Problem 13 - Chemistry and Chemical Reactivity

Question

Using orbital box diagrams and noble gas notation, depict the electron configurations of (a) \(\mathrm{V},\) (b) \(\mathrm{V}^{2+},\) and \((\mathrm{c}) \mathrm{V}^{5+}\) Are any of the ions paramagnetic?

Step-by-Step Solution

Answer

Both V and \(\mathrm{V}^{2+}\) are paramagnetic due to unpaired electrons. \(\mathrm{V}^{5+}\) is not.

Step 1: Understand the Ground State Electron Configuration of Vanadium (V)

The atomic number of vanadium (V) is 23, which means it has 23 electrons in the neutral atom. **Electron configuration:** Start filling the electrons in the increasing order of their energy levels using the Aufbau principle: 1s, 2s, 2p, 3s, 3p, 4s, 3d. So, the configuration for V is: \[\text{V: } \left[ \text{Ar} \right] 3d^3 4s^2 \]**Orbital box diagram:**Fill each suborbital before pairing according to Hund's rule: - 3d: \( \uparrow \uparrow \uparrow \) - 4s: \( \uparrow\downarrow \)

Step 2: Determine the Electron Configuration for \\(\mathrm{V}^{2+}\\)

The ion \( \mathrm{V}^{2+} \) has two fewer electrons than a neutral V atom, giving 21 electrons. **Electron configuration:** Remove the electrons starting from the highest energy level (4s before 3d in this case):\[\text{V}^{2+}: \left[ \text{Ar} \right] 3d^3 \]**Orbital box diagram:** - 3d: \( \uparrow \uparrow \uparrow \) The ion has unpaired electrons in the 3d orbitals, making it paramagnetic.

Step 3: Analyze the Electron Configuration of \\(\mathrm{V}^{5+}\\)

The ion \( \mathrm{V}^{5+} \) has five fewer electrons than the neutral V atom, resulting in 18 electrons, equivalent to the argon configuration. **Electron configuration:** \[\text{V}^{5+}: \left[ \text{Ar} \right] \]There are no electrons in the 3d orbitals, hence no unpaired electrons.

Key Concepts

Orbital Box Diagrams

When learning about electron configurations, orbital box diagrams offer a visual representation to understand the distribution of electrons in an atom's orbitals. Each box represents an orbital, and arrows within these boxes symbolize electrons. The direction of the arrow denotes the electron's spin, either up or down. This helps clearly visualize how electrons fill sublevels following principles like Hund's Rule, which states that electrons occupy orbitals singly first before pairing up with opposite spins.

For example, in a neutral vanadium (V) atom, its electron configuration can be depicted using the [Ar] 3d\(^3\) 4s\(^2\) notation, where an orbital box diagram will show three singly filled 3d orbitals and a filled 4s orbital:

• 3d: \( \uparrow \uparrow \uparrow \)
• 4s: \( \uparrow \downarrow \)

This visual tool aids in quickly identifying unpaired electrons, highlighting paramagnetic characteristics in substances like certain metal ions.

Noble Gas Notation

Simplifying electron configurations for complex atoms can be achieved using noble gas notation. This involves representing the inner-shell electron configuration with a noble gas symbol in brackets, followed by the remaining electrons' configuration. It significantly streamlines the depiction and enhances comprehensibility.

For instance, neutral vanadium (V) has an atomic number of 23. Its full electron configuration is lengthy. By using the noble gas preceding vanadium, argon ([Ar]), in its notation, it becomes: \[ \text{V: } [\text{Ar}] 3d^3 4s^2 \]This notation tells us that vanadium's first 18 electrons match those of argon, which helps in quickly focusing on its outer electron configuration. Noble gas notation is essential in simplifying the understanding of electron distributions, especially for transition elements and their ions, such as in \[ \text{V}^{2+}: [\text{Ar}] 3d^3 \].

Paramagnetism

Paramagnetism is a fascinating property in which materials are attracted by an external magnetic field due to the presence of unpaired electrons. In a material, such unpaired electrons create a magnetic moment since they behave like tiny magnets. Understanding electron configurations, including using orbital box diagrams, aids in determining whether an atom or ion is paramagnetic.

For example, the ion \( \mathrm{V}^{2+} \) has the electron configuration [Ar] 3d\(^3\). Its orbital box diagram for the 3d sublevel is:

• 3d: \( \uparrow \uparrow \uparrow \)

This demonstrates that there are unpaired electrons, thereby confirming paramagnetism in \( \mathrm{V}^{2+} \). On the other hand, \( \mathrm{V}^{5+} \) with the electron configuration [Ar] ends up with no unpaired electrons, making it diamagnetic (not attracted to a magnetic field).

Identifying the unpaired electrons in elements or ions is critical for comprehending their magnetic properties and how they interact with external magnetic fields.