Problem 95 - Chemistry The Science in Context

Question

What are the condensed electron configurations of \(\mathrm{K}, \mathrm{K}^{+}\) \(\mathrm{S}^{2-}, \mathrm{N}, \mathrm{Ba}, \mathrm{Ti}^{4+},\) and \(\mathrm{Al} ?\)

Step-by-Step Solution

Answer

Answer: The condensed electron configurations are as follows: - Potassium (K): [Ar]4s¹ - Potassium Ion (K+): [Ar] - Sulfide Ion (S²⁻): [Ar]3s² 3p⁶ - Nitrogen (N): [He]2s² 2p³ - Barium (Ba): [Xe]6s² - Titanium Ion (Ti⁴⁺): [Ar] - Aluminum (Al): [Ne]3s² 3p¹

Step 1: 1. Atomic Numbers and Electron Counts

First, we need to find the atomic numbers of the given elements which will give us the number of electrons in the neutral atom. The atomic numbers can be found in the periodic table. For ions, adjust the electron count based on the charge. Element or Ion | Symbol | Atomic Number | Electron Count ----------------|--------|---------------|---------------- Potassium | K | 19 | 19 Potassium Ion | \(K^+\) | 19 | 18 Sulfide Ion | \(S^{2-}\) | 16 | 18 Nitrogen | N | 7 | 7 Barium | Ba | 56 | 56 Titanium Ion | \(Ti^{4+}\) | 22 | 18 Aluminum | Al | 13 | 13 2. Write the condensed electron configurations

Step 2: 2. Write Condensed Electron Configurations

Next, we write the electron configurations of the elements and ions while following the Aufbau principle, Hund's rule, and the Pauli exclusion principle. The electron configurations will be condensed by expressing the inner electrons using noble gas shorthand notation. Element or Ion | Electron Configuration ----------------|----------------------- Potassium (K) | \([\mathrm{Ar}]4s^1\) Potassium Ion (\(K^+\)) | \([\mathrm{Ar}]\) Sulfide Ion (\(S^{2-}\)) | \([\mathrm{Ar}]3s^2 3p^6\) Nitrogen (N) | \([\mathrm{He}]2s^2 2p^3\) Barium (Ba) | \([\mathrm{Xe}]6s^2\) Titanium Ion (\(Ti^{4+}\)) | \([\mathrm{Ar}]\) Aluminum (Al) | \([\mathrm{Ne}]3s^2 3p^1\) Now we have found the condensed electron configurations of all the given elements and ions.

Key Concepts

Periodic Table

The periodic table is a tabular display of known chemical elements organized by their atomic numbers, electron configurations, and recurring chemical properties. Elements are presented in order of increasing atomic number, which is the number of protons in an atom's nucleus. The table is structured in rows called periods and columns known as groups, with elements in the same group having similar chemical behaviors. For students, the periodic table is indispensable when determining electron configurations. It helps in identifying the number of electrons that an element has and how they should be distributed based on its position on the table.

For instance, when considering the electron configuration of potassium (K), we note that it is located in group 1 and period 4 of the periodic table. This information tells us that potassium has one electron in its outermost shell, leading to its shorthand electron configuration \(\mathrm{[Ar]}4s^1\). Understanding the periodic table allows us to predict and write out the configurations for any element or ion systematically.

Aufbau Principle

The Aufbau principle is a fundamental guideline used in the arrangement of electrons in an atom’s orbitals during electron configuration. It states that electrons are filled into orbitals starting at the lowest available energy level, before filling higher levels. The principle's name comes from the German word 'Aufbau', meaning 'building up'. According to the Aufbau principle, each electron occupies the lowest energy orbital available, which is why we often see electron configurations start with 1s before moving to 2s, 2p, and so forth.

In practical terms, when we write the electron configuration for Barium (Ba), following the Aufbau principle, we start from the lowest energy level, resulting in \(\mathrm{[Xe]}6s^2\) as its condensed electron configuration. Notice that the previous noble gas, Xenon (Xe), is used as a reference point to denote filled lower energy levels up to that noble gas.

Applying Aufbau Principle to Ions

For ions, the Aufbau principle still applies but we must consider the loss or gain of electrons. For example, \(\mathrm{K^+}\) loses an electron compared to its neutral state \(\mathrm{K}\), so the \(\mathrm{K^+}\) electron configuration is simply \(\mathrm{[Ar]}\) since the 4s orbital loses its one electron.

Hund's Rule

Hund's rule addresses the filling order of electrons within a subshell with more than one orbital such as the p, d, or f orbitals. It states that every orbital in a sublevel is singly occupied before any orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin. This is due to electrons repelling each other, and by occupying different orbitals, they can stay as far apart as possible.

When applying Hund’s rule for nitrogen (N), with an electron configuration \(\mathrm{[He]}2s^2 2p^3\), we realize that the p orbitals are half-filled with one electron each, all aligned with parallel spins. This satisfies Hund's rule by maximizing the number of unpaired electrons and minimizing repulsion. Thus, Hund's rule is crucial when dealing with multiple electrons in the same sublevel to avoid mistakenly pairing electrons too early in the configuration process.

Pauli Exclusion Principle

The Pauli Exclusion Principle is another key concept in electron configurations, which states that no two electrons in an atom can have the same set of four quantum numbers. As a consequence, an atomic orbital can hold a maximum of two electrons, and they must have opposite spins. This principle explains the limited capacity of orbitals and why electrons pair up only when necessary.

For the sulfide ion \(\mathrm{S^{2-}}\), the additional two electrons (due to the 2- charge) pair up in the 3p orbitals after the 3s orbital is filled. Its electron configuration, \(\mathrm{[Ar]}3s^2 3p^6\), shows all the p orbitals filled, each with a pair of electrons with opposite spins. The Pauli Exclusion Principle guarantees that electrons are properly paired and placed in orbitals, ensuring that the electron configuration adheres to the fundamental rules of quantum mechanics.