In complexes off wea field ligands, `Delta_(o) lt P` (pairing energy), the energy difference between `t_(2g) and e_(g)` sets is relatively less. Under the unfluence of strong field ligands, `Delta_(O) gt p` (Pairing energy), the energy difference between `t_(2g) and e_(g)` sets is relatively high.
Q. Select the correct increasing order of 10 Dq. value of chromium complexes:
(1) `[Cr(en)_(3)]^(3+)`
(2) `[Cr(o x)_(3)]^(3-)` ltBrgt (3) `[CrF_(6)]^(3-)`
(4) `[Cr(H_(2)O)_(6)]^(3+)`

Options

A. `4 lt 3 lt 1 lt 2`
B. `3 lt 4 lt 2 lt 1`
C. `4 lt 3 lt 2 lt 1`
D. `3 lt 4 lt 1 lt 2`

Answer

To determine the correct increasing order of the Δ₀ (10 Dq) value of the chromium complexes, we need to analyze the ligands in each complex and their field strength. The ligands can be classified into strong field ligands and weak field ligands based on their ability to split the d-orbitals.

### Step-by-Step Solution:

1. **Identify the Ligands and Their Strengths**:
- **[Cr(en)₃]³⁺**: Ethylenediamine (en) is a strong field ligand.
- **[Cr(ox)₃]³⁻**: Oxalate (ox) is also a strong field ligand, but slightly weaker than ethylenediamine.
- **[CrF₆]³⁻**: Fluoride (F) is a weak field ligand.
- **[Cr(H₂O)₆]³⁺**: Water (H₂O) is a weak field ligand.

2. **Rank the Ligands Based on Field Strength**:
- Strongest: Ethylenediamine (en)
- Moderate: Oxalate (ox)
- Weak: Water (H₂O)
- Weakest: Fluoride (F)

3. **Determine the Δ₀ Values**:
- The Δ₀ value increases with the strength of the ligand. Therefore, we can assign the following order based on the ligand strengths:
- [Cr(en)₃]³⁺ has the highest Δ₀ value.
- [Cr(ox)₃]³⁻ has a lower Δ₀ value than [Cr(en)₃]³⁺ but higher than the weak field ligands.
- [Cr(H₂O)₆]³⁺ has a lower Δ₀ value than both [Cr(en)₃]³⁺ and [Cr(ox)₃]³⁻.
- [CrF₆]³⁻ has the lowest Δ₀ value.

4. **Establish the Increasing Order of Δ₀ Values**:
- Based on the analysis above, we can conclude the increasing order of Δ₀ values for the complexes is:
- [CrF₆]³⁻ < [Cr(H₂O)₆]³⁺ < [Cr(ox)₃]³⁻ < [Cr(en)₃]³⁺

### Final Answer:
The correct increasing order of 10 Dq value of chromium complexes is:
\[ [CrF_6]^{3-} < [Cr(H_2O)_6]^{3+} < [Cr(ox)_3]^{3-} < [Cr(en)_3]^{3+} \]