Problem 106 - Chemistry: Atoms First

Question

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_

Step-by-Step Solution

Answer

The compounds with larger lattice energy are (a) \(\mathrm{Na}_2\mathrm{O}\), (b) \(\mathrm{BaS}\), (c) \(\mathrm{BaS}\), (d) \(\mathrm{BaS}\).

Step 1 - Understand Lattice Energy

Lattice energy is the energy released when gaseous ions come together to form an ionic solid. The larger the charge on the ions and the smaller their radii, the greater the lattice energy.

Step 2 - Compare Ionic Charges and Radii for (a)

For \(\mathrm{K}_2\mathrm{O}\) and \(\mathrm{Na}_2\mathrm{O}\), the ions \(\mathrm{O}^{2-}\) are identical. Therefore, the lattice energy depends on the cations. Na+ has a smaller radius and higher charge density than K+, so \(\mathrm{Na}_2\mathrm{O}\) has higher lattice energy.

Step 3 - Compare Ionic Charges for (b)

In \(\mathrm{K}_2\mathrm{S}\) and \(\mathrm{BaS}\), \(\mathrm{S}^{2-}\) ions are identical. \(\mathrm{Ba}^{2+}\) has a larger charge than \(\mathrm{K}^{+}\). Despite the similar size of \(\mathrm{Ba}^{2+}\) and \(\mathrm{K}^{+}\), the greater charge on \(\mathrm{Ba}^{2+}\) results in a larger lattice energy for \(\mathrm{BaS}\).

Step 4 - Consider Ion Sizes and Charges for (c)

Comparing \(\mathrm{KCl}\) and \(\mathrm{BaS}\), \(\mathrm{K}^{+}\) and \(\mathrm{Ba}^{2+}\) have similar radii, but \(\mathrm{Ba}^{2+}\) has a higher charge. \(\mathrm{S}^{2-}\) and \(\mathrm{Cl}^{-}\) have similar radii, but \(\mathrm{S}^{2-}\) has a higher charge. The \(\mathrm{BaS}\) compound has ions with higher charges, hence larger lattice energy.

Step 5 - Compare Anion Radii for (d)

For \(\mathrm{BaS}\) and \(\mathrm{BaCl}_2\), the cation \(\mathrm{Ba}^{2+}\) is the same in both. Considering the anions, \(\mathrm{S}^{2-}\) has a higher charge than \(\mathrm{Cl}^{-}\), and similar size. Thus, \(\mathrm{BaS}\) has a larger lattice energy due to the higher charge on the anion.

Key Concepts

Ionic Solids

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.

Ionic Charges

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

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.