Problem 65 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of number of unpaired electrons in the ion \(\mathrm{Cu}^{2+} \mathrm{Ni}^{2+}, \mathrm{Fe}^{3+}\) and \(\mathrm{Cr}^{3+}\) is (a) \(\mathrm{Cu}^{2+}>\mathrm{Ni}^{2+}>\mathrm{Cr}^{3+}>\mathrm{Fe}^{3+}\) (b) \(\mathrm{Ni}^{2+}>\mathrm{Cu}^{2+}>\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}\) (c) \(\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}>\mathrm{Ni}^{2+}>\mathrm{Cu}^{2+}\) (d) \(\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}>\mathrm{Cu}^{2+}>\mathrm{Ni}^{2+}\)

Step-by-Step Solution

Answer

The order is (c) \\( \mathrm{Fe}^{3+} > \mathrm{Cr}^{3+} > \mathrm{Ni}^{2+} > \mathrm{Cu}^{2+} \\\\).

Step 1: Determine Electron Configuration of Cu

Copper (Cu) has an atomic number of 29. The electron configuration of \( \mathrm{Cu} \) is \( [\mathrm{Ar}] \ 3d^{10} \ 4s^{1} \). When copper loses two electrons to form \( \mathrm{Cu}^{2+} \), it loses the \( 4s \) electron and one \( 3d \) electron, resulting in \( [\mathrm{Ar}] \ 3d^{9} \). This means \( \mathrm{Cu}^{2+} \) has 1 unpaired electron.

Step 2: Determine Electron Configuration of Ni

Nickel (Ni) has an atomic number of 28. The electron configuration of \( \mathrm{Ni} \) is \( [\mathrm{Ar}] \ 3d^{8} \ 4s^{2} \). Upon losing two electrons to form \( \mathrm{Ni}^{2+} \), it loses the \( 4s \) electrons, resulting in \( [\mathrm{Ar}] \ 3d^{8} \). This gives \( \mathrm{Ni}^{2+} \) 2 unpaired electrons.

Step 3: Determine Electron Configuration of Fe

Iron (Fe) has an atomic number of 26. Its electron configuration is \( [\mathrm{Ar}] \ 3d^{6} \ 4s^{2} \). When it forms \( \mathrm{Fe}^{3+} \), it loses the \( 4s \) electrons and one \( 3d \) electron, becoming \( [\mathrm{Ar}] \ 3d^{5} \). Thus, \( \mathrm{Fe}^{3+} \) has 5 unpaired electrons.

Step 4: Determine Electron Configuration of Cr

Chromium (Cr) has an atomic number of 24. Its configuration is \( [\mathrm{Ar}] \ 3d^{5} \ 4s^{1} \). When forming \( \mathrm{Cr}^{3+} \), it loses 3 electrons (one from \( 4s \) and two from \( 3d \)), becoming \( [\mathrm{Ar}] \ 3d^{3} \). Therefore, \( \mathrm{Cr}^{3+} \) has 3 unpaired electrons.

Step 5: Order the Ions by Unpaired Electrons

Now that we have determined the number of unpaired electrons for each ion: \( \mathrm{Fe}^{3+} \) has 5, \( \mathrm{Cr}^{3+} \) has 3, \( \mathrm{Ni}^{2+} \) has 2, and \( \mathrm{Cu}^{2+} \) has 1. The correct order from most to fewest unpaired electrons is \( \mathrm{Fe}^{3+} > \mathrm{Cr}^{3+} > \mathrm{Ni}^{2+} > \mathrm{Cu}^{2+} \). Therefore, the correct option is (c).

Key Concepts

Unpaired Electrons

Unpaired electrons are electrons that are alone in an atom's or ion's orbital. Such electrons can significantly influence the chemical and magnetic properties of the substance. It is important to understand that elements strive to achieve stability, often through full or empty orbitals with paired electrons. However, some elements, especially transition metals, commonly exhibit unpaired electrons due to their complex electron configurations.

Unpaired electrons are instrumental in various phenomena:

• Magnetic Properties: Atoms or ions with unpaired electrons are often paramagnetic, which means they are attracted by a magnetic field.
• Chemical Reactivity: These lone electrons can sometimes make the element more chemically reactive.

In the exercise, you found how each ion's electron setup affected the number of unpaired electrons, emphasizing their crucial role.

Transition Metals

Transition metals are elements found in the d-block of the periodic table, typically consisting of groups 3 to 12. These metals are noteworthy because they can exhibit multiple oxidation states and complex electron configurations. Understanding these metals requires recognizing their unique properties, primarily due to their ability to lose different numbers of electrons to form ions.

A few defining characteristics include:

• Partially filled d-orbitals: These give rise to a variety of oxidation states.
• Their electron transition between d-orbitals causes rich coloration commonly seen in many transition metal compounds.
• Highly conductive and often possessing catalytic properties.

In the case of the ions like Cu²⁺ and Fe³⁺, recognizing the transformation in electron configuration helps grasp why they have different numbers of unpaired electrons.

Ion Formation

Ion formation involves the process by which an atom gains or loses electrons to achieve a more stable electron configuration. In transition metals, the formation of ions is especially fascinating due to their varied oxidation states, which arise from the loss of electrons not just from the outermost s-orbital, but also from the inner d-orbitals.

Here's what you need to know:

• Formation of positive ions involves the loss of electrons. For transition metals, often more than one electron can be lost, affecting both s and d orbitals.
• This loss leads to different ionic forms, such as Cu²⁺ or Ni²⁺, each with distinct electron arrangements.
• The resulting ion's properties, including its number of unpaired electrons, can significantly shift its chemical behavior.

The differences revealed in the step-by-step solution highlight how each ion's formation impacts its electron configuration and subsequent properties.

Atomic Number

The atomic number is a fundamental property of an element, indicating the number of protons found in the nucleus of an atom or ion. It also represents the number of electrons in a neutral atom, crucial for determining how elements will form ions and interact in chemical reactions.

Why it's important:

• The atomic number defines the identity of the element. For instance, copper has an atomic number of 29, meaning every copper atom has 29 protons.
• It helps determine the electron configuration. Each element's configuration, and consequently its physical and chemical properties, are influenced by this number.
• In ion formation processes, the atomic number remains unchanged, but the total electron count is altered, which changes the charge.

In the exercise, understanding each element's atomic number helped systematically deduce the consequent electron configurations and the resulting number of unpaired electrons in each ion.