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The number of possible sterio isomers in...

The number of possible sterio isomers in `Ma_(3)b_(3)` is equal to
(Here a, b are different monodentate ligands).

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To determine the number of possible stereoisomers for the complex \( MA_3B_3 \), where \( A \) and \( B \) are different monodentate ligands, we will analyze the structure and types of isomers that can arise from this coordination complex. ### Step-by-Step Solution: 1. **Identify the Geometry of the Complex:** - The complex \( MA_3B_3 \) has an octahedral geometry because it consists of six ligands surrounding a central metal atom \( M \). 2. **Determine the Types of Isomers:** - In octahedral complexes with two types of ligands, we can have geometrical isomers. The two main types of geometrical isomers are: - **Facial (fac) Isomers:** where three identical ligands occupy one face of the octahedron. - **Meridional (mer) Isomers:** where three identical ligands are arranged in such a way that two of them are on one side and the other one is on the opposite side. 3. **Draw the Possible Isomers:** - **Facial Isomer:** In this arrangement, the three \( A \) ligands are adjacent to each other, forming a face of the octahedron, while the three \( B \) ligands occupy the opposite face. - **Meridional Isomer:** In this arrangement, two \( A \) ligands are on one side of the octahedron, and the third \( A \) ligand is on the opposite side, with the \( B \) ligands arranged similarly. 4. **Check for Optical Isomers:** - For optical isomers to exist, the complex must lack a plane of symmetry. - In both the facial and meridional arrangements, there is a plane of symmetry present. Therefore, neither of these configurations will have optical isomers. 5. **Count the Total Stereoisomers:** - We have identified two geometrical isomers (fac and mer) and confirmed that there are no optical isomers. - Thus, the total number of stereoisomers for the complex \( MA_3B_3 \) is **2**. ### Final Answer: The number of possible stereoisomers in \( MA_3B_3 \) is **2**. ---
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