Total Number of Possible Isomers for Platinum Complex

To find the total number of possible isomers for the coordination compound $[\text{Pt}(\text{NH}_3)_4\text{Cl}_2]\text{Br}_2$, we need to consider both structural isomerism (specifically, ionization isomerism) and stereoisomerism (specifically, geometrical isomerism).

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1. Ionization Isomerism

Ionization isomers arise when the counter-ions in the ionization sphere exchange places with the anionic ligands inside the coordination sphere.

For the overall molecular formula $\text{Pt}(\text{NH}_3)_4\text{Cl}_2\text{Br}_2$, the possible ionization isomers are:

1. $[\text{Pt}(\text{NH}_3)_4\text{Cl}_2]\text{Br}_2$
2. $[\text{Pt}(\text{NH}_3)_4\text{Cl}\text{Br}]\text{Cl}\text{Br}$
3. $[\text{Pt}(\text{NH}_3)_4\text{Br}_2]\text{Cl}_2$

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2. Geometrical and Optical Isomerism

All three coordination complex ions adopt an octahedral geometry (coordination number of $\text{Pt(IV)} = 6$).

• Case I: $[\text{Pt}(\text{NH}_3)_4\text{Cl}_2]\text{Br}_2$ (Type $[\text{MA}_4\text{B}_2]$)

  • cis-isomer: The two $\text{Cl}^-$ ligands are adjacent (at a $90^\circ$ angle). This complex contains a plane of symmetry and is optically inactive.
  • trans-isomer: The two $\text{Cl}^-$ ligands are opposite to each other (at a $180^\circ$ angle). This complex contains multiple planes of symmetry and is optically inactive.
  • Number of isomers for Case I $= 2$

• Case II: $[\text{Pt}(\text{NH}_3)_4\text{Cl}\text{Br}]\text{Cl}\text{Br}$ (Type $[\text{MA}_4\text{BC}]$)

  • cis-isomer: The $\text{Cl}^-$ and $\text{Br}^-$ ligands are adjacent to each other. This complex contains a plane of symmetry passing through $\text{Pt}$, $\text{Cl}$, $\text{Br}$, and two $\text{NH}_3$ ligands, making it optically inactive.
  • trans-isomer: The $\text{Cl}^-$ and $\text{Br}^-$ ligands are opposite to each other. This complex contains a plane of symmetry and is optically inactive.
  • Number of isomers for Case II $= 2$

• Case III: $[\text{Pt}(\text{NH}_3)_4\text{Br}_2]\text{Cl}_2$ (Type $[\text{MA}_4\text{B}_2]$)

  • cis-isomer: The two $\text{Br}^-$ ligands are adjacent to each other. It contains a plane of symmetry and is optically inactive.
  • trans-isomer: The two $\text{Br}^-$ ligands are opposite to each other. It contains a plane of symmetry and is optically inactive.
  • Number of isomers for Case III $= 2$

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Conclusion

Summing up all the isomers from each case: $\text{Total number of possible isomers} = 2 + 2 + 2 = 6$

Final Answer: The total number of possible isomers for $[\text{Pt}(\text{NH}_3)_4\text{Cl}_2]\text{Br}_2$ is 6.