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-)`
(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 increasing order of 10 Dq (or Δo) values for the given chromium complexes, we need to analyze the ligands attached to chromium in each complex and their respective strengths according to the spectrochemical series. The spectrochemical series ranks ligands based on their ability to split the d-orbitals in transition metal complexes.

### Step-by-Step Solution:

1. **Identify the oxidation state of chromium in each complex:**
- For \([Cr(en)_3]^{3+}\):
- Ethylene diamine (en) is a neutral ligand.
- Let the oxidation state of Cr be \(x\).
- \(x + 0 = +3 \Rightarrow x = +3\).

- For \([Cr(ox)_3]^{3-}\):
- Oxalate (ox) has a charge of -2.
- Let the oxidation state of Cr be \(x\).
- \(x + 3(-2) = -3 \Rightarrow x - 6 = -3 \Rightarrow x = +3\).

- For \([CrF_6]^{3-}\):
- Fluoride (F) has a charge of -1.
- Let the oxidation state of Cr be \(x\).
- \(x + 6(-1) = -3 \Rightarrow x - 6 = -3 \Rightarrow x = +3\).

- For \([Cr(H_2O)_6]^{3+}\):
- Water (H2O) is a neutral ligand.
- Let the oxidation state of Cr be \(x\).
- \(x + 0 = +3 \Rightarrow x = +3\).

**Conclusion:** The oxidation state of chromium is +3 in all complexes.

2. **Determine the ligand strength based on the spectrochemical series:**
- The order of ligand strength (from strong to weak) is:
- Carbon-containing ligands > Nitrogen-containing ligands > Oxygen-containing ligands > Halides.
- For the given complexes:
- \([Cr(en)_3]^{3+}\): Ethylene diamine (strong field ligand).
- \([Cr(ox)_3]^{3-}\): Oxalate (moderate field ligand).
- \([Cr(H_2O)_6]^{3+}\): Water (weaker field ligand).
- \([CrF_6]^{3-}\): Fluoride (weakest field ligand).

3. **Rank the complexes based on ligand strength:**
- \([Cr(en)_3]^{3+}\) (strongest, highest Δo)
- \([Cr(ox)_3]^{3-}\) (moderate strength)
- \([Cr(H_2O)_6]^{3+}\) (weaker strength)
- \([CrF_6]^{3-}\) (weakest, lowest Δo)

4. **Establish the increasing order of Δo values:**
- Based on the ligand strengths, the increasing order of Δo (or 10 Dq) values is:
- \([CrF_6]^{3-} < [Cr(H_2O)_6]^{3+} < [Cr(ox)_3]^{3-} < [Cr(en)_3]^{3+}\)

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