To determine the total number of geometrical isomers for the complex [M(AB)c2 de], we need to consider the possible arrangements of the ligands around the central metal atom.
Let's break down the complex:
- M represents the central metal atom.
- AB is a bidentate ligand, which means it can bind to the metal atom using two donor atoms.
-c, d, and e are monodentate ligands, which means they can bind to the metal atom using only one donor atom each.
Now, let's consider the possible arrangements:
1. AB can bind to M in two different ways: either through one donor atom followed by another (cis configuration) or through one donor atom followed by another in a reversed order (trans configuration). This gives us 2 possibilities for AB.
2. The monodentate ligands c, d, and e can bind to M independently of each other. Since there are three monodentate ligands, there are 3! (3 factorial) ways to arrange them around M. This gives us 6 possibilities for cde.
Therefore, multiplying the possibilities for AB and cde together gives us:
Total number of geometrical isomers = 2 (possibilities for AB) * 6 (possibilities for cde) = 12
So, there are a total of 12 geometrical isomers for the complex [M(AB)c2 de].
