Complex compounds are molecular compounds which retain their identities even when dissolved in water. They do not give all the simple ions in solution but instead furnish complex ions. The complex compounds are often called coordination compounds because certain groups called ligands are attached to the central metal ion by coordinate or dative bonds. coordination compounds exhibit isomerism, both structural and stereoisomerism. the structure, magnetic property, colour and electrical properties of complexes are explained by various theories:
Q. Arrange the following compounds in order of their molar conductance:
(i) `K[Co(NO_(2))_(4)(NH_(3))_(2)]`
(ii) `[Cr(ONO)_(3)(NH_(3))_(2)]`
(iii) `[Cr(NO_(2))(NH_(3))_(5)]_(3)[Co(NO_(2))_(6)]_(2)`
(iv) `Mg[Cr(NO_(2))_(5)(NH_(3))]`

Options

A. `(ii) lt (i) lt (iv) lt (iii)`
B. `(i) lt (ii) lt (iii) lt (iv)`
C. `(ii) lt (i) lt (iii) lt (iv)`
D. `(iv) lt (iii) lt (ii) lt (i)`

Answer

To arrange the given coordination compounds in order of their molar conductance, we need to analyze each compound based on the number of ions produced when they dissolve in water and their charges. Molar conductance is influenced by both the number of ions and the charge on those ions.

### Step-by-Step Solution:

1. **Identify the Compounds:**
- (i) `K[Co(NO2)4(NH3)2]`
- (ii) `[Cr(ONO)3(NH3)2]`
- (iii) `[Cr(NO2)(NH3)5]3[Co(NO2)6]2`
- (iv) `Mg[Cr(NO2)5(NH3)]`

2. **Determine the Number of Ions Produced:**
- **(i) `K[Co(NO2)4(NH3)2]`:**
- Dissociates into: K⁺ + [Co(NO2)4(NH3)2]⁻
- Total ions = 2 (1 cation + 1 anion)

- **(ii) `[Cr(ONO)3(NH3)2]`:**
- This is a neutral complex, does not dissociate into ions.
- Total ions = 1 (the complex itself)

- **(iii) `[Cr(NO2)(NH3)5]3[Co(NO2)6]2`:**
- Dissociates into: 3[Cr(NO2)(NH3)5] + 2[Co(NO2)6]
- Total ions = 5 (3 cations + 2 anions)

- **(iv) `Mg[Cr(NO2)5(NH3)]`:**
- Dissociates into: Mg²⁺ + [Cr(NO2)5(NH3)]²⁻
- Total ions = 2 (1 cation + 1 anion)

3. **Determine the Charges on Ions:**
- **(i)**: K⁺ (charge +1), [Co(NO2)4(NH3)2]⁻ (charge -1)
- **(ii)**: Neutral complex (charge 0)
- **(iii)**: 3[Cr(NO2)(NH3)5] (charge +3), 2[Co(NO2)6] (charge -6)
- **(iv)**: Mg²⁺ (charge +2), [Cr(NO2)5(NH3)]²⁻ (charge -2)

4. **Calculate the Total Charge Contribution:**
- **(i)**: Total charge contribution = 1
- **(ii)**: Total charge contribution = 0
- **(iii)**: Total charge contribution = 3 + 6 = 9
- **(iv)**: Total charge contribution = 2 + 2 = 4

5. **Rank the Compounds Based on Molar Conductance:**
- The molar conductance is directly proportional to the number of ions produced and their charge.
- **(iii)** has the highest total charge and number of ions (5 ions, charge 9).
- **(iv)** has 2 ions with charge 4.
- **(i)** has 2 ions with charge 1.
- **(ii)** has 1 ion with charge 0.

### Final Order of Molar Conductance:
1. **(iii) `[Cr(NO2)(NH3)5]3[Co(NO2)6]2`** (highest)
2. **(iv) `Mg[Cr(NO2)5(NH3)]`**
3. **(i) `K[Co(NO2)4(NH3)2]`**
4. **(ii) `[Cr(ONO)3(NH3)2]`** (lowest)

### Summary:
The order of the compounds in terms of molar conductance is:
**(iii) > (iv) > (i) > (ii)**