Number of sterioisomers of 2,3,5,6-tetrachloroheptane [closed]

What is the total number of stereoisomers for the compound 2,3,5,6-tetrachloroheptane?

I figured the answer to be 16, but the answer given is 10.

Here is a similar question

• Apparently, some of your 16 are the same thing spelled backwards. Aug 11, 2019 at 15:09
• but why 10 ..pls explain for better understanding Aug 11, 2019 at 15:16
• Your link is not similar. It is a tetrachlorooctane, not heptane. Write the 16 possibilities as XXXX using R and S. Now cast out the duplicates. Aug 11, 2019 at 16:10

@Ivan Neretin, in his comment soon after your post, essentially solved the problem for you. In a comment I subsequently tried to set you in the right direction. Now that the ten structures have been posted in an answer and you have had time to think about a solution, here is the methodology to get the correct answer if you haven't solved it on your own.

All of the 16 permutations are drawn as shown in the chart below. The 10 isomers are in black and the 6 duplicates are in red. Within each group, a red assignment has an identical black one. As an example, in the second group of four, RRSR = RSRR owing to the symmetry in the compound. That is, 2-3-5-6 = 6-5-3-2. The central group of six has "four meso structures", two of which are duplicates.

Note that the number of possible permutations in each group are the coefficients of each term in the expansion of (R + S)4.

• I wrote only those that are optically active and have omitted meso and duplicates in my answer. However , I am well aware of these.I corrected my mistake. Aug 12, 2019 at 1:14
• Can you please give the reference of this answer (for example, name of source from which the concept of eliminating R-S left right similarity has been taken)? Jan 21 at 1:44
• @S Das: I have no source, just many years of experience. Imagine a model of the RSSS molecule mounted on the teacher's desk viewed by the class of students reading left to right. The teacher is on the other side of the model. What does s/he see reading left to right? Has the molecule changed? Jan 21 at 18:56

The given compound 2,3,5,6-tetrachloroheptane has 10 isomers. These have been shown below.

The compound 2,3,5,6-tetrachlorooctane in the link does not have a meso compound. The terminal groups, methyl and ethyl are different and therefore meso form is not possible.

The possible combinations have been given below, which are 16.