Which of the following complexes has lowest molar conductance ?

Options

A. `CoCl_(3).3NH_(3)`
B. `CoCl_(3).4NH_(3)`
C. `CoCl_(3).5NH_(3)`
D. `CoCl_(3).6NH_(3)`

Explanation

To determine which of the given complexes has the lowest molar conductance, we need to analyze the number of ions produced by each complex when dissolved in solution. Molar conductance is influenced by the number of ions present; more ions lead to higher conductance, while fewer ions lead to lower conductance.

### Step-by-Step Solution:

1. **Understand Molar Conductance**: Molar conductance (\( \Lambda_m \)) is a measure of the ability of an electrolyte to conduct electricity in solution. It depends on the number of ions and their mobility.

2. **Analyze Each Complex**: We need to evaluate the number of ions produced by each complex when dissolved in solution.

- **Option 1**: Let's denote this complex as [Co(NH3)3Cl3].
- Central metal: Co
- Ligands: 3 NH3 and 3 Cl
- When this complex is formed, it does not dissociate into ions in solution. Thus, it produces **0 ions**.

- **Option 2**: Denote this complex as [Co(NH3)4Cl2].
- Central metal: Co
- Ligands: 4 NH3 and 2 Cl
- This complex dissociates into 1 Cl^- ion and the neutral complex. Thus, it produces **1 ion**.

- **Option 3**: Denote this complex as [Co(NH3)5Cl].
- Central metal: Co
- Ligands: 5 NH3 and 1 Cl
- This complex dissociates into 1 Cl^- ion and the neutral complex. Thus, it produces **1 ion**.

- **Option 4**: Denote this complex as [Co(NH3)6].
- Central metal: Co
- Ligands: 6 NH3
- This complex does not dissociate into ions in solution. Thus, it produces **0 ions**.

3. **Count the Total Ions**:
- Option 1: 0 ions
- Option 2: 1 ion
- Option 3: 1 ion
- Option 4: 0 ions

4. **Determine Lowest Molar Conductance**:
- Since molar conductance increases with the number of ions, the complexes with 0 ions will have the lowest molar conductance.
- Options 1 and 4 both produce 0 ions. However, since they are both equal in terms of conductance, we can conclude that any of these two options would have the lowest molar conductance.

### Conclusion:
The complexes [Co(NH3)3Cl3] and [Co(NH3)6] both have the lowest molar conductance due to the absence of ions in solution.

---