The highest molar conductivity will be exhibited by the complex .

Options

A. `[Cr(NH_(3))_(6)]Cl_(3)`
B. `[Cr(NH_(3))_(6)Cl]Cl_(2)`
C. `[Cr(NH_(3))_(6)Cl_(2)]Cl`
D. `[Cr(NH_(3))_(6)Cl_(3)]`

Answer

To determine which complex exhibits the highest molar conductivity, we need to analyze the number of ions produced when each complex dissociates in solution. Molar conductivity is directly related to the number of ions in solution; more ions result in higher conductivity.

### Step-by-Step Solution:

1. **Understanding Molar Conductivity**:
- Molar conductivity (\( \Lambda_m \)) is a measure of how well a solution can conduct electricity. It increases with the number of ions present in the solution.

2. **Analyzing the Given Complexes**:
- We need to look at the dissociation of each complex to find out how many ions each produces.

3. **Complex 1: \( \text{Cr(NH}_3\text{)}_6\text{Cl}_3 \)**:
- This complex dissociates into:
- 1 \( \text{Cr(NH}_3\text{)}_6^{3+} \) ion (cation)
- 3 \( \text{Cl}^- \) ions (anions)
- Total ions = 1 + 3 = **4 ions**.

4. **Complex 2: \( \text{Cr(NH}_3\text{)}_4\text{Cl}_2 \)**:
- This complex dissociates into:
- 1 \( \text{Cr(NH}_3\text{)}_4^{2+} \) ion (cation)
- 2 \( \text{Cl}^- \) ions (anions)
- Total ions = 1 + 2 = **3 ions**.

5. **Complex 3: \( \text{Cr(NH}_3\text{)}_4\text{Cl} \)**:
- This complex dissociates into:
- 1 \( \text{Cr(NH}_3\text{)}_4^{+} \) ion (cation)
- 1 \( \text{Cl}^- \) ion (anion)
- Total ions = 1 + 1 = **2 ions**.

6. **Complex 4: \( \text{Cr(NH}_3\text{)}_6 \)**:
- This complex does not have any counter ions and does not dissociate in solution.
- Total ions = **1 ion** (the coordination sphere itself).

7. **Comparing the Total Ions**:
- Complex 1: 4 ions
- Complex 2: 3 ions
- Complex 3: 2 ions
- Complex 4: 1 ion

8. **Conclusion**:
- The complex with the highest molar conductivity is the one that produces the most ions upon dissociation. Therefore, **Complex 1: \( \text{Cr(NH}_3\text{)}_6\text{Cl}_3 \)** exhibits the highest molar conductivity with a total of 4 ions.

### Final Answer:
The highest molar conductivity will be exhibited by the complex \( \text{Cr(NH}_3\text{)}_6\text{Cl}_3 \).

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