Question

Give the electronic configurations of the following atoms and ions: \((\mathrm{a}) \mathrm{V}^{3+} ;(\mathrm{b}) \mathrm{Fe} ;(\mathrm{c}) \mathrm{Cr},(\mathrm{d}) \mathrm{Ag}^{+} ;(\mathrm{e}) \mathrm{Fe}(0)\left(\mathrm{in}\left[\mathrm{Fe}(\mathrm{CO})_{5}\right]\right]\) \((f) C u^{2+} ;(g) R u^{2+} ;(h) W^{4+},(\text { Section } 28.1)\)

Short answer

Electron configurations: a) V^{3+}: [Ar] 3d^2 b) Fe: [Ar] 3d^6 4s^2 c) Cr: [Ar] 3d^5 4s^1 d) Ag^{+}: [Kr] 4d^{10} e) Fe(0) in [Fe(CO)_5]: [Ar] 3d^8 4s^2 f) Cu^{2+}: [Ar] 3d^9 g) Ru^{2+}: [Kr] 4d^6 h) W^{4+}: [Xe] 4f^{14} 5d^2

Step-by-step solution

Understand the Basics of Electron Configurations

Electron configurations describe how electrons are distributed in an atom or ion's orbitals. The configuration follows Aufbau's principle, Hund's rule, and Pauli's exclusion principle. The configuration of an atom is determined by its atomic number (number of protons, which equals the number of electrons in a neutral atom). For ions, adjust for the charge: add electrons for negative charges and remove electrons for positive charges.

Electron Configuration for V, V^{3+}

Vanadium (V) has an atomic number of 23. The electron configuration is: \[ \text{V: } [\text{Ar}] \, 3d^3 \, 4s^2 \]For the \( \text{V}^{3+} \) ion, remove three electrons. Electrons are removed from the outermost shell first, so the configuration becomes:\[ \text{V}^{3+}: [\text{Ar}] \, 3d^2 \]

Electron Configuration for Fe

Iron (Fe) has an atomic number of 26. The electron configuration is: \[ \text{Fe: } [\text{Ar}] \, 3d^6 \, 4s^2 \]

Electron Configuration for Cr

Chromium (Cr) has an atomic number of 24. Due to electron configuration stability (half-filled d subshell), it has the configuration: \[ \text{Cr: } [\text{Ar}] \, 3d^5 \, 4s^1 \]

Electron Configuration for Ag, Ag^{+}

Silver (Ag) has an atomic number of 47. The electron configuration is:\[ \text{Ag: } [\text{Kr}] \, 4d^{10} \, 5s^1 \]For \( \text{Ag}^{+} \), remove one electron from the 5s orbital:\[ \text{Ag}^{+}: [\text{Kr}] \, 4d^{10} \]

Electron Configuration for Fe(0) in [Fe(CO)_5]

In a coordination complex like [Fe(CO)_5], iron typically adopts a lower oxidation state than in free metal form. Thus, Fe in Fe(CO)_5 is formally in the zero oxidation state, \[ \text{Fe(0) in } [\text{Fe(CO)}_{5}]: [\text{Ar}] \, 3d^8 \, 4s^2 \]

Electron Configuration for Cu^{2+}

Copper (Cu) has an atomic number of 29. The neutral atom configuration is:\[ \text{Cu: } [\text{Ar}] \, 3d^{10} \, 4s^1 \]For \( \text{Cu}^{2+} \), remove two electrons; one from the 4s and one from the 3d:\[ \text{Cu}^{2+}: [\text{Ar}] \, 3d^9 \]

Electron Configuration for Ru, Ru^{2+}

Ruthenium (Ru) has an atomic number of 44. The neutral configuration is:\[ \text{Ru: } [\text{Kr}] \, 4d^7 \, 5s^1 \]For \( \text{Ru}^{2+} \), remove two electrons, prioritizing first from the 5s then from 4d:\[ \text{Ru}^{2+}: [\text{Kr}] \, 4d^6 \]

Electron Configuration for W^{4+}

Tungsten (W) has an atomic number of 74. The neutral atom configuration is:\[ \text{W: } [\text{Xe}] \, 4f^{14} \, 5d^{4} \, 6s^2 \]For \( \text{W}^{4+} \), remove four electrons; two from 6s and two from 5d:\[ \text{W}^{4+}: [\text{Xe}] \, 4f^{14} \, 5d^2 \]

Key concepts

Vanadium Configuration

Vanadium has an atomic number of 23, which means it has 23 electrons when neutral. The electron configuration for a neutral vanadium atom is \( [\text{Ar}] \, 3d^3 \, 4s^2 \).
To derive the configuration of the vanadium ion \(\text{V}^{3+}\), you remove three electrons.
Electrons are first removed from the highest energy level, which in this case is the 4s orbital, followed by the 3d orbital.
Thus, the configuration becomes \( [\text{Ar}] \, 3d^2 \).
This shows that oxidation states affect electron configuration, especially in transition metals which have close energy levels.

Iron Configuration

Iron, with an atomic number of 26, has 26 electrons. The electron configuration for a neutral iron atom is \( [\text{Ar}] \, 3d^6 \, 4s^2 \).
In its elemental form, iron can form different complexes based on its ability to lose electrons from its 4s and 3d orbitals which have close energy levels.
Iron's configuration is foundational in understanding its magnetic properties and behavior in chemical bonding, as it often forms ferrous \((\text{Fe}^{2+})\) and ferric \((\text{Fe}^{3+})\) ions.

Chromium Configuration

Chromium is unique among transition elements due to its electron configuration. With an atomic number of 24, it adopts the unusual configuration \( [\text{Ar}] \, 3d^5 \, 4s^1 \) instead of the expected \( [\text{Ar}] \, 3d^4 \, 4s^2 \).
This configuration reflects a half-filled d subshell, which offers greater stability due to decreased electron-electron repulsion and increased exchange energy.
This exception to expected filling rules shows how electronic structure principles are adapted based on individual element stability.

Silver Ion Configuration

Silver's atomic number is 47, giving it the neutral configuration \( [\text{Kr}] \, 4d^{10} \, 5s^1 \).
When silver ionizes to form \(\text{Ag}^{+}\), it loses the single 5s electron, resulting in the stable configuration \( [\text{Kr}] \, 4d^{10} \).
The full d subshell in silver ions is highly stable and is a factor in the element's conductivity and luster.

Copper Ion Configuration

Neutral copper, with an atomic number of 29, forms a stable configuration of \( [\text{Ar}] \, 3d^{10} \, 4s^1 \).
When it forms the \(\text{Cu}^{2+}\) ion, two electrons are removed, one from the more mobile 4s and one from the 3d orbital, leading to the configuration \( [\text{Ar}] \, 3d^9 \).
Copper ions with partially filled d subshells play a significant role in their catalytic and thermal properties.

Coordination Complex

In a coordination complex such as \([\text{Fe(CO)}_5]\), the electronic structure of the central metal atom affects the entire complex's properties.
In this example, the iron is in zero oxidation state because it is a complex with neutral ligands (carbon monoxide here).
The configuration of iron in such a complex is \( [\text{Ar}] \, 3d^8 \, 4s^2 \).
This impacts the geometry, oxidation state, and magnetic properties of the entire coordination compound.

Ruthenium Ion Configuration

Ruthenium, with an atomic number of 44, normally has a configuration of \( [\text{Kr}] \, 4d^7 \, 5s^1 \).
When ruthenium forms a \(\text{Ru}^{2+}\) ion, two electrons are extracted, preferably starting from the 5s, then from the more stable 4d orbitals.
This results in the configuration \( [\text{Kr}] \, 4d^6 \).
Understanding the electronic properties of ruthenium is crucial in fields such as catalysis and materials science.

Tungsten Ion Configuration

Tungsten, with an atomic number of 74, has a neutral atom configuration of \( [\text{Xe}] \, 4f^{14} \, 5d^4 \, 6s^2 \).
To form \(\text{W}^{4+}\), four electrons are removed.
Typically, this involves the 6s electrons and two of the 5d electrons, leading to \( [\text{Xe}] \, 4f^{14} \, 5d^2 \).
This rearrangement of electrons influences tungsten's properties, such as high melting point and toughness.

Electronic Structure Principles

Several principles guide the distribution of electrons in atoms and ions:

• Aufbau Principle: Electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels.
• Hund's Rule: Electrons fill degenerate orbitals singly first to maximize parallel spins.
• Pauli Exclusion Principle: No two electrons can have the same set of four quantum numbers; each orbital can hold a maximum of two electrons with opposite spins.

These principles explain why elements have specific electron configurations and why transition metals have unique properties such as multiple oxidation states and variable magnetic characteristics.
Understanding these principles is essential for grasping atomic interactions, chemical bonding, and overall material behavior.