Question

The correct increasing order of stability of the complexes based on \( \Delta \) value is:

• A. IV < III < II < I
• B. III < II < IV < I
• C. I < II < IV < III
• D. II < III < I < IV

Hint:

To determine the stability order based on \( \Delta \), consider the ligand field splitting energy and the ligand's electron-donating or withdrawing effects.

Answer 1

The Correct Option is C

To determine the stability order of complexes based on the \( \Delta \) value, we need to consider the crystal field splitting energy \((\Delta)\). Generally, the greater the \( \Delta \), the more stable the complex.
Given options for the stability order according to their \( \Delta \):

1. Option 1: IV < III < II < I
2. Option 2: III < II < IV < I
3. Option 3: I < II < IV < III
4. Option 4: II < III < I < IV

The correct order based on increasing stability, as indicated, is I < II < IV < III. This order suggests that complex I has the lowest \( \Delta \), making it least stable, while complex III has the highest \( \Delta \), making it most stable.

Conclusion: The correct increasing order of stability based on \( \Delta \) value is I < II < IV < III.

Answer 2

Step 1: Understand the problem.
We are given four coordination complexes and need to arrange them in increasing order of stability based on their crystal field splitting energy (Δ). The complexes are:
I. [Mn(CN)₆]³⁻
II. [Co(CN)₆]⁴⁻
III. [Fe(CN)₆]⁴⁻
IV. [Fe(CN)₆]³⁻

Step 2: Recall the concept.
The stability of a complex in the presence of a strong field ligand like CN⁻ depends on the magnitude of crystal field splitting energy (Δ₀). A larger Δ₀ indicates a more stable complex. The value of Δ₀ increases with:
1. Increasing oxidation state of the metal ion.
2. Increasing charge density (smaller ionic radius and higher positive charge).

Step 3: Analyze each complex.
- [Mn(CN)₆]³⁻: Mn³⁺ (d⁴ configuration). Due to its lower oxidation state and weaker field stabilization, Δ₀ is small.
- [Co(CN)₆]⁴⁻: Co²⁺ (d⁷ configuration). CN⁻ is a strong ligand, but Co²⁺ has lower oxidation state compared to Fe³⁺ or Fe²⁺.
- [Fe(CN)₆]³⁻: Fe³⁺ (d⁵ configuration). Higher oxidation state, hence stronger field stabilization.
- [Fe(CN)₆]⁴⁻: Fe²⁺ (d⁶ configuration). CN⁻ forms a low-spin complex with Fe²⁺, giving maximum field splitting among these.

Step 4: Determine the increasing order of Δ₀ (and thus stability).
From the above analysis, the increasing order of crystal field splitting energy (Δ₀) — and therefore increasing order of stability — is:
\[ [\text{Mn(CN)}_6]^{3-} \lt [\text{Co(CN)}_6]^{4-} \lt [\text{Fe(CN)}_6]^{3-} \lt [\text{Fe(CN)}_6]^{4-} \]

Step 5: Final Answer.
\[ \boxed{I \lt II \lt IV \lt III} \]