Problem 4 - Chemistry and Chemical Reactivity

Question

Using spdf notation, give the electron configuration of vanadium, \(\mathrm{V},\) an element found in some brown and red algae and some toadstools.

Step-by-Step Solution

Answer

Vanadium has the electron configuration \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3 \).

Step 1: Understand the Atomic Number

To find the electron configuration of vanadium (V), we first need to identify its atomic number. Vanadium is element number 23 on the periodic table, which means it has 23 electrons.

Step 2: Write the Electron Configuration Result from Aufbau Principle

Using the Aufbau principle, we fill the orbitals in the order of increasing energy: the 1s level first, then 2s, 2p, 3s, 3p, 4s, and finally 3d as follows: \[ 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3 \].Here, the sum of the superscripts equals the 23 electrons.

Step 3: Verify the Configuration

Double-check your configuration to ensure the sum of electrons matches vanadium's atomic number (23). The configuration correctly uses up all 23 electrons across different orbitals, complying with the Aufbau principle and Hund's rule.

Key Concepts

Aufbau principle

In chemistry, the Aufbau principle plays a key role in determining the electron configuration of an atom. This principle suggests that electrons fill atomic orbitals in order of increasing energy levels. An easy way to remember this is by using the phrase "aufbau" which means "building up" in German.
Initially, electrons occupy the lowest energy level available and, once filled, they move to the next higher level.

• The sequence is 1s, 2s, 2p, 3s, 3p, 4s, and then 3d.
• Each orbital can hold a specific number of electrons, with s holding 2, p holding 6, and d holding 10.
• For vanadium, you'll place its 23 electrons by following this orbital filling order, ensuring you don't skip any orbital unless it's fully filled.

This systematic approach helps ensure that we account for all electrons properly, getting the exact electron configuration needed.

Hund's rule

Hund's rule is another important guideline that tells us how electrons distribute themselves among orbitals. This rule states that electrons will fill an unoccupied orbital before they pair up. Think of it like friends sitting on a bus. They prefer to sit alone rather than sharing a seat with others.

• For example, in a p or d orbital set, each orbital gets one electron before any of them get a second one.
• This helps to minimize electron-electron repulsion, keeping the atom as stable as possible.
• In the case of vanadium, once the 4s orbital is filled with 2 electrons, its extra electrons start to fill the 3d orbitals, each occupying a different d orbital until they're all sitting unpaired.

Applying Hund's rule ensures we have a configuration that is low in energy and high in stability for the atom.

atomic number

An atom's atomic number is its identity card within the periodic table. It tells you the number of protons an atom has, which usually also equals the number of electrons in a neutral atom. This number not only defines the element but is crucial in writing electron configurations, like that of vanadium.

• Vanadium's atomic number is 23, indicating it has 23 electrons.
• Knowing the atomic number is the first step in determining any element's electron configuration.
• The number of protons, hence electrons, helps you fill orbitals correctly according to the Aufbau principle and Hund's rule.

This understanding is fundamental to learning how electrons are distributed around an atom, which influences its chemical properties and reactivity.

vanadium

Vanadium is a fascinating element found in some natural sources like algae and toadstools. With an atomic number of 23, it has a distinctly unique electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³. This configuration showcases the correct application of both the Aufbau principle and Hund's rule.

• Vanadium belongs to the transition metals, found in the middle of the periodic table between groups 3 and 12.
• Its properties are influenced by the partially filled d orbitals, which give rise to its various oxidation states.
• This makes vanadium valuable in industries, especially in steel-making and chemical reactions, because of its robustness and versatility.

Understanding its electron configuration helps explain why vanadium can form different compounds and participate in diverse chemical reactions.