Problem 38 - Chemistry and Chemical Reactivity

Question

The rare earth elements, or lanthanides, commonly exist as \(3+\) ions. Using an orbital box diagram and noble gas notation, show the electron configurations of the following elements and ions. (a) Ce and \(\mathrm{Ce}^{3+}\) (cerium) (b) Ho and \(\mathrm{Ho}^{3+}\) (holmium)

Step-by-Step Solution

Answer

Ce: [Xe] 6s² 4f¹ 5d¹ Ce³⁺: [Xe] 4f¹ Ho: [Xe] 6s² 4f¹¹ Ho³⁺: [Xe] 4f¹⁰

Step 1: Identify the Element's Atomic Number

The atomic number of cerium (Ce) is 58, and holmium (Ho) is 67. This tells us how many electrons are present in each neutral atom.

Step 2: Determine the Electron Configuration for Ce

For Ce, the full electron configuration is determined by filling the orbitals until reaching atomic number 58: \[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^1 \, 5d^1 \] Using noble gas notation, this becomes \[ [Xe] \, 6s^2 \, 4f^1 \, 5d^1 \]

Step 3: Determine the Electron Configuration for \\mathrm{Ce}^{3+}

Ce loses 3 electrons to form a \( \mathrm{Ce}^{3+} \) ion. The electrons are usually removed from the outermost energy levels: \[ [Xe] \, 6s^2 \, 4f^1 \, 5d^1 \rightarrow [Xe] \, 4f^1 \] as the 5d and 6s orbitals lose electrons first.

Step 4: Use Orbital Box Diagrams for Ce and \\mathrm{Ce}^{3+}

Draw the orbital box diagrams for Ce with the configuration \[ [Xe] \, 6s^2 \, 4f^1 \, 5d^1 \] showing single electrons in the 4f and 5d boxes along with filled 6s. For \mathrm{Ce}^{3+}, the box for \( 5d \) and one \( 6s \) electron is empty.

Step 5: Determine the Electron Configuration for Ho

For Ho, the full electron configuration fills orbitals for atomic number 67:\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{11} \] Using noble gas notation, this becomes \[ [Xe] \, 6s^2 \, 4f^{11} \]

Step 6: Determine the Electron Configuration for \\mathrm{Ho}^{3+}

Ho loses 3 electrons forming \( \mathrm{Ho}^{3+} \), which are removed from \( 6s^2 \) and \( 4f^1 \): \[ [Xe] \, 6s^2 \, 4f^{11} \rightarrow [Xe] \, 4f^{10} \]

Step 7: Use Orbital Box Diagrams for Ho and \\mathrm{Ho}^{3+}

Draw the orbital box diagram for Ho with \[ [Xe] \, 6s^2 \, 4f^{11} \], showing filled 6s boxes and partially filled 4f boxes. For \( \mathrm{Ho}^{3+} \), the 6s box is empty and 4f has 10 electrons.

Key Concepts

Lanthanides

Lanthanides, also known as rare earth elements, are a group of 15 elements in the periodic table from lanthanum (La) to lutetium (Lu). These elements are found in the f-block and are characterized by filling of the 4f sublevel. They typically have similar properties:

• They are all metals with a shiny and silvery-white appearance.
• Most lanthanides are known to have high melting points.
• They are known for forming stable +3 oxidation states, known as 3+ ions, due to the loss of three electrons, which makes them quite common when contributing to chemical reactions.

The electron configurations of lanthanides include filling the 4f orbitals, which can contain up to 14 electrons. This unique characteristic makes them particularly important in high-tech industries, including electronics, magnets, and alloys.

Orbital Box Diagram

An orbital box diagram is a visual tool used to represent the electron configuration of an atom explicitly showing how electrons populate the orbitals. Each box represents an orbital, and each arrow within the box represents an electron. These diagrams help convey important information about electron configuration such as:

• The number of electrons in each orbital or sublevel.
• The spin of the electrons, which is indicated by the direction of the arrow.

For instance, in the case of the electron configuration for cerium (Ce), using the notation \[ [Xe] \, 6s^2 \, 4f^1 \, 5d^1 \] the orbital box diagram would include filled boxes for 6s, 4f, and 5d, with the relevant electrons indicated by arrows. When dealing with ions like \( \mathrm{Ce}^{3+} \), which have lost electrons, the diagram would show empty spaces in the boxes where electrons were removed. This visual representation is pivotal in understanding how electrons are distributed in various energy levels and sublevels.

Noble Gas Notation

Noble gas notation is a shorthand method of writing electron configurations. It allows us to abbreviate the configuration by using the symbol of the noble gas that precedes an element on the periodic table. Noble gases, such as xenon (Xe), have completely filled electron shells, which are stable and energy-efficient to use as a reference point. For example, the full electron configuration for cerium (Ce) can be quite lengthy, but with noble gas notation, it becomes more manageable as \[ [Xe] \, 6s^2 \, 4f^1 \, 5d^1 \]. Here, \([Xe]\) stands in place of the completely filled shells up to that point. This notation not only simplifies writing but also improves clarity and understanding, making it easier to focus on the electron changes in chemical reactions or ion formation.

Ions

Ions are atoms or molecules that have gained or lost electrons, resulting in a net electrical charge. An ion forms when an atom either gives up or gains one or more electrons to achieve a more stable, lower-energy electron configuration. When an atom loses electrons, it becomes positively charged and is referred to as a cation. Conversely, gaining electrons will result in a negatively charged ion, known as an anion. In the context of lanthanides, such as cerium (Ce) and holmium (Ho), forming cations with a 3+ charge is common. This occurs by the removal of their outermost electrons, reducing their electron count from three of the outermost shells. For cerium, when forming \( \mathrm{Ce}^{3+} \), electrons are specifically lost from the 6s and 5d orbitals. Understanding ions is crucial for grasping the ionic nature of bonds in compounds and the behavior of elements during chemical reactions.