both share the same metal ion (Na⁺). As the Te²⁻ ion is larger than the Se²⁻ ion (same reasoning as before), the lattice energy of Na₂Te is lower than that of Na₂Se.

Rationalize the overall trend

Lower lattice energies correspond to larger interionic distances (and thus weaker electrostatic attractions between ions), while higher lattice energies correspond to smaller interionic distances (stronger electrostatic attractions). In this case, the main reason for the observed trends in lattice energies for the given compounds is the difference in ionic radii of the anions (Se²⁻ and Te²⁻) as well as the charge of the cations (Na⁺ and Ca²⁺). To summarize: - Compounds with Ca²⁺ ions have more negative (higher) lattice energies because of the higher positive charge on Ca²⁺ than on Na⁺. - Compounds with larger anions (Te²⁻) have less negative (lower) lattice energies because the greater interionic distance reduces the electrostatic attraction between the ions.

Key concepts

Ionic Bonds

An ionic bond is a type of chemical bond formed when one atom donates or accepts electrons from another atom, resulting in the formation of ions. These ions are then held together by the forces of electrostatic attraction. Ionic bonds typically form between metals and nonmetals. Metals, which tend to lose electrons, form positively charged ions known as cations. Nonmetals, which tend to gain electrons, form negatively charged ions called anions. When a metal like calcium (Ca) bonds with a nonmetal like selenium (Se), it forms calcium selenide (CaSe) through ionic bonding.

Key characteristics of ionic bonds include:

• Formation of well-defined crystal lattice structures.
• High melting and boiling points due to strong intermolecular forces.
• Good electrical conductivity when melted or dissolved in water.

Understanding ionic bonds helps in analyzing the lattice energies of compounds such as CaSe and Na₂Te.

Electrostatic Attractions

Electrostatic attractions refer to the force that draws oppositely charged ions towards each other. In ionic compounds, this is the primary force that holds the ions in place. The strength of the electrostatic attraction depends greatly on the magnitude of the charges involved and the distance between the ions.

For instance, a cation with a charge of +2, such as calcium (Ca²⁺), will attract an anion with a charge of -2, like telluride (Te²⁻), more strongly than a cation with a charge of +1, such as sodium (Na⁺). Consequently, the stronger the electrostatic attraction, the higher the lattice energy of the compound. This explains why compounds like CaSe have higher lattice energies than Na₂Se despite having larger anions like Te²⁻.

Strong electrostatic attractions often result in:

• Greater stability in the ionic lattice structure
• Higher lattice energy values
• More energy being required to break the lattice apart

Ionic Radii

The ionic radius is the measure of an ion's size. It plays a crucial role in determining the characteristics of ionic compounds. When ions form a compound, the distance between them—the interionic distance—impacts the strength of the electrostatic attraction. Smaller ions, having lesser distances between them, result in stronger electrostatic attractions, whereas larger ions with greater interionic distances have weaker attractions.

In compounds where the anions are the same but the cations vary, it is the cation’s charge that affects the lattice energy. However, with differing anions like Se²⁻ and Te²⁻, the ionic radius becomes a deciding factor. Since Te²⁻ is larger than Se²⁻ due to its additional electron shell, compounds with telluride ions often have lower lattice energies compared to those with selenide ions. This is why CaSe has a higher lattice energy compared to CaTe.

Influences of ionic radii include:

• Affecting the compound’s melting and boiling points
• Influencing the hardness of the compounds
• Changing the color of the ionic solids

Alkaline Earth Metals

Alkaline earth metals are elements found in Group 2 of the periodic table and include beryllium, magnesium, calcium, strontium, barium, and radium. These metals are characterized by having two electrons in their outermost energy level, which they readily lose to form cations with a +2 charge. This charge leads to the formation of strong ionic bonds when they combine with nonmetals.

Calcium (Ca), an alkaline earth metal, easily forms compounds like calcium selenide (CaSe) with nonmetals by providing its valence electrons. This results in a cation with a +2 charge, which contributes significantly to the high lattice energy of such compounds due to increased electrostatic attraction.

Characteristics of alkaline earth metals include:

• High reactivity, but not as reactive as alkali metals
• Significant role in the formation of minerals
• Tendency to form colorless or white ionic compounds

Alkaline earth metals like calcium are crucial to understanding lattice energy trends in ionic compounds.