Problem 4 - Chemistry and Chemical Reactivity

Question

Use the periodic table to identify the elements in the following list with unfilled \(3 d\) orbitals: cadmium, cerium, cobalt, chromium, copper.

Step-by-Step Solution

Answer

Cobalt and chromium have unfilled 3d orbitals.

Step 1: Understand the Question

We need to determine which elements in the list: cadmium, cerium, cobalt, chromium, and copper have unfilled (partially filled) 3d orbitals. The task involves using the periodic table to find the electronic configuration of each element.

Step 2: Review Electronic Configurations

Obtain the electronic configuration for each element based on their position in the periodic table: - Cadmium: [Kr] 4d^{10} 5s^2 - Cerium: [Xe] 4f^1 5d^1 6s^2 - Cobalt: [Ar] 3d^7 4s^2 - Chromium: [Ar] 3d^5 4s^1 - Copper: [Ar] 3d^{10} 4s^1

Step 3: Analyze Filled and Unfilled 3d Orbitals

Evaluate the electron configurations for the presence of 3d orbitals: - Cadmium: No 3d orbitals (starts with 4d) - Cerium: No 3d orbitals (starts with 4f) - Cobalt: 3d^7, thus 3d orbitals are unfilled - Chromium: 3d^5, thus 3d orbitals are unfilled - Copper: 3d^{10}, thus 3d orbitals are fully filled

Step 4: Identify Elements with Unfilled 3d Orbitals

Based on the above analysis, cobalt and chromium both have unfilled 3d orbitals, as less than 10 electrons populate them. The other elements have either no 3d orbitals or fully filled 3d orbitals.

Key Concepts

Periodic Table

The periodic table is like a map that helps us understand the properties and relationships of elements. It organizes all known chemical elements in a tabular format where elements are placed in order of increasing atomic number. This arrangement not only reflects the periodic recurrence of similar properties but also assists in predicting the behavior of elements.

Each column in the periodic table is known as a group or family, while each row is called a period. Groups comprise elements that have similar valence electron configurations. Hence, these elements often exhibit similar chemical behavior. Periods represent elements with the same number of electron shells. For instance, all elements in the fourth period have electrons populating up to four different electron shells.

• The elements in the center, known as transition metals, often have special properties like the ability to conduct electricity and high melting points.
• The periodic table provides reliable information about electron configurations, which are vital for determining an element's reactivity and bonding capabilities.

Using the periodic table, you can predict which orbitals are filled and identify elements with partially filled orbitals, which greatly affect their chemistry.

Electron Configuration

Electron configuration describes how the electrons are distributed in an atom's orbitals. This layout follows the principles of quantum mechanics and is key to understanding how elements interact chemically.

Electrons in atoms fill orbitals in a specific order, following the Aufbau principle. According to this principle, electrons fill orbitals starting from the lowest energy level to higher ones. This filling process can be described in terms of sublevels, such as the 3d orbital. A fully filled 3d sublevel contains 10 electrons. If it has fewer electrons, it is considered unfilled or partially filled.

• This configuration influences an element's properties, such as magnetism and color. For instance, when you look at the electron configuration of cobalt \(\text{[Ar] 3d}^7 \text{4s}^2\), its unfilled 3d orbitals play a significant role in its magnetic properties.
• Understanding electron configurations helps in identifying how elements will bond with one another. For example, elements tend to form bonds to achieve a stable electron configuration, akin to that of noble gases.

Transition Metals

Transition metals occupy the central block of the periodic table, ranging from group 3 to group 12. These metals are distinct due to their ability to form various oxidation states and complex ions. The versatility of transition metals primarily arises from their partially filled d orbitals.

The presence of d orbitals allows these metals to exhibit unique properties such as variable valency, the ability to form colored compounds, and to act as catalysts in chemical reactions. For example, iron, a transition metal, can display oxidation states of +2 and +3, which contributes to its capacity to engage in redox reactions.

• Chromium \(\text{[Ar] 3d}^5 \text{4s}^1\) and cobalt \(\text{[Ar] 3d}^7 \text{4s}^2\) are transition metals with unfilled 3d orbitals, which manifest in certain magnetic and chemical properties.
• These metals often serve as catalysts, increasing the rate of chemical reactions without being consumed, which is vital in industrial processes.

Transition metals' ability to form colored compounds comes from electronic transitions between d orbitals. These aspects make transition metals considerably important in both scientific research and practical applications, such as in metallurgy and as catalysts in various industries.