Problem 81 - General Chemistry: Principles and Modern Applications

Question

The only diamagnetic ion of the following group is (a) \(\mathrm{Cr}^{2+} ;\) (b) \(\mathrm{Zn}^{2+} ;\) (c) \(\mathrm{Fe}^{3+} ;\) (d) \(\mathrm{Ag}^{2+} ;\) (e) \(\mathrm{Ti}^{3+}\).

Step-by-Step Solution

Answer

The only diamagnetic ion out of the given groups is \(\mathrm{Zn}^{2+}\)

Step 1: Understand the electronic configuration of Ions

Know the electronic configuration of given ions. An ion is diamagnetic if it does not have any unpaired electrons in its outer shell. Thus, we have to identify the ion with all paired electrons.

Step 2: Analyze each given ion

Analyze each ion: Chromium ion \(\mathrm{Cr}^{2+}\) has configuration [Ar] 3d4. Zinc ion \(\mathrm{Zn}^{2+}\) has configuration [Ar] 3d10. Iron ion \(\mathrm{Fe}^{3+}\) has configuration [Ar] 3d5. Silver ion \(\mathrm{Ag}^{2+}\) has configuration [Kr] 4d8. Titanium ion \(\mathrm{Ti}^{3+}\) has configuration [Ar] 3d1.

Step 3: Identify the diamagnetic ion

From the configurations given above, only zinc ion \(\mathrm{Zn}^{2+}\) has all paired electrons. It has no unpaired electrons in its outer shell. Therefore, out of the given ions, \(\mathrm{Zn}^{2+}\) is diamagnetic.

Key Concepts

Electronic Configuration

Electronic configuration refers to the distribution of electrons in an atom or ion's orbitals. It is fundamental in determining many chemical properties of an element, including its magnetic behavior. Each orbital can hold a specific maximum number of electrons, and these electrons occupy the lowest available energy levels first. This arrangement is guided by principles such as the Aufbau Principle, Pauli Exclusion Principle, and Hund's Rule.

When writing electronic configurations:

• Identify the number of electrons in the atom or ion.
• Fill the orbitals following the order of increasing energy levels (1s, 2s, 2p, 3s, etc.).
• Consider the charge of ions: a positive charge denotes a loss of electrons while a negative charge indicates a gain.

For example, the electronic configuration of Zn is [Ar] 3d10 4s2, but for \(\mathrm{Zn}^{2+}\), it becomes [Ar] 3d10 due to the loss of 2 electrons, resulting in all electrons being paired.

Unpaired Electrons

Unpaired electrons are single electrons in an orbital, without a partner of opposite spin. They play a crucial role in determining whether an ion or atom exhibits magnetic properties. If there are unpaired electrons, the atom or ion can be paramagnetic. If all electrons are paired, it is diamagnetic.

In the context of the question, an ion is diamagnetic if it has no unpaired electrons. Zinc ion, \(\mathrm{Zn}^{2+}\), with an electronic configuration of [Ar] 3d10, has all its electrons paired.
To find unpaired electrons:

• Refer to the electronic configuration of the ion.
• Identify the highest occupied orbitals.
• Count how many unpaired electrons are present.

Having unpaired electrons implies that electrons are not completely filling an orbital, leaving them free to impact magnetic properties.

Transition Metals

Transition metals are elements found in the d-block of the periodic table. They are intriguing due to their partially filled d-orbitals and the ability to form various oxidation states. These characteristics lead to interesting magnetic properties and complex chemistry.

Transition metals characteristically have electrons in the d-orbital, which makes their electronic configurations unique and can lead to different magnetic properties. For example:

• \(\mathrm{Cr}^{2+}\) is [Ar] 3d4, with partially filled d-orbitals.
• \(\mathrm{Fe}^{3+}\) is [Ar] 3d5, each electron occupying a separate d-orbital.

The variable oxidation states mean that while some configurations can be diamagnetic, others can be paramagnetic. Situations where all d-orbitals are filled, leading to paired electrons, tend to show diamagnetism, like in \(\mathrm{Zn}^{2+}\).

Paramagnetism

Paramagnetism occurs in atoms or ions with unpaired electrons. When these unpaired electrons align in response to an external magnetic field, they exhibit strong magnetic properties. This alignment is not seen in diamagnetic substances, where pairing neutralizes magnetic effects.

For a substance to exhibit paramagnetism:

• It must have unpaired electrons.
• Apply an external magnetic field.

The presence of unpaired electrons allows unaligned magnetic moments to align alongside the field, thus creating an overall magnetic moment. This behavior contrasts sharply with diamagnetism, where the evenly paired electrons result in no net magnetic field. In our exercise, ions like \(\mathrm{Cr}^{2+}\) or \(\mathrm{Fe}^{3+}\) with unpaired electrons display this phenomenon.