How many stereoisomers exist with the following basic connectivity? . ch3chclch2chclch3

What you've got is C5H10Cl2 as the molecular formula. 

Those 5 carbons could be all in a line, giving dichloropentanes 
The two chlorines can be in the following positions: 
1,1 (both on an end carbon) 
1,2 
1,3 (one on the end, one on the middle carbon) 
1,4 
1,5 (one at each end) 
So far, that's 5 different position isomers of dichloropentane 
but you can also make: 
2,2 
2,3 and even 3,3 
altogether 8 position isomers of dichloropentane. 

Then, the carbons could be on a branched chain, giving a methylbutane structure, and the chlorines can go in 9 different arrangements around that 

The carbon chain could also be based on dimethylpropane, when the central carbon is attached to four methyl groups; 2,2 dimethylpropane. There are just two possible ways to attach the chlorines to that 'skeleton' 
Altogether, that makes 19 different structural isomers. 

Finally, you could consider those structural isomers in which one of the carbon atoms is attached to 4 different groups. An asymmetric carbon or chrial centre will generate two optical isomers. Non-superimposable mirror images. A left hand and a right hand version of the structure. 
I think there are 8 such structures with asymmetric carbons, 4 on the straight chain, and 4 on the methylbutane. 
So 8 of those 19 we counted before can exist as one of two mirror images 
Which makes a total of 27 isomers. 

You really need to build the models to appreciate the different forms.



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