Problem 7 - Chemical Principles: The Quest for Insight

Question

2.7 Give the ground-state clectron configuration expected for cach of the following ions: (a) \(\mathrm{Sb}^{3+}\); (b) \(\mathrm{Sn}^{2+}\); (c) \(\mathrm{W}^{2+}\); (d) \(\mathrm{S}^{2-}\).

Step-by-Step Solution

Answer

Ground-state electron configurations: (a) \text{Sb}^{3+}: [Kr] 4d^{10} 5s^{2} 5p^{1}, (b) \text{Sn}^{2+}: [Kr] 4d^{10} 5s^{2} 5p^{2}, (c) \text{W}^{2+}: [Xe] 4f^{14} 5d^{4}, (d) \text{S}^{2-}: [Ne] 3s^{2} 3p^{6}.

Step 1 - Write the atomic number

Find the atomic number of each element from the periodic table. Antimony (Sb) has atomic number 51, Tin (Sn) has atomic number 50, Tungsten (W) has atomic number 74, and Sulfur (S) has atomic number 16.

Step 2 - Determine the number of electrons in the ions

For cations, subtract the charge from the atomic number to find the number of electrons. For anions, add the charge to the atomic number. Sb^{3+} has 51 - 3 = 48 electrons; Sn^{2+} has 50 - 2 = 48 electrons; W^{2+} has 74 - 2 = 72 electrons; S^{2-} has 16 + 2 = 18 electrons.

Step 3 - Write electron configurations

Write the ground-state electron configuration for each ion, following the Aufbau principle, the Pauli Exclusion Principle, and Hund's Rule.(a) Sb^{3+}: [Kr] 4d^{10} 5s^{2} 5p^{1}(b) Sn^{2+}: [Kr] 4d^{10} 5s^{2} 5p^{2}(c) W^{2+}: [Xe] 4f^{14} 5d^{4}(d) S^{2-}: [Ne] 3s^{2} 3p^{6}

Key Concepts

Electron Configuration ions

Understanding how ions form is an essential aspect of chemistry that involves electron configurations.
An ion is an atom or molecule that has a net electrical charge due to the loss or gain of one or more electrons. Cations are positively charged ions, which occur when an atom loses electrons. Conversely, anions are negatively charged ions, resulting from the gain of electrons.

• For cations, we subtract the positive charge from the atomic number to determine the number of electrons left in the ion.
• For anions, we add the negative charge to the atomic number to find the total number of electrons.

Understanding this is crucial when predicting the properties of substances and for explaining reactivity and trends in the periodic table.

Periodic Table Atomic Number

The periodic table is organized by atomic number, which is the number of protons in the nucleus of an atom. This number is important because it defines the identity of the element and determines the element's position in the periodic table.
When solving problems related to electron configuration, the atomic number is the starting point. It tells us the number of protons, and for a neutral atom, also equals the number of electrons. However, when dealing with ions, the number of electrons will differ from the atomic number as electrons are either lost or gained.

Aufbau Principle

The Aufbau principle is a fundamental concept in quantum chemistry. It helps us determine the ground-state electron configuration of an atom or ion. The principle states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels.
For example, the 1s orbital will fill up before the 2s orbital begins to fill.

• This principle helps to accurately construct the electron configuration of ions by adding or removing electrons from the neutral atom's configuration based on whether it is a cation or an anion.

Applying the Aufbau principle correctly is vital to understanding how atoms and ions will bond and react chemically.

Pauli Exclusion Principle

The Pauli Exclusion Principle is essential when determining electron configurations. It states that no two electrons in an atom can have the same set of four quantum numbers.
This implies that an atomic orbital can hold a maximum of two electrons, and these electrons must have opposite spins. When applying this rule to ions, it becomes especially important to ensure that the electron configuration reflects this restriction, as it influences the placement of electrons in orbitals and thus the final electron configuration of the ion.

Hund's Rule

Hund's Rule addresses how electrons occupy orbitals of the same energy, known as degenerate orbitals. It states that electrons will fill degenerate orbitals singly first, with parallel spins, before pairing up.
This rule minimizes electron repulsion and keeps the energy of the atom or ion as low as possible. When writing electron configurations for ions, Hund’s Rule guides the distribution of electrons in the orbitals to reflect the lowest energy arrangement. Correct application of this rule is fundamental to interpret spectroscopic data and predict molecular geometry.