Problem 46 - A Complete Resource Book in Chemistry for JEE Main

Question

Two stable ions of first transition series which have the largest number of unpaired electrons and have the highest magnetic moment are (a) \(\mathrm{Ni}^{2+}\) and \(\mathrm{Co}^{2+}\) (b) \(\mathrm{Cr}^{3+}\) and \(\mathrm{Fe}^{2+}\) (c) \(\mathrm{Fe}^{3+}\) and \(\mathrm{Mn}^{2+}\) (d) \(\mathrm{Ti}^{4+}\) and \(\mathrm{Cr}^{3+}\)

Step-by-Step Solution

Answer

(c) \( \mathrm{Fe}^{3+} \) and \( \mathrm{Mn}^{2+} \)

Step 1: Understand Magnetic Moment

The magnetic moment of an ion is related to the number of unpaired electrons it has. The formula for calculating the magnetic moment, in Bohr magnetons (B.M.), is given by \( \mu = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons. Thus, more unpaired electrons mean a higher magnetic moment.

Step 2: Count Unpaired Electrons

Determine the number of unpaired electrons for each ion. - \( \mathrm{Ni}^{2+} \): [Ar] 3d^8, with 2 unpaired electrons. - \( \mathrm{Co}^{2+} \): [Ar] 3d^7, with 3 unpaired electrons. - \( \mathrm{Cr}^{3+} \): [Ar] 3d^3, with 3 unpaired electrons. - \( \mathrm{Fe}^{2+} \): [Ar] 3d^6, with 4 unpaired electrons. - \( \mathrm{Fe}^{3+} \): [Ar] 3d^5, with 5 unpaired electrons. - \( \mathrm{Mn}^{2+} \): [Ar] 3d^5, with 5 unpaired electrons. - \( \mathrm{Ti}^{4+} \): [Ar], with 0 unpaired electrons.

Step 3: Compare Magnetic Moments

The ions with the most unpaired electrons and, thus, the highest magnetic moments are \( \mathrm{Fe}^{3+} \) and \( \mathrm{Mn}^{2+} \), both with 5 unpaired electrons. This results in the highest magnetic moment possible given the options, according to the formula \( \mu = \sqrt{n(n+2)} \).

Step 4: Determine the Answer

Among the choices given, the pair \( \mathrm{Fe}^{3+} \) and \( \mathrm{Mn}^{2+} \) (option (c)) meets the criteria of having the maximum number of unpaired electrons, hence the highest magnetic moment.

Key Concepts

Unpaired Electrons

Unpaired electrons are crucial in determining the magnetic properties of an atom or ion. Think of them as solo travelers in an electron orbital: when they are alone, they contribute to a magnetic field.
Oxygen, for instance, has two unpaired electrons and is paramagnetic, meaning it is attracted by a magnetic field. The more unpaired electrons an ion has, the stronger its magnetic behavior becomes.

To identify the number of unpaired electrons in a transition metal ion, examine its electron configuration. For example, the electron configuration of ext{Ni}^{2+} is [ ext{Ar}] 3d^8 , meaning there are two unpaired electrons in the d orbital. This information can help predict how the ion will interact with magnetic fields.

Transition Metal Ions

Transition metal ions are elements found in the d-block of the periodic table. They display unique chemical properties due to their partially filled d orbitals. This partial filling allows them to form colorful compounds and display varied oxidation states, making them vital in many chemical reactions.
Their ability to have different numbers of unpaired electrons contributes significantly to their magnetic properties.

Let's take ext{Fe}^{3+} as an example. This ion stems from the element iron, and has the electron configuration of [ ext{Ar}] 3d^5
Since it has five unpaired electrons, it exhibits a high magnetic moment. Transition metal ions like ext{Fe}^{3+} and ext{Mn}^{2+} , having numerous unpaired electrons, demonstrate strong magnetic qualities and are often subjects of study in coordination chemistry and material science.

Bohr Magnetons (B.M.)

Bohr magnetons (B.M.) are the standard unit for expressing the magnetic moment of atoms, ions, or molecules in quantum chemistry.
The magnetic moment of an ion indicates how strong a magnetic field it can produce.

The formula \( \mu = \sqrt{n(n+2)} \) is employed to calculate the magnetic moment of a species, where \( n \) denotes the number of unpaired electrons. The more unpaired electrons present, the higher the value of \( \mu \) results in stronger magnetism.

For instance, ext{Fe}^{3+} with five unpaired electrons has a calculated magnetic moment of about 5.92 BM. In contrast, ext{Ti}^{4+}, which has no unpaired electrons, has a magnetic moment of 0 B.M., indicating no magnetic properties. Understanding Bohr magnetons helps in predicting the behavior of transition metal ions in magnetic fields.