Which of the following pairs of complexes are isomeric with each their but their aqueous solutions exhibit different molar conductivities ?

Explanation

To solve the problem of identifying which pairs of complexes are isomeric with each other but exhibit different molar conductivities in their aqueous solutions, we can follow these steps:

### Step 1: Understand the Types of Isomerism
Isomerism in coordination compounds can occur in several forms, including:
- **Ionization Isomerism**: Different ions can be produced when the complex dissociates in solution.
- **Linkage Isomerism**: Different donor atoms in ligands can coordinate to the metal center.

### Step 2: Analyze Each Option
We need to analyze each pair of complexes provided in the options to determine if they are isomers and if they exhibit different molar conductivities.

#### Option A:
- **Complex 1**: PtCl2(NH3)4^2+ + 2Br^-
- **Complex 2**: PtBr2(NH3)4^2+ + 2Cl^-

**Analysis**: Both complexes yield the same total charge when dissociated (2+ from the cation and 2- from the anion), resulting in the same molar conductivity. Thus, they are not the correct answer.

#### Option B:
- **Complex 1**: CoCl2(NH3)4^+ + NO2^-
- **Complex 2**: CoCl2(NO2)(NH3)4^+ + Cl^-

**Analysis**: The coordination number in the second complex exceeds 6, which is not possible. Therefore, these complexes cannot be isomers.

#### Option C:
- **Complex 1**: Co(NH3)5(NO2)^2+
- **Complex 2**: Co(NH3)5(Cl)^2+

**Analysis**: Both complexes yield the same ions upon dissociation, leading to the same molar conductivity. Hence, they are not the correct answer.

#### Option D:
- **Complex 1**: CoBr(NH3)5^2+ + SO4^2-
- **Complex 2**: CoSO4(NH3)5^+ + Br^-

**Analysis**: Upon dissociation, the first complex yields a total charge of 4 (2+ from the cation and 2- from the anion), while the second complex yields a total charge of 2 (1+ from the cation and 1- from the anion). Since the total charges differ, the molar conductivities will also differ. Thus, this pair is isomeric and exhibits different molar conductivities.

### Conclusion:
The correct answer is **Option D**.

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