Question

Given below are two statements:

Statement (I): In octahedral complexes, when \( \Delta_o < P \) high spin complexes are formed. When \( \Delta_o > P \) low spin complexes are formed.
Statement (II): In tetrahedral complexes because of \( \Delta_t < P \), low spin complexes are rarely formed.

In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Statement I is correct but Statement II is incorrect
• B. Statement I is incorrect but Statement II is correct
• C. Both Statement I and Statement II are incorrect
• D. Both Statement I and Statement II are correct

Hint:

High spin complexes generally form in weak field ligands, while low spin complexes form in strong field ligands due to the splitting of d-orbitals.

Answer 1

The Correct Option is D

The problem presents two statements regarding the formation of high spin and low spin coordination complexes in octahedral and tetrahedral geometries. We need to evaluate the correctness of each statement.

Concept Used:

The solution is based on the principles of Crystal Field Theory (CFT).

1. d-Orbital Splitting: In the presence of ligands, the d-orbitals of a central metal ion split into different energy levels.
   • In an octahedral field, the orbitals split into a lower-energy \( t_{2g} \) set and a higher-energy \( e_g \) set. The energy gap is the Crystal Field Splitting Energy, \( \Delta_o \).
   • In a tetrahedral field, the splitting is inverted, with a lower-energy \( e \) set and a higher-energy \( t_2 \) set. The energy gap is \( \Delta_t \).
2. Pairing Energy (P): This is the energy required to overcome the electrostatic repulsion when placing two electrons into the same d-orbital.
3. High Spin vs. Low Spin Complexes: For metal ions with d\(^4\) to d\(^7\) configurations, there are two possible ways to arrange the electrons. The choice depends on the comparison between the splitting energy (\( \Delta \)) and the pairing energy (P).
   • If \( \Delta < P \), it is energetically cheaper to place an electron in a higher-energy orbital than to pair it up. This results in a high spin complex with the maximum number of unpaired electrons.
   • If \( \Delta > P \), it is energetically cheaper to pair electrons in lower-energy orbitals than to promote them across the large energy gap. This results in a low spin complex with the minimum number of unpaired electrons.
4. Magnitude of Splitting: The magnitude of splitting in a tetrahedral field is significantly smaller than in an octahedral field for the same metal and ligands, with the approximate relationship being \( \Delta_t \approx \frac{4}{9} \Delta_o \).

Step-by-Step Solution:

Step 1: Evaluation of Statement I.

Statement I says: "In octahedral complexes, when \( \Delta_o < P \) high spin complexes are formed. When \( \Delta_o > P \) low spin complexes are formed."

• When \( \Delta_o < P \), the crystal field splitting energy is smaller than the pairing energy. It requires less energy for an electron to occupy a higher-energy \( e_g \) orbital than to pair up in a lower-energy \( t_{2g} \) orbital. This leads to a configuration with the maximum possible number of unpaired electrons, which is the definition of a high spin complex. The first part of the statement is correct.
• When \( \Delta_o > P \), the crystal field splitting energy is larger than the pairing energy. It requires less energy for an electron to pair up in a \( t_{2g} \) orbital than to be promoted to an \( e_g \) orbital. This leads to a configuration with the minimum possible number of unpaired electrons, which is the definition of a low spin complex. The second part of the statement is also correct.

Since both parts of the statement are correct, Statement I is correct.

Step 2: Evaluation of Statement II.

Statement II says: "In tetrahedral complexes because of \( \Delta_t < P \), low spin complexes are rarely formed."

• The crystal field splitting in tetrahedral complexes, \( \Delta_t \), is inherently small. This is due to having fewer ligands (4 instead of 6) and the ligands not pointing directly at the d-orbitals.
• Because \( \Delta_t \) is small, it is almost always less than the pairing energy, P. So, the condition \( \Delta_t < P \) holds true for nearly all tetrahedral complexes.
• As a consequence of \( \Delta_t < P \), it is almost always energetically favorable for electrons to occupy the higher-energy \( t_2 \) orbitals rather than pairing in the lower-energy \( e \) orbitals.
• This means that tetrahedral complexes almost exclusively adopt a high spin configuration. Low spin configurations are energetically unfavorable and thus are very rarely observed.

The statement correctly identifies the reason (\( \Delta_t < P \)) and the consequence (low spin complexes are rare). Therefore, Statement II is correct.

Final Conclusion:

Based on the analysis, both Statement I and Statement II are correct descriptions of the principles of Crystal Field Theory.

Thus, the most appropriate answer is: Both Statement I and Statement II are correct.