Question

Which of the following sets are isoelectronic? (1) \(\mathrm{N}_{2}, \mathrm{O}_{2}^{2}\) (2) \(\mathrm{N}_{2}, \mathrm{O}_{2}^{21}\) (3) \(\mathrm{N}_{2}^{-}, \mathrm{O}_{2}^{-}\) (4) \(\mathrm{N}_{2}, \mathrm{O}_{2}^{-}\)

Short answer

None of the sets are isoelectronic.

Step-by-step solution

- Define Isoelectronic Sets

Isoelectronic sets are groups of molecules or ions that have the same number of electrons. To determine which sets are isoelectronic, we first need to calculate the total number of electrons in each molecule.

- Calculate Electrons in \(\textrm{N}_{2}\)

The nitrogen molecule \(\textrm{N}_{2}\) consists of two nitrogen atoms. Each nitrogen atom has 7 electrons, so the total number of electrons in \(\textrm{N}_{2}\) is \(7 + 7 = 14\) electrons.

- Calculate Electrons in \(\textrm{O}_{2}^{2-}\)

The oxygen molecule ion \(\textrm{O}_{2}^{2-}\) consists of two oxygen atoms, each with 8 electrons, and an additional 2 electrons due to the \(-2\) charge. Therefore, the total number of electrons is \(8 + 8 + 2 = 18\) electrons.

- Calculate Electrons in \(\textrm{O}_{2}^{21}\)

There seems to be a typographical error in the exercise. The notation \(\textrm{O}_{2}^{21}\) is not standard. Assuming it was meant to be \(\textrm{O}_{2}^{2+}\) (or another valid ion), let's skip this option for clarity.

- Calculate Electrons in \(\textrm{N}_{2}^{-}\)

The nitrogen molecule ion \(\textrm{N}_{2}^{-}\) consists of two nitrogen atoms, each with 7 electrons, and an additional electron due to the negative charge. Thus, the total number of electrons is \(7 + 7 + 1 = 15\) electrons.

- Calculate Electrons in \(\textrm{O}_{2}^{-}\)

The oxygen molecule ion \(\textrm{O}_{2}^{-}\) consists of two oxygen atoms, each with 8 electrons, and an additional electron due to the negative charge. Therefore, the total number of electrons is \(8 + 8 + 1 = 17\) electrons.

- Compare Electrons to Determine Isoelectronic Sets

Now compare the total number of electrons for each molecule or ion: \(\textrm{N}_{2}\) has 14 electrons, \(\textrm{O}_{2}^{2-}\) has 18 electrons, \(\textrm{N}_{2}^{-}\) has 15 electrons, and \(\textrm{O}_{2}^{-}\) has 17 electrons. None of the provided sets have molecules or ions with the same number of electrons.

Key concepts

Electron Configuration

Electron configuration refers to the distribution of electrons of an atom or molecule in atomic or molecular orbitals. It's essential for understanding chemical bonding, reactivity, and electronic properties of substances. Here are the basics:
Each electron in an atom is arranged into orbitals following three main rules: Aufbau principle, Pauli-exclusion principle, and Hund's rule. These rules help us to know how electrons fill up the orbitals in an atom sequential order.

To illustrate, let’s look at nitrogen (N). Nitrogen has 7 electrons. According to the rules:

• Aufbau principle - electrons start filling from the lowest energy orbitals: 1s, then 2s, and finally 2p.
• Pauli-exclusion principle - an orbital can hold a maximum of 2 electrons with opposite spins.
• Hund's rule - electrons will fill each degenerate orbital singly first before pairing up.

The electron configuration for nitrogen is 1s² 2s² 2p³.
Now let’s apply it to molecular ions. For example, in the case of \(\textrm{N}_2^{-}\), each nitrogen atom has 7 electrons, and the negative charge adds one more electron, giving a total of 15 electrons.
Knowing electron configurations helps to understand whether molecules or ions are isoelectronic.

Molecular Ions

Molecular ions are created when a molecule gains or loses one or more electrons, resulting in a net electrical charge. Molecular ions play a significant role in chemistry and spectroscopy.

Let's explore a few examples:

• \(\textrm{O}_2^{2-}\) – This is an oxygen molecule that has gained two extra electrons, resulting in a negative two charge. Each \(\textrm{O}\) atom contributes 8 electrons, plus the two additional electrons from the charge: \(8 + 8 + 2 = 18\).
• \(\textrm{N}_2^{-}\) – This is a nitrogen molecule that has one extra electron, giving it a negative charge. Each \(\textrm{N}\) atom provides 7 electrons, plus one additional electron from the charge: \(7 + 7 + 1 = 15\).

Thus, molecular ions differ from their neutral counterparts in their electron configuration and properties. These changes in electron count can affect molecular geometry, bonding and even reactivity.
By calculating the number of electrons, you can determine if different species are isoelectronic, meaning they have the same number of electrons.

Electron Counting

Electron counting is a method used by chemists to determine the total number of electrons present in a molecule or ion. This is crucial for figuring out molecular geometry, bonding properties, and whether molecules or ions are isoelectronic.

Here’s a simple way to count electrons for any species:

• Identify the total number of protons for each atom. This will equal the atomic number (for example, nitrogen has 7).
• Add these up for the entire molecule or ion.
• Adjust the total for any charges. If an ion is negative, add electrons equal to the charge. If positive, subtract electrons equal to the charge.

For example, let’s do electron counting for \(\textrm{N}_2\):

1. Each nitrogen atom has 7 protons, giving a total of 14 electrons for the molecule.

Now, for \(\textrm{O}_2^{-}\),

1. Each oxygen atom has 8 protons, adding up to 16 electrons. An extra electron due to the negative charge makes it 17 electrons.

In all these steps, remember to accurately account for each electron. Proper electron counting ensures correct identification of isoelectronic species.
With these principles, determining if sets like \(\textrm{N}_2\) and \(\textrm{O}_2^{2-}\) are isoelectronic becomes straightforward. By following these steps, you can easily check the number of electrons and compare them across different molecules and ions.