Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following pairs of ions have same paramagnetic moment? (a) \(\mathrm{Cu}^{2+}, \mathrm{Ti}^{3+}\) (b) \(\mathrm{Ti}^{3+}, \mathrm{Ni}^{2+}\) (c) \(\mathrm{Ti}^{4+}, \mathrm{Cu}^{2+}\) (d) \(\mathrm{Mn}^{2+}, \mathrm{Cu}^{2+}\)

Step-by-Step Solution

Answer

(a) Cu^{2+}, Ti^{3+} have the same paramagnetic moment.

Step 1: Understand Paramagnetic Moment

The paramagnetic moment of an ion is determined by the number of unpaired electrons it has. This is because unpaired electrons contribute to magnetic properties.

Step 2: Determine Electronic Configuration

Determine the electronic configuration for each ion to find the number of unpaired electrons. - \(\text{Cu}^{2+} : [Ar] 3d^9\) has 1 unpaired electron.- \(\text{Ti}^{3+} : [Ar] 3d^1\) has 1 unpaired electron.- \(\text{Ni}^{2+} : [Ar] 3d^8\) has 2 unpaired electrons.- \(\text{Ti}^{4+} : [Ar]\) has 0 unpaired electrons.- \(\text{Mn}^{2+} : [Ar] 3d^5\) has 5 unpaired electrons.

Step 3: Identify Pairs with Same Number of Unpaired Electrons

Compare the number of unpaired electrons for each pair:- \(\text{Cu}^{2+} : 1\) and \(\text{Ti}^{3+} : 1\)- \(\text{Ti}^{3+} : 1\) and \(\text{Ni}^{2+} : 2\)- \(\text{Ti}^{4+} : 0\) and \(\text{Cu}^{2+} : 1\)- \(\text{Mn}^{2+} : 5\) and \(\text{Cu}^{2+} : 1\)The only pair with the same number of unpaired electrons is \(\text{Cu}^{2+}\) and \(\text{Ti}^{3+}\).

Key Concepts

Electronic Configuration

The electronic configuration of an atom or ion describes the distribution of electrons in its atomic orbitals. Understanding the electronic configuration is crucial as it determines the chemical properties and the reactivity of the element. For ions, this configuration changes as electrons are added or removed to form stable structures. Let's look at the example of various ions given in the exercise:

• For \( ext{Cu}^{2+}\), the electronic configuration is \[\text{[Ar]} 3d^9\]. This means that the copper ion, when losing 2 electrons, arranges its electrons to fill up the orbitals such that nine electrons are in the 3d orbitals.
• Similarly, \( ext{Ti}^{3+}\) becomes \[\text{[Ar]} 3d^1\], with one electron in the 3d orbitals.
• The \( ext{Ni}^{2+}\) ion configures as \[\text{[Ar]} 3d^8\].
• While \( ext{Mn}^{2+}\) ends up as \[ \text{[Ar]} 3d^5 \].

Knowing how electrons occupy these orbitals is essential to predict the magnetic behavior of an ion. Electrons fill orbitals starting from the lowest energy level and spread out to higher levels, which influences the magnetic properties.

Unpaired Electrons

Unpaired electrons in an atom or ion are those which do not have a partner with opposite spin in the same orbital. Since these singly occupied orbitals contribute to magnetism, identifying unpaired electrons allows us to understand the paramagnetic potential of an atom or ion. To find unpaired electrons, you examine the electronic configuration of the ion. Let's see this in action using our exercise examples:

• \( ext{Cu}^{2+}\) with configuration \[\text{[Ar]} 3d^9\] has 9 electrons in the 3d orbitals, meaning one of these electrons is unpaired.
• The \( ext{Ti}^{3+}\) ion is configured as \[\text{[Ar]} 3d^1\], indicating there is 1 unpaired electron in that single occupied orbital.
• \( ext{Ni}^{2+}\), \[ \text{[Ar]} 3d^8 \], has two orbitals with unpaired electrons.
• \( ext{Mn}^{2+}\), having \[ \text{[Ar]} 3d^5 \], has each of the five d orbitals singly occupied and hence each electron unpaired.

The presence of unpaired electrons is key to understanding the magnetic behavior of ions. The more unpaired electrons there are, the stronger the magnetic properties generally will be.

Magnetic Properties of Ions

The magnetic properties of atoms and ions are driven by their electronic structure, particularly the presence of unpaired electrons. An electron's spin creates a magnetic moment, and thus each unpaired electron contributes to the overall magnetic behavior of the ion. Magnetic properties can be categorized as follows:

• **Diamagnetism**: Occurs in substances with no unpaired electrons. These materials are generally repulsed by magnetic fields.
• **Paramagnetism**: Involves materials that have one or more unpaired electrons, like \( ext{Cu}^{2+}\) and \( ext{Ti}^{3+}\), resulting in weak attraction to magnetic fields.
• **Ferromagnetism**: Characteristic of materials with numerous unpaired electrons and individually strong magnetic moments aligning together, such as in iron, resulting in strong magnetism.

In the context of the exercise, \( ext{Cu}^{2+}\) and \( ext{Ti}^{3+}\) are both paramagnetic because each possesses one unpaired electron contributing to a magnetic moment but not to the extent of ferromagnetic materials. In general, analyzing the number of unpaired electrons helps predict how an ion will behave in the presence of a magnetic field. This is a vital aspect in fields like chemistry and materials science, where magnetic properties are important for determining an element's applications and behaviors.