Question

Draw a partial (valence-level) orbital diagram, and write the condensed ground-state electron configuration for each: (a) Ti (b) Cl (c) V

Short answer

(a) Ti: [Ar] 4s^2 3d^2 (b) Cl: [Ne] 3s^2 3p^5 (c) V: [Ar] 4s^2 3d^3

Step-by-step solution

Title - Understand the number of electrons

Identify the number of electrons for each element by looking at their atomic number: (a) Ti: 22 electrons (b) Cl: 17 electrons (c) V: 23 electrons.

Title - Write the ground-state electron configuration

Using the electron configuration order (1s, 2s, 2p, 3s, 3p, 4s, 3d, etc.), write the full electron configurations for each element. To simplify: (a) Ti: [Ar] 4s^2 3d^2 (b) Cl: [Ne] 3s^2 3p^5 (c) V: [Ar] 4s^2 3d^3

Title - Draw the partial (valence-level) orbital diagram

Focus on the valence level (the highest principal quantum number and partially filled d orbitals if any). (a) Ti: 4s: ↑↓ 3d: ↑ ↑ 3 unpaired electrons. (b) Cl: 3s: ↑↓ 3p: ↑↓ ↑↓ ↑ One unpaired electron. (c) V: 4s: ↑↓ 3d: ↑ ↑ ↑ 2 unpaired electrons.

Title - Condense into shorthand notation

For conciseness, we summarize by denoting the noble gas corresponding to inner electrons: (a) Ti: [Ar] 4s^2 3d^2 (b) Cl: [Ne] 3s^2 3p^5 (c) V: [Ar] 4s^2 3d^3

Key concepts

Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom. They play a crucial role in chemical reactions and bonding because they are the electrons most likely to interact with other atoms. For example, consider the elements Titanium (Ti), Chlorine (Cl), and Vanadium (V):

• Titanium (Ti) has atomic number 22, hence it has 22 electrons.
• Chlorine (Cl) has atomic number 17, hence it has 17 electrons.
• Vanadium (V) has atomic number 23, hence it has 23 electrons.

The valence electrons for these atoms are:

• Ti: The valence electrons are in the 4s and 3d orbitals. So, Ti has 4 valence electrons (2 in 4s and 2 in 3d).
• Cl: The valence electrons are in the 3s and 3p orbitals. So, Cl has 7 valence electrons (2 in 3s and 5 in 3p).
• V: The valence electrons are in the 4s and 3d orbitals. So, V has 5 valence electrons (2 in 4s and 3 in 3d).

Understanding valence electrons helps predict how different elements might react or bond with each other.

Orbital Diagrams

Orbital diagrams are visual representations of the electron configurations within an atom's orbitals. They can provide insight into the distribution of electrons among orbitals and help determine the number of unpaired electrons. This is important for understanding magnetic properties and reactivity.
In an orbital diagram:

• Each orbital is represented by a box.
• Each electron is represented by an arrow (↑ or ↓).
• Electrons fill orbitals in a specific order following the Aufbau principle, Hund's rule, and the Pauli Exclusion Principle.

Let's take a closer look at the valence-level (partial) orbital diagrams for Ti, Cl, and V:

• Ti:
  4s: ↑↓
  3d: ↑ ↑
• Cl:
  3s: ↑↓
  3p: ↑↓ ↑↓ ↑
• V:
  4s: ↑↓
  3d: ↑ ↑ ↑

These diagrams indicate the arrangement of valence electrons in the highest energy levels of the atoms, with unpaired electrons easily identifiable.

Ground-State Configuration

Ground-state electron configuration refers to the arrangement of electrons in an atom's orbitals when the atom is in its lowest energy state. The order of filling is governed by the Aufbau principle, which states that electrons occupy the lowest available energy levels first. This is complemented by Hund's rule and the Pauli Exclusion Principle.
Here's how you write ground-state configurations:

• Follow the order of orbitals: 1s, 2s, 2p, 3s, 3p, 4s, and so on.
• Use the element's atomic number to determine the total number of electrons.
• Allocate electrons to each orbital following the principles mentioned.

For the elements Ti, Cl, and V:

• Ti: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²
• Cl: 1s² 2s² 2p⁶ 3s² 3p⁵
• V: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³

The configurations show how electrons are distributed across the different shells and subshells, providing a clear picture of an atom's electron structure in its most stable form.

Shorthand Notation

Shorthand notation, also known as condensed electron configuration, simplifies electron configurations by abbreviating the inner (core) electrons with the symbol of the nearest noble gas. This makes it easier to focus on the valence electrons, which are crucial for chemical reactions and bonding.
Here's how to do it:

1. Identify the noble gas that precedes the element in question.
2. Write the noble gas in brackets.
3. Continue the electron configuration from the next orbital after the noble gas.

For example, for Ti, Cl, and V:

• Ti: [Ar] 4s² 3d²
• Cl: [Ne] 3s² 3p⁵
• V: [Ar] 4s² 3d³

Shorthand notation provides a more concise way to represent electron configurations. It highlights the valence electrons while omitting the core electrons that do not participate in chemical bonding.