Problem 80 - General Chemistry: Principles and Modern Applications

Question

Use orbital diagrams to show the distribution of electrons among the orbitals in (a) the \(4 p\) subshell of Br; (b) the \(3 d\) subshell of \(\mathrm{Co}^{2+},\) given that the two electrons lost are \(4 s ;\) (c) the \(5 d\) subshell of \(\mathrm{Pb}\).

Step-by-Step Solution

Answer

The electron distribution in: (a) the \(4 p\) subshell of Br is \(_{4p}\uparrow\downarrow, \uparrow\downarrow, \uparrow\), (b) the \(3 d\) subshell of \(\mathrm{Co}^{2+}\) is \(_{3d}\uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow, \uparrow, \uparrow\), and (c) the \(5 d\) subshell of Pb is \(_{5d}\uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow\).

Step 1: Distribution in the \(4 p\) subshell of Br

Bromine (Br) has an atomic number of 35, which means it has 35 electrons in its neutral state. Thus, it has 3 electrons in its \(4p\) subshell. Using Hund's Rule which states that orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and further, that all electrons in singly occupied orbitals have the same spin, the electron distribution in the \(4 p\) subshell of Br would be \(_{4p}\uparrow\downarrow, \uparrow\downarrow, \uparrow\). There are two arrows in the first two orbitals indicating the two electrons with opposite spins (up and down), and one arrow in the last orbital indicating the third electron.

Step 2: Distribution in the \(3 d\) subshell of \(\mathrm{Co}^{2+}\)

Cobalt (Co) has an atomic number of 27, and it has lost two 4s electrons to become \(\mathrm{Co}^{2+}\), so, it now has 25 electrons. When filling the energy levels, the \(3 d\) subshell will have 7 electrons. Using Hund's Rule again, the \(3 d\) subshell of \(\mathrm{Co}^{2+}\) will look like this: \(_{3d}\uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow, \uparrow, \uparrow\), with five orbitals showing two paired electrons and the last two orbitals showing single electrons.

Step 3: Distribution in the \(5 d\) subshell of Pb

Lead (Pb) has an atomic number of 82 and it has a total of 10 electrons in the \(5d\) subshell. Based on the Pauli Exclusion Principle (which states that no two electrons in an atom could be in the same state or configuration) and Hund's Rule, the electron distribution of \(5d\) subshell in Pb is as follows: \(_{5d}\uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow, \uparrow\downarrow\). All five orbitals in the \(5d\) subshell are filled with two electrons each, with opposite spins.

Key Concepts

Understanding Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom's orbitals. It is vital in determining the chemical properties of an element. Orbitals are regions around the nucleus where electrons are likely to be found. These orbitals have different shapes and energy levels.

Electrons fill orbitals starting from the lowest energy level to the highest. This process follows the Aufbau principle, which dictates the order of energy levels. This can be represented by the sequence:

• 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and so on.

The notation for electron configuration shows the energy level and type of orbital, followed by a superscript number denoting the quantity of electrons.

In Bromine's case, its electron configuration involves having 3 electrons in the 4p subshell. Understanding electron configuration helps in visualizing how an element bonds and reacts chemically.

Exploring Hund's Rule

Hund's Rule is crucial when establishing how electrons occupy orbitals within the same subshell. According to this rule:

• Every orbital in a subshell is singly occupied by an electron before any orbital gets a second electron.
• All the electrons in singly occupied orbitals should have the same spin to minimize repulsion and ensure stability.

This rule effectively prevents paired electrons from immediately occurring, reducing electron-electron repulsion and instability.

Let's consider the distribution of electrons in the 3d subshell of Co²⁺. The 3d subshell will distribute seven electrons according to Hund's Rule, filling each orbital with one electron each before pairing begins. This rule is why we see unpaired electrons on the last two orbitals in Co²⁺'s electron configuration.

The Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental concept in quantum mechanics, stating that no two electrons in an atom can have identical sets of quantum numbers. Essentially, this means:

• No more than two electrons can occupy the same orbital.
• These electrons must have opposite spins, symbolized as "up" and "down" arrows.

This principle is behind the need for distributing two electrons per orbital with opposite spins, as seen in the orbital diagrams. It ensures that each electron in an atom or molecule is uniquely identified.

In Lead's 5d subshell, for example, the Pauli Exclusion Principle dictates that each of the five orbitals houses two electrons with opposite spins, accounting for a total of 10 electrons in the subshell. This ensures that each electron has a distinct set of quantum numbers, safeguarding the stability of the element.