Problem 3 - Chemistry The Molecular Science

Question

What is Hund's rule? Give an example of its use.

Step-by-Step Solution

Answer

Hund's rule dictates that electrons fill degenerate orbitals singly with parallel spins. Example: In carbon atom, 2p orbitals are filled singly first.

Step 1: Understand Hund's Rule

Hund's rule states that electrons will fill degenerate orbitals (orbitals with the same energy) singly before filling them doubly. This means that in any given sublevel, one electron will occupy each orbital before any orbital gets a second electron, and all singly occupied orbitals have parallel spins.

Step 2: Illustrate with an Example

Consider the carbon atom, which has six electrons. The electron configuration is 1s² 2s² 2p². The 2p sublevel has three degenerate orbitals. According to Hund's rule, the two 2p electrons will occupy separate orbitals with parallel spins, resulting in the configuration: \[ \uparrow \uparrow \_ \]This ensures electrons are spread out as much as possible in the subshell.

Step 3: Confirm Compliance with Hund's Rule

By filling 2p orbitals singly first before pairing, we comply with Hund's rule. The electron configuration for the 2p sublevel shows two electrons in different orbitals with parallel spins. This avoids electron-electron repulsions that occur when electrons pair up.

Key Concepts

Electron Configuration

Electron configuration describes the distribution of electrons among the various orbitals in an atom or molecule. Each electron occupies an orbital, and each orbital can hold up to two electrons with opposite spins. The configuration is often written as a series of numbers and letters, which represent the principal energy levels, sublevels, and the number of electrons within those sublevels.

For example, in the case of the carbon atom with six electrons, the electron configuration is denoted as 1s² 2s² 2p². This notation indicates that:

• Two electrons fill the 1s orbital,
• Two electrons fill the 2s orbital,
• Two electrons are in the 2p sublevel.

Understanding electron configurations helps predict and explain the chemical behavior of elements as well as their placement in the periodic table. It also lays the foundation for understanding more complex principles like Hund's rule and Pauli Exclusion Principle.

Degenerate Orbitals

Degenerate orbitals are orbitals within the same subshell that have the same energy level. Each sublevel (s, p, d, f) can contain multiple orbitals. For instance, the p sublevel consists of three orbitals (p_x, p_y, and p_z) all having equal energy.

When filling these degenerate orbitals, Hund's rule states that electrons will fill each one singly before any orbital receives a second electron. This approach minimizes repulsion between electrons and stabilizes the atom.

In the context of Hund's rule, degenerate orbitals are critical because they determine how electrons are distributed in a given sublevel. For the carbon atom, we see this concept in action where the 2p sublevel contains three equal-energy orbitals. Electrons in the degenerate orbitals prefer to spread out rather than pair up, which reduces the energy of the arrangement.

Parallel Spins

Parallel spins refer to the phenomenon where electrons occupying separate degenerate orbitals have their spins aligned in the same direction. In accordance with Hund's rule, when electrons fill degenerate orbitals, they do so in a way that maximizes the number of electrons with parallel spins.

This means if the first electron in a degenerate set is spin-up, the next electron will also be spin-up, and so forth, until all orbitals in the set contain one electron. Only then will electrons start pairing up with opposite spins.

For example, in the carbon atom discussed earlier, the electron configuration \[ \text{2p}^2 \] can be depicted as having two electrons in separate orbitals with their spins in the same direction: \[ \uparrow \uparrow \_ \]This alignment minimizes electron-electron repulsions, contributing to the stability of the electronic structure.