An octahedral complex has the type MA₂B₂CD with monodentate ligands…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
An octahedral complex has the type with monodentate ligands. (a) In how many ways can the six ligands be placed on six numbered corners? (b) What is that number divided by the 24 turns? (c) What is the true number of stereoisomers?
Need a reminder? The key ideaShow
Write the complex as trans pairs. The same pairs mean the same geometrical isomer. For monodentate ligands a mirror plane exists if one pair is two identical ligands or two pairs are the same. A ring takes two cis corners. Stereoisomers = geometrical isomers + chiral isomers.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Placements. .
Step 2. Division. . A count of isomers cannot be a fraction, so something is wrong with the idea that every isomer appears 24 times.
Step 3. The true count. The trans pair sets number 6. Of them, those with an identical pair or two matching pairs have a mirror plane. The others are chiral and count twice, which gives 8 stereoisomers in all.
Step 4. Why 7.5. An achiral isomer is turned onto itself by some of the 24 turns, so it appears fewer than 24 times in the 180. The division then undercounts the isomers by half an isomer.
Answer: 180 placements, 7.5 after division, and 8 stereoisomers.
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