Problem 21 - Chemical Principles: The Quest for Insight

Question

\(2.21\) What is the ground-state clectron configuration expected for each of the folluwing ions: (a) \(B i^{34}\); (b) \(\mathrm{Sn}^{4+} ;\) (c) \(\mathrm{P}^{3-} ;\) (d) \(\mathrm{Br}^{-} ;\)(e) \(\mathrm{Ni}^{2+}\) ?

Step-by-Step Solution

Answer

The ground-state electron configurations are: (a) Bi^3+: [Xe]4f^14 5d^10 6s^2 6p^0; (b) Sn^4+: [Kr]4d^10; (c) P^3-: [Ne]3s^2 3p^6; (d) Br^-: [Ar]3d^10 4s^2 4p^6; (e) Ni^2+: [Ar]3d^8.

Step 1: Finding the Atomic Number

To find the electron configuration for ions, first determine the atomic number of the neutral atoms. The atomic number corresponds to the number of protons and, in a neutral atom, an equal number of electrons. For ions, the atomic number does not change, but the electron count does. For (a) Bi, the atomic number is 83; for (b) Sn, it is 50; for (c) P, it is 15; for (d) Br, it is 35; and for (e) Ni, it is 28.

Step 2: Accounting for the Charge

Next, adjust the number of electrons for the charge of the ion. A positive charge indicates that electrons have been lost, while a negative charge indicates that electrons have been gained. For (a) Bi^3+, three electrons are lost, so there are 80 electrons in the ion. For (b) Sn^4+, four electrons are lost (46 electrons remain); for (c) P^3-, three electrons are gained (18 electrons total); for (d) Br^-, one electron is gained (36 electrons total); and for (e) Ni^2+, two electrons are lost (26 electrons remain).

Step 3: Writing the Electron Configurations

Write the ground-state electron configurations for the ions using noble gas notation. The electron configurations should end with the orbitals that contain the adjusted number of electrons due to ionization. This will be based on the principles of electron configuration, including the Aufbau principle, Pauli exclusion principle, and Hund's rule.

Step 4: Determining the Electron Configurations

The electron configurations are: (a) Bi^3+: [Xe]4f^14 5d^10 6s^2 6p^3 - 3e- = [Xe]4f^14 5d^10 6s^2 6p^0; (b) Sn^4+: [Kr]4d^10 5s^2 5p^2 - 4e- = [Kr]4d^10; (c) P^3-: [Ne]3s^2 3p^3 + 3e- = [Ne]3s^2 3p^6; (d) Br^-: [Ar]3d^10 4s^2 4p^5 + 1e- = [Ar]3d^10 4s^2 4p^6; (e) Ni^2+: [Ar]3d^8 4s^2 - 2e- = [Ar]3d^8.

Key Concepts

Aufbau Principle

The Aufbau principle is a fundamental concept in understanding how electrons occupy available energy levels within an atom. It states that electrons fill the lowest energy orbitals first before moving on to higher energy orbitals.

This principle helps us predict the electron configurations of atoms and ions, with electrons filling sublevels in a specific order: 1s, 2s, 2p, 3s, and so on. It's based on the idea that lower energy states are more stable and thus, more preferable for electrons. When an atom transforms into an ion, the Aufbau principle still applies, but the total number of electrons changes based on the charge of the ion.

Pauli Exclusion Principle

The Pauli exclusion principle is another key concept that governs the arrangement of electrons in an atom or ion. It asserts that no two electrons in an atom can have the same set of four quantum numbers, which implies that each orbital can hold a maximum of two electrons, and they must have opposite spins.

Under this principle, when we write electron configurations, we ensure that electrons are paired correctly in orbitals. For example, in a Sn^4+ ion, the electrons are paired up until the 4d sublevel, adhering to the Pauli exclusion principle, and accommodating the loss of four electrons due to the ion's positive charge.

Hund's Rule

Hund's rule addresses the distribution of electrons across orbitals of the same sublevel. It states that electrons will occupy empty orbitals singly before doubling up in any one orbital, and all singly occupied orbitals will have electrons with the same spin.

For instance, in the case of the P^3- ion, after following the Aufbau principle to reach the 3p sublevel, Hund's rule dictates filling each of the three 3p orbitals with one electron before any pairing occurs. When the phosphorus atom gains three electrons to become a P^3- ion, these additional electrons fill the remaining 3p orbitals, thereby obeying Hund's rule and completing the sublevel.

Noble Gas Notation

Noble gas notation is a shorthand representation used to simplify the expression of electron configurations, especially for atoms with many electrons. It involves starting with the electron configuration of the nearest noble gas element with fewer electrons and then showing the remaining electrons in their respective orbitals.

For example, for Br^-, which has one more electron than the neutral bromine atom, the noble gas notation begins with [Ar], the noble gas prior to bromine, and then adds the configuration for the extra electron: 4p^6. This notation is helpful in quickly identifying the valence electron configuration, which shows the electrons that are important in chemical bonding.