Problem 44 - Chemistry A Molecular Approach

Question

Rubidium iodide has a lattice energy of \(-617 \mathrm{kj} / \mathrm{mol},\) 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?

Step-by-Step Solution

Answer

Potassium bromide has more exothermic lattice energy than rubidium iodide because potassium and bromide ions are smaller than rubidium and iodide ions, allowing for a more closely packed crystal lattice and stronger electrostatic attractions.

Step 1: Understand Lattice Energy

Lattice energy is the energy required to break apart an ionic compound into gaseous ions, or conversely, the energy released when gaseous ions combine to form an ionic solid. A more negative lattice energy indicates a stronger ionic bond and a more exothermic lattice formation.

Step 2: Consider the Ionic Radii

Compare the radii of the ions involved in both compounds. Rubidium (Rb) is larger than potassium (K) because Rb is lower on the periodic table, meaning it has more electron shells. Similarly, iodide (I) is larger than bromide (Br). Smaller ions can pack more closely together, increasing the electrostatic interactions between the ions, which makes the lattice energy more exothermic.

Step 3: Recognize the Charges

Both rubidium iodide (RbI) and potassium bromide (KBr) are composed of ions with a +1 and -1 charge respectively. Since the charges are the same, they do not account for the difference in lattice energies.

Step 4: Compare Ion Sizes and Lattice Energy

Having established that the charge is the same, the difference in lattice energies between RbI and KBr must be due to the differences in ionic radii. Potassium ions are smaller than rubidium ions and bromide ions are smaller than iodide ions, so potassium bromide can form a more closely packed lattice, resulting in a more exothermic lattice energy.

Key Concepts

Ionic Compounds

Ionic compounds are chemical substances made of ion pairs held together by strong electrostatic forces known as ionic bonds. They form when metals transfer electrons to non-metals, creating cations (positively charged ions) and anions (negatively charged ions). This transfer leads to a characteristic crystalline structure known as a lattice, where ions are fixed in an extensive three-dimensional network.

For students to have a concrete understanding of the underlying principles, imagine ionic compounds as a highly organized dance of particles, with each ion following strict spatial rules to maintain the stability and integrity of the structure. Their unique properties, such as high melting and boiling points, are a direct result of the strong attractions within the lattice.

Ionic Radii

The ionic radius is a measure of the size of an ion in a crystal lattice and is crucial in determining the properties of an ionic compound. Ions have different sizes because of the number of electrons they possess and the way those electrons are arranged in shells around the nucleus.

Understanding ionic radii is similar to knowing the space required for each dancer in a group performance; if the dancers are smaller, they can stand closer together and move more efficiently. In ionic compounds, smaller ions result in a tighter lattice and greater electrostatic attraction between them. Therefore, when comparing ions, expect those with fewer electron shells (due to being higher up on the periodic table) to have smaller radii. Similarly, when an atom loses electrons to become a cation, its radius decreases, whereas gaining electrons to become an anion increases the radius.

Periodic Table Trends

The periodic table is a map of chemical elements, providing insights into the trends and properties of these elements. One of the key trends observed is atomic and ionic size, which generally increases as we move down a group and decreases as we move across a period from left to right.

These trends can be visualized as the arrangement of seats in a theater; rows correspond to periods and columns to groups. Seats become wider as you move towards the back (down a group) and narrower as you move from left to right (across a period). This analogy helps students to understand why rubidium ions are larger than potassium ions, as rubidium is located lower in the periodic table, and why bromide ions are smaller than iodide ions, as bromine is located above iodine.

Electrostatic Interactions

Electrostatic interactions are the forces that hold ions together in ionic compounds. Just like magnets, ions with opposite charges attract each other. The strength of this attraction is influenced by the size of the ions (ionic radii) and the magnitude of their charges.

Consider it as a dance where the partners, the ions, must maintain hand contact (the ionic bond). The smaller the hands (ionic radii), the stronger they can hold onto each other, and the closer they can be. For ions with the same charge, the smaller ions will result in a more compact structure, hence, a more negative lattice energy, indicating a stronger bond forming process. This is why potassium bromide, with its smaller ions compared to rubidium iodide, has stronger electrostatic interactions and, consequently, a more exothermic lattice energy.