Which compound in each of the following pairs has the larger lattice energy? Note: \(\mathrm{Ba}^{2+}\) and K 'have similar radii; S^- and Cl- have similar radii. Explain your choices. (a) \(\mathrm{K}_{2} \mathrm{O}\) or \(\mathrm{Na}_{2} \mathrm{O}\) (b) \(\mathrm{K}_{2} \mathrm{S}\) or \(\mathrm{BaS}\) (c) KCl or BaS (d) BaS or BaCl_

Ionic solids are crystalline substances composed of ions bound together by strong electrostatic forces known as ionic bonds. The structure of an ionic solid is a lattice, a regular arrangement of ions extending in three dimensions. Each ion in this lattice is surrounded by ions of opposite charge, which maximizes attraction and minimizes repulsion, leading to the stabilization of the solid.

The energy required to separate these ions into gaseous states is known as lattice energy. It quantifies the strength of the bonding in the ionic solid and is a crucial factor in determining the physical properties of the substance, such as melting point, hardness, and solubility. High lattice energy results in an ionic solid being more stable and having a higher melting point.

The charge of an ion is a fundamental characteristic that significantly impacts the lattice energy of an ionic solid. Generally, the larger the charge on an ion, the stronger the electrostatic force of attraction between ions. Consequently, compounds with highly charged ions tend to have higher lattice energies.

For instance, comparing ions with similar radii, an ion with a 2+ charge will attract an ion with a 2- charge more strongly than an ion with a 1+ charge would attract an ion with a 1- charge. The difference in the magnitude of the charges leads to variations in lattice energy, with the compound consisting of ions with higher charges possessing a larger lattice energy, other factors being equal.

Ion radii, the approximate size of ions, are equally pivotal in determining lattice energy. As the size of an ion increases, its charge density decreases, leading to a reduction in the electrostatic forces of attraction between ions and therefore a lower lattice energy. Smaller ions are able to pack more closely together, intensifying these attractive forces, and resulting in a higher lattice energy.

When comparing ions with the same charge, the ion with the smaller radius will typically contribute to a greater lattice energy in the compound it forms. This is why when analyzing two ionic solids with identical ionic charges, the solid with smaller ions will usually be the one with the larger lattice energy.