Arrange the following complexes in the increasing order of conductivity of their solution
`[Co(NH_(3))_(3)Cl_(3)], [Co(NH_(3))_(4)Cl_(2)]Cl, [Co(NH_(3))_(6)]Cl_(3), [Cr(NH_(3))_(5)Cl] Cl_(2)`

Options

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

Explanation

To determine the increasing order of conductivity of the given coordination complexes, we need to analyze the number of ions produced when each complex dissociates in solution. The conductivity of a solution is directly related to the number of ions present; more ions lead to higher conductivity.

### Step-by-Step Solution:

1. **Identify the complexes:**
- Complex 1: \([Co(NH_3)_3Cl_3]\)
- Complex 2: \([Co(NH_3)_4Cl_2]Cl\)
- Complex 3: \([Co(NH_3)_6]Cl_3\)
- Complex 4: \([Cr(NH_3)_5Cl]Cl_2\)

2. **Determine the number of ions produced by each complex:**
- **Complex 1: \([Co(NH_3)_3Cl_3]\)**
- This complex does not dissociate into any additional ions in solution. It remains as one unit.
- Total ions = 1 (the complex itself)

- **Complex 2: \([Co(NH_3)_4Cl_2]Cl\)**
- This complex dissociates into one complex ion and one chloride ion.
- Total ions = 2 (1 complex ion + 1 Cl⁻)

- **Complex 3: \([Co(NH_3)_6]Cl_3\)**
- This complex dissociates into one complex ion and three chloride ions.
- Total ions = 4 (1 complex ion + 3 Cl⁻)

- **Complex 4: \([Cr(NH_3)_5Cl]Cl_2\)**
- This complex dissociates into one complex ion and two chloride ions.
- Total ions = 3 (1 complex ion + 2 Cl⁻)

3. **Summarize the total ions for each complex:**
- Complex 1: 1 ion
- Complex 2: 2 ions
- Complex 3: 4 ions
- Complex 4: 3 ions

4. **Arrange the complexes in increasing order of conductivity:**
- Since conductivity increases with the number of ions, we can arrange them as follows:
- Complex 1: 1 ion (lowest conductivity)
- Complex 2: 2 ions
- Complex 4: 3 ions
- Complex 3: 4 ions (highest conductivity)

### Final Order:
The increasing order of conductivity is:
\[ [Co(NH_3)_3Cl_3] < [Co(NH_3)_4Cl_2]Cl < [Cr(NH_3)_5Cl]Cl_2 < [Co(NH_3)_6]Cl_3 \]