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

Step 1: Understanding Electron Configuration Basics

First, we need to understand how to find the electron configuration for each ion. Remember that when you remove electrons to form a cation, they come from the outermost shell. For transition metals, the electron removal starts from the 4s orbital instead of the 3d orbital. Additionally, remember to apply Hund's Rule for determining unpaired electrons.

Step 2: Determine Electron Configuration for \( \mathrm{Cu}^{2+} \)

Copper's electron configuration is \([\mathrm{Ar}] \, 3d^{10} \, 4s^1\). For \( \mathrm{Cu}^{2+} \), two electrons are removed, primarily from the 4s orbital: \([\mathrm{Ar}] \, 3d^9\). In this configuration, there is 1 unpaired electron in the \(3d\) orbitals.

Step 3: Determine Electron Configuration for \( \mathrm{Ni}^{2+} \)

Nickel's electron configuration is \([\mathrm{Ar}] \, 3d^8 \, 4s^2\). For \( \mathrm{Ni}^{2+} \), remove two electrons from the \(4s\) and \(3d\) orbitals: \([\mathrm{Ar}] \, 3d^8\). Here, there are 2 unpaired electrons in the \(3d\) orbitals due to Hund's Rule.

Step 4: Determine Electron Configuration for \( \mathrm{Fe}^{3+} \)

Iron's electron configuration is \([\mathrm{Ar}] \, 3d^6 \, 4s^2\). For \( \mathrm{Fe}^{3+} \), remove three electrons, mainly from the \(4s\) and \(3d\) orbitals: \([\mathrm{Ar}] \, 3d^5\). Here, there are 5 unpaired electrons because no pairing occurs until all orbitals have one electron.

Step 5: Determine Electron Configuration for \( \mathrm{Cr}^{3+} \)

Chromium's electron configuration is \([\mathrm{Ar}] \, 3d^5 \, 4s^1\). For \( \mathrm{Cr}^{3+} \), remove three electrons from the \(4s\) and then the \(3d\) orbitals: \([\mathrm{Ar}] \, 3d^3\). In this configuration, there are 3 unpaired electrons.

Step 6: Compare Unpaired Electrons Count

Now, we compare the number of unpaired electrons: \( \mathrm{Fe}^{3+}: 5, \ \mathrm{Cr}^{3+}: 3, \ \mathrm{Ni}^{2+}: 2, \ \mathrm{Cu}^{2+}: 1\). Therefore, the correct order based on the number of unpaired electrons is \( \mathrm{Fe}^{3+} > \mathrm{Cr}^{3+} > \mathrm{Ni}^{2+} > \mathrm{Cu}^{2+} \).

Key Concepts

Electron Configuration

Electron configuration is a method to represent the arrangement of electrons in an atom or ion. It is essential for understanding how elements interact and form chemical bonds. Each electron occupies an orbital, and the configuration indicates the level, subshell, and the number of electrons within each subshell. Transition metals like copper (Cu) and nickel (Ni) can lose electrons to form ions. Their electron configuration appears intriguing because they deviate from the expected filling order.

• Start by identifying the neutral atom configuration.
• When forming cations, remove electrons from the outermost shell, typically starting from the 4s subshell before the 3d.
• This distinct pattern affects properties like magnetism and electrical conductivity.

For example, copper's ground state electron configuration is ([[Ar\([\mathrm{Ar}] \ 3d^{10} \ 4s^1\). When you form \(\mathrm{Cu}^{2+}\), two electrons are removed, resulting in \([\mathrm{Ar}]\ 3d^9\). The distribution can impact the number of unpaired electrons, which are crucial for reactivity and stability.

Transition Metals

Transition metals are elements found in the d-block of the periodic table, characterized by their ability to form various oxidation states and complex ions. These elements include metals like iron (Fe), nickel (Ni), copper (Cu), and chromium (Cr). Their properties vary due to their specific electron configurations.

• They generally have electrons filling the \(3d\), \(4d\), or \(5d\) orbitals.
• These elements can exhibit magnetic properties due to unpaired electrons.
• Their capacity to form colored compounds arises from electron transitions within the d orbitals, influencing a material's optical properties.

Understanding these metals' unpaired electrons helps elucidate behaviors such as catalysis in chemical reactions and the formation of alloys. For instance, examining \(\mathrm{Fe}^{3+}\) and \(\mathrm{Ni}^{2+}\), we observe different numbers of unpaired electrons that affect their magnetic characteristics and chemical behavior.

Hund's Rule

Hund's Rule is a principle used in quantum chemistry to determine the lowest energy electron configuration in orbitals. Simply put, it states that electrons will fill an empty orbital before they pair up in a filled orbital. This minimizes electron repulsions and stays consistent with the principle that systems favor lowest energy states.

• Consideration of electron spin: Electrons will have parallel spins before pair-up occurs.
• This rule is significant for predicting the number of unpaired electrons in transition metals.
• Example: In filling \(3d\) orbitals of \(\mathrm{Fe}^{3+}\), all five available \(3d\) orbitals receive one electron; hence, they remain unpaired according to Hund's Rule.

Applying Hund's Rule helps us understand the behavior of elements in various chemical contexts. For transition metal ions like \(\mathrm{Fe}^{3+}\) or \(\mathrm{Cr}^{3+}\), it clarifies why these ions have maximum unpaired electrons, explaining characteristics such as their magnetic properties and reactive tendencies.