Problem 58 - General Chemistry: Principles and Modern Applications

Question

Although the triiodide ion, \(\mathrm{I}_{3}^{-}\), is known to exist in aqueous solutions, the ion is stable in only certain ionic solids. For example, \(\mathrm{CsI}_{3}\) is stable with respect to decomposition to CsI and \(\mathrm{I}_{2},\) but \(\mathrm{LiI}_{3}\) is not stable with respect to LiI and I \(_{2}\). Draw a Lewis structure for the \(I_{3}^{-}\) ion and suggest a reason why \(\mathrm{CsI}_{3}\) is stable with respect to decomposition to the iodide but \(\mathrm{LiI}_{3}\) is not.

Step-by-Step Solution

Answer

The \(I_{3}^{-}\) ion has a linear structure with the middle iodine atom bonded to the two terminal iodine atoms. \(\mathrm{CsI}_{3}\) is more stable than \(\mathrm{LiI}_{3}\) due to its lower lattice energy, which is the result of the larger size of the cesium ion compared to the lithium ion.

Step 1: Drawing the Lewis Structure for \(I_{3}^{-}\)

The Lewis structure for the \(I_{3}^{-}\) ion is as follows: Three iodine atoms are arranged linearly, with the middle iodine bonded to the two terminal iodines. On each terminal iodine there are three pairs of non-bonding electrons, while on the central iodine there is one pair of nonbonding electrons and one additional electron. These additional two electrons gives the ion negative charge.

Step 2: Analyze the stability of \(\mathrm{CsI}_{3}\) and \(\mathrm{LiI}_{3}\)

The stability of ionic solids like \(\mathrm{CsI}_{3}\) and \(\mathrm{LiI}_{3}\) can be related to the lattice energy of the solid. Lattice energy refers to the energy required to separate one mole of an ionic compound into its gas phase ions. Higher lattice energy implies higher stability.

Step 3: Explain the difference in stability

The lattice energy depends on the size and charge of the ions, and their packing in the solid. Cesium (Cs) ions are larger than lithium (Li) ions. Larger ions tend to have lower lattice energies because the ions are farther apart and the electrostatic attractive forces are therefore weaker. Therefore, \(\mathrm{CsI}_{3}\) is likely to have a lower lattice energy (hence more stability) as compared to \(\mathrm{LiI}_{3}\).

Key Concepts

Lewis Structure

Understanding the Lewis structure is essential for predicting the geometry and reactivity of molecules. In the case of the triiodide ion (\(I_{3}^{-}\)), the Lewis structure showcases a linear arrangement with a central iodine atom bonded to two terminal iodine atoms. Each bond between iodine atoms is actually a coordinate covalent bond where one iodine donates a pair of electrons.

The central iodine has one lone pair, while the terminal iodines have three lone pairs each, spreading out to minimize repulsion in a linear shape. The negative charge indicates an extra electron, which is typically depicted on the central iodine atom. This structure can help explain the properties and the stability of ionic compounds containing the triiodide ion. Visualizing the electron distribution through the Lewis structure can also give insights into the molecule's polarizability, which affects intermolecular interactions.

Lattice Energy

Moving to the concept of lattice energy, it's the measure of an ionic compound's stability determined by the energy required to separate its ions in the gas phase. This energy reflects the strength of the electrostatic forces between oppositely charged ions.

Higher lattice energy correlates with stronger ionic bonds and therefore more stable compounds. It is affected by both the charge on the ions and their sizes. Larger ions have a lower charge density and therefore weaker attractions, leading to lower lattice energy. Conversely, smaller ions or those with higher charges have higher lattice energy. In the case of triiodide ions in CsI3 and LiI3, the size difference between Cs+ and Li+ ions influences their lattice energies significantly and hence their stabilities.

Ionic Solids

The stability of ionic solids, such as those containing triiodide ions, is inherently tied to the concepts of lattice energy and ionic bonding. Ionic solids are structured in a lattice framework, where ions are locked in a repeating pattern that maximizes the attraction between oppositely charged ions while minimizing repulsion.

In the context of CsI3 and LiI3, we can infer that the lattice structure of CsI3 is more stable because of the larger size of Cs+ ions compared to Li+ ions, yielding a more substantial overall lattice that adheres more robustly to its components. Consequently, ionic solids with the right balance of ion size and charge can create highly stable structures.

Chemical Decomposition

Finally, when discussing chemical decomposition, we're considering the breakdown of a compound into more basic substances. This can occur through various processes, including thermal decomposition, electrolysis, and reaction with other chemicals.

Relating this to CsI3 and LiI3, we look at the tendency of these compounds to decompose into smaller ionic and molecular species, such as CsI and I2. The decomposition will depend largely on the compound's lattice energy, with lower lattice energy often leading to easier chemical decomposition. Therefore, the higher stability of CsI3 compared to LiI3 can be attributed to its resistance to decomposition, which is a consequence of its lower lattice energy and the larger cesium's ability to stabilize the larger triiodide ion.