Problem 24 - Chemistry An Atoms First Approach

Question

Write electron configurations for each of the following. a. \(\mathrm{Cr}, \mathrm{Cr}^{2+}, \mathrm{Cr}^{3+}\) b. \(\mathrm{Cu}, \mathrm{Cu}^{+}, \mathrm{Cu}^{2+} \quad\) c. \(\mathrm{V}, \mathrm{V}^{2+}, \mathrm{V}^{3+}\)

Step-by-Step Solution

Answer

a. Cr: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5\); Cr²⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^4\); Cr³⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^3\) b. Cu: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{10}\); Cu⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10}\); Cu²⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^9\) c. V: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3\); V²⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^3\); V³⁺: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^2\)

Step 1: Find the atomic number of Chromium

Using the periodic table, we can see that the atomic number of Chromium (Cr) is 24.

Step 2: Fill electron orbitals for Cr

Following the aufbau principle, we will fill the electron orbitals until we reach 24 electrons: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵

Step 3: Determine the electron configuration for Cr²⁺ and Cr³⁺ ions

Cr²⁺: Remove 2 electrons (one from 4s and one from 3d): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁴ Cr³⁺: Remove 3 electrons (one from 4s and two from 3d): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d³ b. Copper (Cu)

Step 1: Find the atomic number of Copper

Using the periodic table, we can find that the atomic number of Copper (Cu) is 29.

Step 2: Fill electron orbitals for Cu

Following the aufbau principle, we will fill the electron orbitals until we reach 29 electrons: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰

Step 3: Determine the electron configuration for Cu⁺ and Cu²⁺ ions

Cu⁺: Remove 1 electron from 4s: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ Cu²⁺: Remove 2 electrons (one from 4s and one from 3d): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁹ c. Vanadium (V)

Step 1: Find the atomic number of Vanadium

Using the periodic table, we can find that the atomic number of Vanadium (V) is 23.

Step 2: Fill electron orbitals for V

Following the aufbau principle, we will fill the electron orbitals until we reach 23 electrons: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³

Step 3: Determine the electron configuration for V²⁺ and V³⁺ ions

V²⁺: Remove 2 electrons from 4s: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d³ V³⁺: Remove 2 electrons from 4s and 1 from 3d: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d²

Key Concepts

Aufbau Principle

The Aufbau principle is a fundamental concept in quantum chemistry used to determine the electron configurations of atoms. According to this principle, electrons are added to an atom in such a way that they occupy the lowest energy orbitals first before moving to higher energy levels. This is often visualized as "building up" electron configurations by adding one electron at a time, starting from the lowest energy orbital and proceeding to the next. For instance, with elements like Chromium (Cr), even though the expected order is to fill the 4s orbital completely before the 3d orbital, the actual observed configuration is 4s¹ 3d⁵. This unusual pattern occurs because having a half-filled 3d subshell offers extra stability to the atom.

Electron Orbitals

Electron orbitals are regions around the nucleus of an atom where electrons are likely to be found. These orbitals are solutions to the Schrödinger equation and are defined by quantum numbers.

• The principal quantum number (\(n\) can be 1, 2, 3, ...) describes the energy level.
• The azimuthal quantum number (\(l\) ) defines the shape of the orbital, such as s, p, d, and f.
• The magnetic quantum number (\(m_l\) ) describes the orientation of the orbital.
• The spin quantum number (\(m_s\) ) accounts for the spin of the electron.

Each electron orbital can hold a maximum of two electrons with opposite spins. The understanding of electron orbitals is crucial for determining chemical reactivity and bonding behavior in different elements, such as the electron configurations of Chromium, Copper, and Vanadium.

Oxidation States

Oxidation states (or oxidation numbers) indicate the degree of oxidation of an atom in a chemical compound. They help in understanding how electrons are distributed among the atoms present in a compound.

• An increase in oxidation state reflects more oxidation (loss of electrons).
• A reduction in oxidation state indicates reduction (gain of electrons).

In transition metals, multiple oxidation states are common. For example, Chromium can exist in oxidation states ranging from +2 to +6. Copper commonly displays +1 and +2 states, while Vanadium can be found in +2, +3, +4, and +5 states. Observing these states involves removing electrons from the outermost electron shells, often starting with the 4s orbital before affecting the 3d.

Periodic Table

The periodic table is an organized arrangement of elements, ordered by their atomic number, electron configurations, and recurring properties. Mendeleev first developed it to predict the properties of undiscovered elements. Today, the periodic table helps us to understand the properties and behaviors of elements in their individual as well as collective capacity.

• Each period on the table corresponds to the filling of a new electron shell.
• Groups or columns show elements with similar chemical properties, attributed largely to their electron configurations.

Transition metals, located in the d-block of the periodic table, exhibit unique characteristics, such as varying oxidation states and the ability to form colored compounds, which are directly tied to their electron configurations as seen in elements like Chromium, Copper, and Vanadium.

Transition Metals

Transition metals, positioned in the central block of the periodic table, are unique due to their d subshell electrons. These elements, ranging from groups 3 to 12, display properties that differ from those of other groups.

• They can exhibit variable oxidation states, giving rise to great versatility in bonding and reactions.
• Many transition metals form colored compounds, a result of d-d electronic transitions.
• They often possess high melting points and boiling points.

Elements like Chromium, Copper, and Vanadium are classic examples of transition metals. They often participate in complex formation, catalysis, and display magnetic properties, influenced by their unpaired d electrons and peculiar electron configurations as demonstrated by configurations such as 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵ for Chromium.