Draw all geometrical isomers of \(\mathrm{Pt}(\mathrm{CN})_{2} \mathrm{Br}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} .\) Which of these isomers has an optical isomer? Draw the various optical isomers.

Short Answer

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The complex \(\mathrm{Pt}(\mathrm{CN})_{2}\mathrm{Br}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\) has an octahedral geometry with three different ligands and can form two geometrical isomers: fac-isomer and mer-isomer. The fac-isomer has optical activity, as it has an enantiomeric pair of optical isomers with ligands in clockwise and counterclockwise sequences, whereas the mer-isomer does not possess optical isomers.

Step by step solution

01

Identifying the coordination geometry

As the platinum atom has a coordination number of 6, the coordination geometry is octahedral. In an octahedral geometry, the central atom is located at the center of an octahedron, with the six ligands surrounding it at equal distances and angles.
02

Arranging the ligands into geometrical isomers

For the given complex, we have three different ligands: CN, Br, and H2O. As there are six potential positions around the platinum atom for these ligands, we can draw different geometrical isomers with this arrangement. We look for fac (facial) and mer (meridian) isomers in the complex: 1. fac-isomer: Three different ligands (CN, Br, H2O) occupy adjacent positions on the same face of the octahedron, while the other face has similar ligands in the same arrangement. 2. mer-isomer: The three different ligands (CN, Br, H2O) occupy three alternate positions, creating a meridian on the octahedron.
03

Identifying optical isomers

For the given complex, the fac-isomer is the only one that displays optical activity, as it has a non-superimposable mirror image. The mer-isomer does not have a mirror image that is non-superimposable, so it does not possess optical isomers.
04

Drawing optical isomers of the fac-isomer

The fac-isomer has an enantiomeric pair as its optical isomers. These isomers are non-superimposable mirror images of each other: - In the first enantiomer, we can label the positions of the ligands as [CN]-[Br]-[H2O] in a clockwise arrangement on the front face and in the opposite sense on the back face. - In the second enantiomer (the mirror image of the first), the arrangement of ligands will be in a counterclockwise sequence on the front face and in a clockwise sequence on the back face. The resulting optical isomers are the enantiomeric pair of the fac-isomer, distinguished by their arrangement of ligands in a clockwise or counterclockwise sequence.

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