Question

Rubidium iodide has a lattice energy of \(-617 \mathrm{k} / \mathrm{mol},\) while potassium bromide has a lattice energy of \(-671 \mathrm{kJ} / \mathrm{mol}\) . Why is the lattice energy of potassium bromide more exothermic than the lattice energy of rubidium iodide?

Short answer

Potassium bromide (KBr) has a more exothermic lattice energy than rubidium iodide (RbI) because K+ has a smaller ionic radius than Rb+ and Br- has a smaller ionic radius than I-, leading to a tighter, more energetically stable ionic lattice.

Step-by-step solution

Identify the Elements Involved

Rubidium (Rb) is in Group 1, Period 5 and iodide (I) is in Group 17, Period 5. Potassium (K) is in Group 1, Period 4 and bromide (Br) is in Group 17, Period 4 in the periodic table. We need to consider their positions to understand the lattice energy.

Understand Lattice Energy Trends

Lattice energy is the energy released when ions in the gas phase come together to form a solid ionic lattice. It generally increases with the charge of the ions and decreases as the ionic radius increases. Higher charge and smaller ionic radii lead to a more exothermic lattice energy.

Compare Ionic Radii

Potassium ions are smaller than rubidium ions since potassium is higher up on the periodic table. Smaller ions allow for a tighter ionic lattice resulting in a more exothermic lattice energy.

Consider Anion Size

The bromide anion is smaller than the iodide anion which also contributes to a tighter lattice and hence a higher lattice energy.

Analyze Ion Charges

Both KBr and RbI involve ions with a single positive or negative charge, so the difference in lattice energies must be due to the ionic sizes, not the charges.

Combine Effects of Ionic Size

Since both potassium and bromide ions are smaller than rubidium and iodide ions respectively, potassium bromide (KBr) will form a tighter lattice than rubidium iodide (RbI), resulting in a more exothermic lattice energy.

Key concepts

Ionic Radii

When exploring the world of ionic compounds, understanding ionic radii is essential. Think of it as the measure of an ion's size which plays a critical role in determining many properties of the compound, including lattice energy. As ions come together to form a solid structure, the smaller the ions, the closer they can pack together. This closer packing results in stronger electrostatic attraction between the positive and negative ions, leading to higher lattice energy.

Let's take the textbook example of potassium bromide (KBr) and rubidium iodide (RbI). The smaller ionic radii of potassium compared to rubidium allow for a tighter packing in the KBr lattice. This is mainly due to potassium ion being in a higher period on the periodic table – meaning it has one less electron shell than rubidium, thus it's smaller. Similarly, bromide ions are smaller than iodide ions; as a result, KBr has significantly stronger ionic bonds and consequently a more exothermic lattice energy compared to RbI.

Periodic Trends

Periodic trends are patterns in the periodic table that fundamentally affect the behavior and properties of elements, including their ionic forms. As you move from left to right across a period, the ionic radii decrease because the increasing positive charge of the nucleus pulls electrons closer. Conversely, as you move down a group, ionic radii increase due to the addition of electron shells.

Relevance to Lattice Energy

These trends are directly connected to our example of lattice energies for KBr and RbI. Potassium resides above rubidium in Group 1 of the periodic table, meaning its ions are smaller as per the down-a-group trend. Likewise, bromide is above iodide in Group 17, sharing the same trend. Therefore, the periodic trends help explain why KBr has higher lattice energy than RbI. Recognizing these trends will significantly enhance your ability to predict and rationalize the properties of ionic compounds.

Ionic Bonding

Ionic bonding is at the heart of the ionic compounds and dictates many of their physical properties, such as the lattice energy. These bonds form when one atom gives up an electron to another, resulting in positively charged cations and negatively charged anions which are held together by strong electrostatic forces.

An ideal ionic bond requires a cation with a small radius and high charge to bond with an anion with a relatively large radius and charge. This inequality in size allows the smaller cation to get close to the larger anion, maximizing the electrostatic attraction, which translates to a more stable, and thus more exothermic, lattice energy.

In the context of our textbook problem, although KBr and RbI both consist of ions with single charges, the smaller ions of K+ and Br- lead to a more compact and stronger ionic bonding in KBr, compared to the larger Rb+ and I- ions in RbI. This is a prime example of how ionic radii can influence the strength of ionic bonding and highlight the nuanced yet impactful role of structure at the ionic level in determining compound properties.