Question

The red color of rubies is the result of the substitution of some \(\mathrm{Cr}^{3+}\) ions for \(\mathrm{Al}^{3+}\) ions in solid \(\mathrm{Al}_{2} \mathrm{O}_{3}\). (a) Using spáf notation with the noble gas notation, write the electron configuration for the Cr atom and for the \(\mathrm{Cr}^{3+}\) ion? (b) Is \(\mathrm{Cr}^{2+}\) paramagnetic? Is \(\mathrm{Cr}^{3+} ?\) (c) The radius of the \(\mathrm{Cr}^{3+}\) ion is \(64 \mathrm{pm}\). How does this compare with the radius of the \(\mathrm{Al}^{3+}\) ion?

Short answer

Cr atom: \([Ar] \, 3d^5 \, 4s^1\), Cr³⁺: \([Ar] \, 3d^3\); both Cr²⁺ and Cr³⁺ are paramagnetic; Cr³⁺ is larger than Al³⁺.

Step-by-step solution

Determine Electron Configuration for Cr Atom

The atomic number of chromium (Cr) is 24. Using the noble gas notation, we begin from argon (Ar) which covers 18 electrons.The remaining electrons are arranged primarily in the 3d and 4s subshells. The electron configuration for Cr is \[[Ar] \, 3d^5 \, 4s^1\]due to its stability with a half-filled d subshell.

Determine Electron Configuration for Cr³⁺ Ion

The Cr³⁺ ion is formed by the loss of 3 electrons from the Cr atom. These electrons are removed from the highest energy level, starting with the 4s subshell and then the 3d subshell.Thus, the electron configuration for Cr³⁺ is \[[Ar] \, 3d^3\]since the 4s electron is removed, and two 3d electrons are removed.

Identify Paramagnetic Nature of Cr²⁺ and Cr³⁺

An ion is paramagnetic if it has unpaired electrons. For the Cr²⁺ ion, which is \[[Ar] \, 3d^4\], there are 4 electrons in the 3d subshell, which results in 4 unpaired electrons, making it paramagnetic.For the Cr³⁺ ion, \[[Ar] \, 3d^3\], there are 3 unpaired electrons in the 3d subshell, also making it paramagnetic.

Compare Ionic Radii of Cr³⁺ and Al³⁺

The radius of a \(\mathrm{Cr}^{3+}\) ion is \(64\,\text{pm}\). The radius of an \(\mathrm{Al}^{3+}\) ion is approximately \(53.5\,\text{pm}\).This shows that the \(\mathrm{Cr}^{3+}\) ion is larger than the \(\mathrm{Al}^{3+}\) ion even though both carry a +3 charge. The greater size of \(\mathrm{Cr}^{3+}\) can be attributed to the addition of electrons in higher energy d-orbitals, which experience less nuclear attraction compared to the s and p orbitals in \(\mathrm{Al}^{3+}\).

Key concepts

Electron Configuration

Electron configuration is like a map of where the electrons reside around an atom's nucleus. Transition metals, like chromium (Cr), have a fascinating electron configuration that doesn't strictly follow the anticipated pattern. Typically, electrons fill the lowest energy levels first. However, in the case of chromium, a special situation arises at its electron configuration, which stabilizes due to having a half-filled d-sublevel, seen as \[[ ext{Ar}] \, 3d^5 \, 4s^1\].This configuration is favored because half-filled and fully filled sub-levels tend to have lower energy and thus are more stable. For the \( ext{Cr}^{3+}\) ion, losing three electrons means two are removed from the 3d sublevel and one from the 4s. This gives \[[ ext{Ar}] \, 3d^3\] as its electron configuration.Understanding these patterns helps explain the unique properties of transition metals.

Paramagnetism

Paramagnetism happens when unpaired electrons within an atom or ion generate a magnetic field, causing the atom to be attracted to external magnetic fields. In the periodic table, transition metals often exhibit paramagnetism because their d-orbitals don't fully fill, leading to unpaired electrons.For instance, with chromium ions, both \( ext{Cr}^{2+}\) and \( ext{Cr}^{3+}\) display paramagnetism. Looking at their configurations, \[[ ext{Ar}] \, 3d^4\] for \( ext{Cr}^{2+}\) and \[[ ext{Ar}] \, 3d^3\] for \( ext{Cr}^{3+}\), we can note that they each have unpaired electrons. Hence, both ions are paramagnetic.This magnetic behavior is important in various applications, such as in MRI machines and in the study of material properties.

Ionic Radii

Ionic radii describe the size of an ion in a crystal lattice. It's crucial to understanding how ions pack together in a solid. Interestingly, ionic radii can vary significantly even among ions with similar charges due to differences in electron sublevels.For example, the \( ext{Cr}^{3+}\) ion is larger than the \( ext{Al}^{3+}\) ion even though both have a +3 charge.

• The \( ext{Cr}^{3+}\) radius is about 64 pm, while \( ext{Al}^{3+}\) is around 53.5 pm.
• The presence of electrons in higher energy d-orbitals in \( ext{Cr}^{3+}\) reduces the effective nuclear charge experienced by the electrons, making the ion larger.
• In contrast, the s and p orbitals in \( ext{Al}^{3+}\) lead to a closer electron-nucleus interaction, resulting in a smaller size.

This concept is important in exploring and designing materials at the atomic level, particularly in metallurgy and solid-state chemistry.

Oxidation States

Oxidation states indicate the degree of oxidation of an atom in a compound. They are important because they help in understanding how elements combine and react with each other, particularly in redox reactions.Transition metals typically exhibit multiple oxidation states because they have varying electron configurations particularly in their d-orbitals that can participate in bonding. For chromium (Cr), the oxidation states range notably from +2 to +6, with \( ext{Cr}^{3+}\) being one of the most stable and common.

• The high number of oxidation states in transition metals stems from the relatively small energy differences between their s and d electrons.
• This flexibility allows these metals to form a plethora of compounds with various properties.

Understanding oxidation states is vital in predicting the properties and behaviors of compounds, especially in industrial applications involving catalysts and colorants.