Problem 127 - 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) Mn (b) \(\mathrm{Fe}\) (c) \(\mathrm{Cr}\) (d) \(\mathrm{V}\)

Step-by-Step Solution

Answer

Therefore, chromium (Cr) is expected to have the highest second ionization enthalpy.

Step 1: Understanding Second Ionization Enthalpy

Second ionization enthalpy refers to the energy required to remove a second electron from a singly charged cation of an element. This typically requires more energy than the first because it involves an electron from a positively charged ion.

Step 2: Looking at Electron Configurations

Examine the electron configurations for these elements: \( \mathrm{V}: [\mathrm{Ar}] 3d^3 4s^2 \), \( \mathrm{Cr}: [\mathrm{Ar}] 3d^5 4s^1 \), \( \mathrm{Mn}: [\mathrm{Ar}] 3d^5 4s^2 \), \( \mathrm{Fe}: [\mathrm{Ar}] 3d^6 4s^2 \). After the first ionization, vanadium becomes \( [\mathrm{Ar}] 3d^3 4s^1 \), chromium becomes \( [\mathrm{Ar}] 3d^5 \), manganese becomes \( [\mathrm{Ar}] 3d^5 4s^1 \), and iron becomes \( [\mathrm{Ar}] 3d^6 4s^1 \).

Step 3: Evaluate Stability After First Ionization

Stability of the electronic configuration following first ionization is crucial for determining the second ionization enthalpy. You should consider that half-filled and fully-filled electron configurations are more stable. Post-first ionization, chromium has a stable half-filled \(3d^5\) configuration, which means the second ionization will require significantly more energy as it disrupts this stability.

Step 4: Conclusion on Second Ionization Enthalpy

Given chromium's stable \(3d^5\) configuration after the first ionization, removing another electron would disrupt this stable state, leading to higher second ionization enthalpy compared to vanadium, manganese, and iron. Thus, chromium is expected to have the highest second ionization enthalpy.

Key Concepts

Electron Configuration

Electron configuration is a way to represent the arrangement of electrons around the nucleus of an atom. For transition metals like vanadium (V), chromium (Cr), manganese (Mn), and iron (Fe), we utilize the Aufbau principle, which helps us determine their ground state electron configurations.

• Vanadium (V) has an electron configuration of: \( [\text{Ar}] 3d^3 4s^2 \).
• Chromium (Cr) uniquely prefers a half-filled arrangement: \( [\text{Ar}] 3d^5 4s^1 \).
• Manganese (Mn) aligns with a full 4s orbital and half-filled 3d: \( [\text{Ar}] 3d^5 4s^2 \).
• Iron (Fe) adds up to: \( [\text{Ar}] 3d^6 4s^2 \).

The electron configuration helps us understand how electrons fill atomic orbitals and the relative stability of these configurations. Notably, certain arrangements such as half-filled or completely filled d subshells offer extra stability. Chromium exemplifies a stable half-filled \(3d^5\) configuration, which significantly impacts its second ionization enthalpy.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. The first ionization energy removes one electron; the second continues with the removal of another from an already charged ion.
This process demands even more energy because:

• The cation after the first ionization has a positive charge, increasing nuclear attraction.
• Removing an electron often leaves a configuration closer to stability, making further removal more difficult.

The second ionization energy is closely tied to how electron configurations change upon the first removal. In chromium's case, after ejecting one 4s electron, the resulting \(3d^5\) configuration becomes highly stable. Disturbing this balance by removing yet another electron involves breaking a stable electron state, which requires extra energy.

Transition Metals

Transition metals, situated in the d-block of the periodic table, are characterized by their partially filled d orbitals and are known for their unique chemical and physical properties. These metals exhibit several distinct traits:

• They often form colored compounds due to d-d electronic transitions within their d orbitals.
• They can have multiple oxidation states, enabling a variety of chemical reactions.
• Many possess magnetic properties owing to unpaired electrons.

Transition metals’ distinctive electron configurations, notable in the second series from scandium (Sc) through zinc (Zn), contribute to their complex ionization processes. Such configurations, underscored by examples like chromium's exceptional half-filled \(3d^5\) state, illustrate the factors influencing their ionization energies. Understanding these metals' electron arrangements is crucial for predicting a wide range of behaviors, including which might exhibit the highest second ionization enthalpy, as seen with chromium's significant energy requirement to disrupt its stable state.