Question

Which compound in each of the following pairs of ionic substances has the most exothermic lattice energy? Justify your answers a. \(\mathrm{LiF}, \mathrm{CsF} \quad\) d. \(\mathrm{Na}_{2} \mathrm{SO}_{4}, \mathrm{CaSO}_{4}\) b. \(\mathrm{NaBr}, \mathrm{Nal} \quad\) e. \(\mathrm{KF}, \mathrm{K}_{2} \mathrm{O}\) c. \(\mathrm{BaCl}_{2}, \mathrm{BaO} \quad\) f. \(\mathrm{Li}_{2} \mathrm{O}, \mathrm{Na}_{2} \mathrm{S}\)

Short answer

a. LiF has the most exothermic lattice energy because of its smaller ionic radii, compared to CsF. b. NaBr has the most exothermic lattice energy due to the smaller ionic radius of Br⁻, compared to I⁻. c. BaO has the most exothermic lattice energy because of the greater charge of the O²⁻ ion, compared to Cl⁻. d. CaSO₄ has the most exothermic lattice energy owing to the higher charge of Ca²⁺ ions compared to Na⁺ ions. e. K₂O has the most exothermic lattice energy due to the greater charge of O²⁻ ions, compared to F⁻ ions. f. Li₂O has the most exothermic lattice energy because of the smaller ionic radii of Li⁺ and O²⁻, compared to Na₂S.

Step-by-step solution

a. LiF, CsF

Firstly, let us compare the ionic radii of Li and Cs ions. Given that Cs+ (167 pm) has a larger ionic radius than Li+ (76 pm), and both compounds have F– ions (F–: 133 pm) in the lattice, the sum of the ionic radii will be larger for CsF. Since lattice energy is inversely proportional to the sum of the ionic radii, the lattice energy of LiF is greater than CsF. Therefore, LiF has the most exothermic lattice energy in this pair.

b. NaBr, NaI

For this pair, we have Na+ ions (Na+ : 116 pm) in both the compounds. Br–(196 pm) and I (220 pm) ions differ in size. Since lattice energy is inversely proportional to the sum of the ionic radii, NaBr would have a greater lattice energy because the Br– ion has a smaller ionic radius than the I– ion. Therefore, NaBr has the most exothermic lattice energy in this pair.

c. BaCl2, BaO

For this pair, we have Ba2+ ions (Ba: 149 pm) in both compounds. The charges of Cl– (181 pm) and O2– (140 pm) ions differ, but their sizes are not significantly different. However, the charge of the O2– ion is greater than the charge of Cl– ion which increases lattice energy. Since lattice energy is directly proportional to the charges of ions, BaO will have a greater lattice energy. Therefore, BaO has the most exothermic lattice energy in this pair.

d. Na2SO4, CaSO4

In this pair, both compounds have SO42- ions. Na2SO4 has Na+ ions (116 pm) , and CaSO4 has Ca2+ ions (114 pm). Comparing the charges, Na+ ions have a charge of +1, while Ca2+ ions have a charge of +2. Since lattice energy is directly proportional to the charges of the ions, CaSO4 has greater lattice energy. Therefore, CaSO4 has the most exothermic lattice energy in this pair.

e. KF, K2O

For this pair, we have K+ ions (K+: 152 pm) in both compounds. F– ions (133 pm) and O2– ions (140 pm) differ in both charge and size. Since lattice energy is directly proportional to the charges, K2O has a greater lattice energy due to the presence of O2– ions. Therefore, K2O has the most exothermic lattice energy in this pair.

f. Li2O, Na2S

In this pair, both compounds have ions with charges of +1 and -2. Comparing Ionic radii, Li+ ions (76 pm) have a smaller radius than Na+ ions(116 pm), while O2– ions (140 pm) have a smaller radius than S2– ions (184 pm). Since lattice energy is inversely proportional to the sum of the ionic radii, Li2O with the smaller ionic radii will have a greater lattice energy. Therefore, Li2O has the most exothermic lattice energy in this pair.

Key concepts

Ionic Compounds

Ionic compounds are chemical compounds composed of ions held together by electrostatic forces, known as ionic bonds. These ions are atoms or molecules that have lost or gained electrons, thus acquiring an electric charge. Ionic compounds are generally formed between metallic elements, which typically lose electrons to become positively charged cations, and non-metallic elements, which gain electrons to become negatively charged anions.

These compounds are typically characterized by high melting points, due to the strong attraction between the ions. They also exhibit unique solubility properties, often dissolving well in water and other polar solvents. Ionic compounds are usually solid at room temperature and can conduct electricity when melted or dissolved in water, as the ions are free to move. Examples of ionic compounds include sodium chloride (NaCl), magnesium oxide (MgO), and calcium fluoride (CaF extsubscript{2}). By understanding the nature of ionic compounds, we can better comprehend conceptually challenging topics, like lattice energy and its dependency on ionic radii and ion charges.

• Formed between metals and non-metals
• Feature ionic bonds due to electron transfer
• Exhibit high melting points and solubility in polar solvents

Ionic Radii

Ionic radii refer to the effective radius an ion exerts within an ionic crystal lattice, impacting the structural arrangement and the properties of the material. When an atom loses or gains electrons, it forms an ion whose size will be different from the radius of the original neutral atom.

Cations, which are positively charged ions formed by the loss of electrons, are generally smaller in size than their parent atom because they have less electron cloud. On the other hand, anions, which are negatively charged and formed by the gain of electrons, are larger because they have gained additional electron density. The size of an ion influences the lattice energy significantly; smaller ions will form more stable lattices with higher lattice energy due to the reduced distance between the oppositely charged ions.

For example, lithium fluoride (LiF) has a higher lattice energy compared to cesium fluoride (CsF) because the lithium ion is smaller than the cesium ion, making the ions closer in the lattice and more strongly attracted.

• Ionic radii affect lattice energy
• Cations are smaller than their parent atoms
• Anions are larger than their parent atoms

Charge of Ions

The charge of ions, both positive and negative, is a fundamental factor in determining the properties of ionic compounds, particularly lattice energy. The charge of an ion arises from the loss or gain of electrons compared to the neutral atom. A more positively or negatively charged ion will exert a stronger electrostatic force in the lattice.

According to Coulomb's law, the force of attraction between oppositely charged ions is directly proportional to the product of the charges involved. As a result, ionic compounds composed of ions with higher charges will typically have higher lattice energies, leading to more exothermic reactions when the lattice forms.

For example, consider barium oxide (BaO) over barium chloride (BaCl extsubscript{2}). BaO exhibits greater lattice energy due to the higher charge of the oxide ion ( extsuperscript{2-}) compared to the chloride ion ( extsuperscript{-}). This increased charge results in a stronger attraction within the lattice.

• Ions with higher charges result in higher lattice energies
• Charge directly influences the strength of electrostatic forces
• Greater charge difference leads to more exothermic lattice formations