Problem 37 - Chemistry and Chemical Reactivity

Question

Using an orbital box diagram and noble gas notation, show the electron configurations of uranium and of the uranium(IV) ion. Is either of these paramagnetic?

Step-by-Step Solution

Answer

Both uranium and uranium(IV) ion are paramagnetic due to unpaired electrons in the 5f orbital.

Step 1: Understanding Uranium's Atomic Configuration

The atomic number of uranium is 92, indicating it has 92 electrons. Following the Aufbau principle, determine its electron configuration. Start filling the orbitals: - 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f.Complete the sequence using the Aufbau diagram. The configuration is \[ [Rn] 5f^3 6d^1 7s^2 \]

Step 2: Drawing the Orbital Box Diagram for Uranium

For the electron configuration elements beyond radon \([Rn]\), draw boxes representing orbitals 5f, 6d, and 7s:- 5f has 7 boxes: Fill three boxes with a single electron each (half-filled, following Hund's rule).- 6d has 5 boxes: Fill one box with a single electron.- 7s has 1 box: Fill with two electrons (paired).

Step 3: Electron Configuration of Uranium(IV) Ion

The uranium(IV) ion, \( \text{U}^{4+} \), loses 4 electrons from the neutral uranium atom. Remove electrons from the highest energy levels first (7s and 5f):- Remove 2 electrons from 7s and 2 electrons from 5f.The resulting electron configuration is: \[ [Rn] 5f^2 6d^1 \]

Step 4: Drawing the Orbital Box Diagram for Uranium(IV) Ion

For \([Rn] \), only the 5f orbitals are relevant after electron removal:- 5f has 7 boxes: Place 2 single electrons in separate boxes.- 6d has 5 boxes: Place 1 electron in one of the boxes (half-filled state maintained). The 7s orbital is now empty.

Step 5: Determining Paramagnetism

Paramagnetism arises from unpaired electrons. Analyze the configurations:- Uranium \( [Rn] 5f^3 6d^1 7s^2 \): In the 5f orbital, there are 3 unpaired electrons, making it paramagnetic.- Uranium(IV) ion \( [Rn] 5f^2 6d^1 \): The 5f orbital has 2 unpaired electrons, which means it is also paramagnetic.

Key Concepts

Orbital Box Diagram

To understand the electron configuration of elements, an orbital box diagram is a crucial tool. This diagram visually represents how electrons fill up atomic orbitals. Each box stands for an orbital, and arrows within them illustrate the presence of electrons. By using Hund's rule and the Aufbau principle, we can determine the filling order and electron arrangements. The boxes are filled starting from the lowest energy orbitals to the higher ones:

• Hund's rule ensures that each orbital in a sub-level is half-filled before any orbital is completely filled.
• The Aufbau principle orders orbitals by increasing energy levels, ensuring they are filled systematically.

For uranium, beyond radon ( obreak [Rn] obreak), the orbitals 5f, 6d, and 7s need to be represented. Here, electrons are added: - 7 boxes for 5f with three electrons placed singly to follow Hund's rule. - 5 boxes for 6d, with one electron. - A single box for 7s, holding a pair of electrons. Uniquely, for the uranium(IV) ion, some electrons are removed, especially from the higher energy 7s and 5f orbitals.

Paramagnetism

Paramagnetism is a characteristic that arises due to the presence of unpaired electrons in an atom's electron configuration. In essence, atoms with one or more unpaired electrons display a tendency to be attracted to a magnetic field. Here's how it connects to uranium and its ions:

• Uranium Atom: The original atomic configuration shows three unpaired electrons in the 5f orbital, resulting in paramagnetic properties.
• Uranium(IV) Ion: After electron removal, it has two unpaired electrons within the 5f orbital, which still indicates paramagnetism.

For students, the key takeaway is understanding that whenever there are unpaired electrons, the atom will experience paramagnetic effects. This knowledge is essential for predicting an atom's response to external magnetic fields.

Uranium(IV) Ion

The uranium(IV) ion, denoted as obreak U^{4+} obreak, represents the uranium atom after losing four electrons. It starts from the neutral uranium atom, with 92 electrons. Once four electrons are removed, the electronic configuration changes dramatically. Here’s what happens:

• Subtractive Electron Removal: The electrons are first taken out from the highest energy orbitals available, the 7s and 5f orbitals. This accounts for the removal order: 2 from 7s and 2 from 5f.
• Remaining Configuration: The resulting electron configuration after electron removal becomes obreak [Rn] 5f^2 6d^1 obreak.

This transformation alters its chemical behavior and magnetic properties. Understanding the ion formation and electron configurations are fundamental to studies involving nuclear chemistry and advanced materials.

Noble Gas Notation

Noble gas notation is an efficient method used to express electron configurations. It makes the process quicker and simpler by relying on the last noble gas preceding the element. It acts as a shortcut to list all occupied electron shells up to that noble gas symbol.

• Example: For uranium ( obreak [Rn] 5f^3 6d^1 7s^2 obreak), radon ( obreak [Rn] obreak) is used as a reference, simplifying its configuration.
• Beyond noble gas: It involves specifying only the electron configuration post the reference noble gas.

The purpose of noble gas notation is to simplify and streamline the way chemists write electron configurations, making complex elements like uranium easier to handle, especially when combined with concepts such as initial orbital filling and electron loss in ions.