Question

Write the electron configuration for each ion. What do all of the electron configurations have in common? (a) \(\mathrm{Ca}^{2+}\) (b) \(\mathrm{K}^{+}\) (c) \(\mathrm{S}^{2-}\) (d) \(\mathrm{Br}^{-}\)

Short answer

The electron configurations are \(\mathrm{Ca}^{2+}: 1s^2 2s^2 2p^6 3s^2 3p^6\), \(\mathrm{K}^{+}: 1s^2 2s^2 2p^6 3s^2 3p^6\), \(\mathrm{S}^{2-}: 1s^2 2s^2 2p^6 3s^2 3p^6\), and \(\mathrm{Br}^{-}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6\). All ions have electron configurations of noble gases, implying filled s and p orbitals in their outermost energy levels.

Step-by-step solution

Determine the electron configuration for the neutral atom

Before determining the electron configuration for an ion, one must know the electron configuration for the neutral atom. Find the atomic number of the atom on the periodic table; this number also represents the number of electrons in the neutral atom. Use the Aufbau principle, Pauli exclusion principle, and Hund's rule to fill the orbitals in order of increasing energy.

Adjust for the Charge for Calcium Ion (Ca2+)

Calcium (Ca) has an atomic number of 20, giving it the electron configuration of the neutral atom as 1s2 2s2 2p6 3s2 3p6 4s2. Since it is a 2+ ion, we remove two electrons from the outermost energy level resulting in the electron configuration for \(\mathrm{Ca}^{2+}\) as 1s2 2s2 2p6 3s2 3p6, which is the configuration of Argon.

Adjust for the Charge for Potassium Ion (K+)

Potassium (K) has an atomic number of 19, leading to the electron configuration of the neutral atom as 1s2 2s2 2p6 3s2 3p6 4s1. As a 1+ ion, potassium loses one electron, so the electron configuration for \(\mathrm{K}^{+}\) is 1s2 2s2 2p6 3s2 3p6, which is the electron configuration of Argon.

Adjust for the Charge for Sulfur Ion (S2-)

Sulfur (S) has an atomic number of 16, which gives it the electron configuration of 1s2 2s2 2p6 3s2 3p4 in the neutral state. With a 2- charge, sulfur gains two electrons to complete its 3p sublevel, resulting in the electron configuration for \(\mathrm{S}^{2-}\) as 1s2 2s2 2p6 3s2 3p6 which is the electron configuration of Argon.

Adjust for the Charge for Bromine Ion (Br-)

Bromine (Br) has an atomic number of 35, and its electron configuration in the neutral state is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5. The \(\mathrm{Br}^{-}\) ion has gained one electron, filling the 4p sublevel and thus the electron configuration becomes 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6, which is the configuration of Krypton.

Identify the Commonality in the Electron Configurations

Now that we have the electron configurations for each ion, we examine them to find a common feature. Each of the ions has the electron configuration of a noble gas: \(\mathrm{Ca}^{2+}\), \(\mathrm{K}^{+}\), and \(\mathrm{S}^{2-}\) have the electron configuration of Argon (Ar), while \(\mathrm{Br}^{-}\) has the electron configuration of Krypton (Kr). The common trait is that all ions have electron configurations corresponding to that of noble gases, having full s and p orbitals in their outermost energy levels.

Key concepts

Aufbau Principle

The Aufbau principle is a fundamental guideline in chemistry that dictates the order in which electrons populate atomic orbitals. It states that electrons fill the lowest energy orbitals first before moving to higher energy levels. Imagine a hotel where guests must occupy the rooms starting from the lowest floor upwards; the Aufbau principle does the same but for electrons in atoms.

For example, the first electron in a hydrogen atom would occupy the 1s orbital, the lowest energy level, before any other. Following the Aufbau principle helps in predicting the electronic structures of atoms, which is essential to understand chemical properties and behaviors.

Pauli Exclusion Principle

The Pauli exclusion principle is a quantum mechanical concept introduced by Wolfgang Pauli in 1925. This principle states that no two electrons in an atom can have the same set of four quantum numbers. Each orbital can hold a maximum of two electrons, and they must have opposite spins. This is similar to a rule that says no two people can have the same seat at a concert; in the atomic realm, no two electrons can share the same quantum state completely.

When applying the Pauli exclusion principle to electron configurations, it ensures that electrons are properly distributed among the available orbitals, adhering to the fundamental rules of quantum mechanics.

Hund's Rule

Hund's rule addresses the way electrons distribute themselves among orbitals of the same sublevel (like 2p or 3d). According to Hund's rule, electrons will fill an unoccupied orbital before they pair up in an already occupied one. This can be likened to individuals preferring to sit alone on a bus seat before having to share it when it becomes unavoidable.

In the context of electron configuration, this means if there are several orbitals of the same energy (degenerate orbitals), one electron goes into each until all are half-full. Only then do the electrons start to pair up. Hund's rule explains the magnetic properties of atoms and contributes to the overall stability of their electron configurations.

Noble Gas Configuration

The noble gas configuration represents the stable electronic arrangement that noble gases naturally possess. Atoms generally tend to achieve this stable configuration through ionic or covalent bonding. For ions, this often means gaining or losing electrons to end up with a filled outer shell, like the nearest noble gas.

As seen in the problem's step-by-step solution, ions tend to lose or gain electrons to mimic the electron configurations of noble gases, such as argon or krypton. This is because noble gases have complete valence shells, which makes them very stable and chemically inert. When other elements achieve this configuration, they have attained a particularly stable electronic state known also as the octet rule for main-group elements.

Orbital Energy Levels

Orbital energy levels refer to the various positions that electrons can occupy around an atom's nucleus, each with a different energy. These levels are organized by principal quantum numbers (n=1, 2, 3,...) and sublevels (s, p, d, f). Lower energy orbitals, such as 1s, fill up first following the Aufbau principle, and energy increases with the principal quantum number and the complexity of the sublevel.

In simplified terms, you could think of these energy levels as the floors in a building, with the ground floor being the least energy-intensive to reach. As electrons are added to an atom, they fill up these 'floors' from the bottom up, according to their increasing energy levels, which is consistent with the step-by-step example provided in the original exercise.