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Complexes
along with many other molecules can have isomerism of several different
kinds. Two or more species with different chemical or physical properties but
the same formula are known as isomers. There are a number of different
types of isomerism: the discussion below is about geometric isomerism,
where the ligands differ in spatial orientation.
Square
planar complexes can show isomerism. If you consider a molecule like
Pt(Cl)2(NH3)2, there are two different ways to
arrange the ligands around the central atom.

The complex with the
chlorines on opposite sides of the square is known as the trans isomer,
the one with the chlorines next to each other is known as the cis isomer.
All the other possible ways to arrange the molecule are the same as one of these
two isomers: if you draw another structure like the one below
you can see that it is the same as the trans-platin structure
above: just rotate the complex by 900 and you'll see the same
structure. If you have more than two different substituents you may be able to
make more isomers. For example, a square planar complex with the formula
M(A)(B)(C)(D) has three possible unique isomers: can you identify them?
Octahedral
complexes can have geometric isomerism as well. For example, the complex
Co(Cl)2(NH3)4 has two possible isomers: one
where the chlorines are on opposite sides of the octahedron, and one where they
are adjacent.

If you play with a model kit, you will realize that these are the
only two possible isomers: all other arrangements are just one of the above two
rotated.
Example: How many isomers does the complex
[Pt(Cl)3(NH3)]- have?
Solution: Draw out the structure of the complex.
.
There are four
possible ways to draw this: put the ammonia on the top, left, right and bottom.
However, all of these are really the same: the above complex rotated. Thus, the
complex has only one isomer.
Example: How many isomers does the complex
[Pt(Cl)2(NH3)(CO)]- have?
Solution: Here, we have two possibilities.
 
If you play with a model of the
above complex, you should be able to see that these are the only two unique
structures: everything else is either the above rotated or flipped.
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