Problem 121 - Chemistry

Question

Draw orbital diagrams for atoms with the following electron configurations: (a) \(1 s^{2} 2 s^{2} 2 p^{5}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{7}\)

Step-by-Step Solution

Answer

The orbital diagrams for these electron configurations should follow the pattern of the structure of the atom (number of orbitals and electrons in each energy level). Application of Hund's rule ensures that each orbital in a subshell is singly occupied before any orbital becomes doubly occupied.

Step 1: Orbital Diagram of \(1 s^{2} 2 s^{2} 2 p^{5}\)

This electron configuration states that there are 2 electrons in the 1s orbital, 2 electrons in the 2s orbital, and 5 electrons in the 2p orbitals. An orbital diagram represents each orbital as a box and each electron as an arrow. Arrows pointing up and down represent electrons with opposite spins. Draw one box for the 1s orbital and place two arrows (one up, one down) in it. Draw another box for the 2s orbital and place two arrows (one up, one down) in it. For the 2p orbitals, draw three boxes (they represent 2px, 2py, 2pz) and place 5 arrows in them (use Hund's rule: fill each box with one electron before pairing up electrons).

Step 2: Orbital Diagram of \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\)

This configuration states that there are 2 electrons in the 1s orbital, 2 in the 2s orbital, 6 in the 2p orbitals, 2 in the 3s orbital, and 3 in the 3p orbitals. Depict each orbital as a box and fill it with arrows (representing electrons) as done previously. Draw one box for 1s, one box for 2s, three boxes for 2p, one box for 3s, and three boxes for 3p. Fill the boxes accordingly with arrows representing electrons. Always remember to follow Hund's rule.

Step 3: Orbital Diagram of \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{7}\)

This electron configuration has 2 electrons in the 1s orbital, 2 in the 2s orbital, 6 in the 2p orbitals, 2 in the 3s orbital, 6 in the 3p orbitals, 2 in the 4s orbital, and 7 in the 3d orbitals. Use the box and arrow method as before. One box is used for 1s, one for 2s, three for 2p, one for 3s, three for 3p, one for 4s, and five for 3d (as there are five 3d orbitals: 3dx²-y², 3dxy, 3dxz, 3dyz, 3dz²). Assign the electrons to the boxes and maintain the order of filling. Consult the periodic table if you're unsure about the order.

Key Concepts

Electron Configuration

Electron configuration is a representation that describes how electrons are distributed in atoms and molecules. It is depicted using numbers, letters, and superscripts and follows the principle that electrons fill orbitals in a predictable order, starting from the lowest energy level.

• The numbers indicate the principal energy levels.
• The letters (s, p, d, f) represent the type of orbital (shape and energy).
• The superscripts denote the number of electrons in those orbitals.

Understanding electron configuration is crucial because it helps predict an element's chemical properties and behavior during reactions. The order in which electrons fill these orbitals typically follows the Aufbau principle, which states that electrons occupy the lowest energy orbitals first. For instance, a filled 1s orbital is succeeded by the 2s orbital, and so on. In certain cases, configurations like that of the 3d orbitals may deviate slightly from the straightforward sequence due to their energy levels being very close to the 4s.
Accurate electron configuration provides a foundation for understanding more advanced topics such as chemical bonding and the formation of ions.

Hund's Rule

Hund's rule is a principle that helps determine how electrons are distributed among orbitals in a sublevel. It states that electrons will fill an unoccupied orbital before they pair up in an occupied one.
This occurs because electrons are negatively charged particles that repel each other. By occupying separate orbitals of the same energy (degenerate orbitals), electrons can minimize the repulsion between them, leading to a more stable electron configuration.
When using this rule to build orbital diagrams:

• Ensure each box (representing an orbital) in a sublevel has one electron before any box gets a second electron.
• Note that the arrows in diagrams indicate electron spin; an upward arrow represents a "+1/2" spin, while a downward arrow represents a "-1/2" spin.

Hund's rule underscores the importance of electron spin in electronic structure and provides significant insight when applying quantum mechanical principles to chemistry.

Periodic Table

The periodic table is an organized arrangement of all known chemical elements. It categorizes elements based on their atomic number, electron configuration, and recurring chemical properties.
Key details about the periodic table include:

• Elements in the same group (vertical columns) typically share similar properties and have the same number of valence electrons, impacting their chemical reactivity.
• Periods (horizontal rows) depict elements with increasing atomic number and show how electron configurations gain more electrons in higher energy levels as you move right.
• The table is divided into blocks (s, p, d, and f) which indicate the sublevel in which the "last" electron is added during electron configuration.

The periodic table provides a valuable reference for determining possible combinations of elements and predicting chemical reactions and properties based on an element's location in the table. It bridges the understanding between electron configuration and chemical characteristics.

3d Orbitals

3d orbitals are part of the d subshell and can hold up to 10 electrons as there are five 3d orbitals available. These five orbitals are labeled: 3dx²-y², 3dxy, 3dxz, 3dyz, and 3dz².
Key characteristics include:

• 3d orbitals are higher in energy than the 4s orbital, which is why they are filled after 4s in elements such as transition metals.
• They have complex shapes and a higher angular momentum compared to s and p orbitals.
• The filling of the 3d orbitals for an element significantly affects its properties, including magnetic characteristics and its ability to participate in chemical bonding.

Understanding the behavior and filling sequence of 3d orbitals is essential for explaining the properties of transition elements and the formation of complex ions. This knowledge facilitates predictions about electron transitions, which affect properties like color and magnetism in compounds.