Problem 126 - A Complete Resource Book in Chemistry for JEE Main

Question

The atomic number of \(\mathrm{V}, \mathrm{Cr}, \mathrm{Mn}\) and \(\mathrm{Fe}\) are respectively \(23,24,25\) and 26 . which one of these may be expected to have the highest second ionization enthalpy? (a) \(\mathrm{Mn}\) (b) \(\mathrm{Fe}\) (c) \(\mathrm{Cr}\) (d) \(\mathrm{V}\)

Step-by-Step Solution

Answer

Manganese (Mn) will have the highest second ionization enthalpy due to its stable half-filled d⁵ configuration after first ionization.

Step 1: Understanding Ionization Enthalpy

The second ionization enthalpy is the energy required to remove the second electron after the first has already been removed. It's important to consider electron configuration and stability when evaluating which element will have the highest second ionization enthalpy.

Step 2: Electron Configuration Analysis

Let's analyze the electron configuration for Mn (25): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵. After removing the first electron, the configuration becomes 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵. This half-filled d-orbital configuration is very stable due to its symmetry.

Step 3: Comparison with Other Elements

For V (23): Removing the first electron from V leaves a configuration that is not as stable as Mn's. For Cr (24): The first ionization results in a half-filled d⁵, which is stable, but Mn is more stable given it retains this after one ionization. For Fe (26): The ionization of Fe results in a less stable configuration compared to Mn.

Step 4: Conclusion

The configuration after the first ionization determines the energy required to remove the second electron. Mn's half-filled 3d⁵ configuration is particularly stable, making the second ionization process require considerably more energy than the others.

Key Concepts

Electron Configuration

Electron configuration is the way electrons are distributed in an atom's orbitals. This distribution dictates many properties of the element. For example, vanadium (V) has an atomic number of 23, so its electron configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3\). Chromium (Cr), with 24 electrons, is configured as \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5\), demonstrating a slight anomaly for increased stability. Manganese (Mn), with 25 electrons, has a configuration \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5\). Finally, iron (Fe), atomic number 26, is arranged as \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6\).

• Configurations determine chemical reactivity.
• Stable configurations resist change.

Understanding electron configurations allows chemists to predict many properties, like ionization enthalpy.

Second Ionization Energy

Second ionization energy is the energy required to remove a second electron after the first has been taken away. It consider how stable an atom becomes after losing one electron.

• High second ionization energy implies the atom's new state is stable and resists electron removal.
• Mn retains a stable, half-filled configuration \(3d^5\) after its first electron is removed, making it less willing to lose another.

The role of electron configuration is critical here. Mn's half-filled d-orbitals are particularly stable, causing its second ionization energy to be higher compared to others like iron or chromium.

Transition Elements

Transition elements form a group in the periodic table known for their partially filled d-orbitals. These elements exhibit unique properties including multiple oxidation states and colored compounds. Vanadium (V), Chromium (Cr), Manganese (Mn), and Iron (Fe) are transition metals.

• They have versatile electron configurations.
• Unique for their d-electron properties.

For example, the d orbitals fluctuate in filling, creating different states of stability for each electron transition. These features contribute to the varying ionization enthalpies observed among them.

Stability of Half-filled Orbitals

Half-filled orbitals, like Mn's \(3d^5\) configuration, are particularly stable. This stability derives from the symmetric distribution of electrons, which pairs with their spin, minimizing repulsion among them.

• Symmetrical distribution lowers energy.
• Stability results in higher ionization energies.

Electrons filling or half-filling orbitals translate into extra stability due to exchange energy. Hence, half-filled d-orbitals, despite external changes like ionization, tenaciously hold onto their electrons due to minimized repulsions.