The ionic substances KF, CaO, and Sc N are isoelectronic (they have the same number of electrons

step 1 In this problem, first I'm just writing the lattice energy. So lattice energy of KF is equal to

The ionic substances KF, CaO, and Sc N are isoelectronic...

The ionic substances $\mathrm{KF}, \mathrm{CaO}$, and $\mathrm{Sc} \mathrm{N}$ are isoelectronic (they have the same number of electrons). Examine the lattice energies for these substances in Table $8.2$, and account for the trends you observe.

Key Concepts

Lattice Energy

Lattice energy is the energy released when gaseous ions combine to form an ionic solid. It reflects the strength of the ionic bonds in the crystal lattice and is primarily determined by the charges of the ions and the distances between them. A higher lattice energy indicates stronger electrostatic interactions, leading to greater stability of the ionic compound.

Coulomb's Law

Coulomb's law describes the electrostatic force between charged particles, and it is a key factor in understanding lattice energy. The law states that the force—and thereby the potential energy—between two ions is directly proportional to the product of their charges and inversely proportional to the distance between them. This principle explains why ionic compounds with higher charges or smaller ionic radii exhibit higher lattice energies.

Ionic Charges

The magnitude of the ionic charges greatly influences the lattice energy in an ionic compound. In general, the larger the charges on the cation and anion, the stronger the electrostatic attraction between them. This concept is crucial for comparing compounds in an isoelectronic series, where differences in charge can lead to variations in lattice energies despite having the same number of electrons.

Ionic Radii and Trends

The size of the ions, or ionic radii, impacts the distance between the centers of the ions in the lattice and therefore the magnitude of the lattice energy. In isoelectronic series, although the ions have the same number of electrons, differences in nuclear charge cause variations in ionic size. Smaller ions lead to shorter interionic distances, resulting in stronger Coulombic interactions and higher lattice energies.

Isoelectronic Series

An isoelectronic series consists of ions or atoms that have the same number of electrons. In such a series, differences in properties like ionic radius and effective nuclear charge become apparent. Higher nuclear charge draws electrons closer to the nucleus, reducing the ionic radius and enhancing the electrostatic attractions when forming ionic compounds, which in turn affects the lattice energy.

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