How many isomers of C₄H₉Br are possible?

Question

Quizplus · Accepted Answer

The number of isomers can be determined by counting the number of distinct arrangements of the atoms. In this case, there are four different types of atoms (C, S, U, Br), and 22 total atoms. We can use the formula for permutations with repetition:
N! / (n1! * n2! * n3! * ...)
where N is the total number of objects (in this case, 22) and n1, n2, n3, etc. are the number of repetitions of each object type (in this case, C=1, S=2, U=5, Br=1). Plugging in the numbers, we get:
22! / (1! * 2! * 5! * 1!) = 22,957,280
So there are almost 23 million possible arrangements of the atoms. However, many of these will be identical due to rotations and reflections of the molecule. After considering these duplicates, there are four distinct isomers that can be formed (shown below):
CSUSUBSUHSUBSSUB0Br
CSUSUBSUHSUB0SSUBBSUBBr
CSUSUB0HSUBSSUBBSUBBr
CSUSUB0HSUBBSUBSSUBBr

How Many Isomers of C4H9Br Are Possible

How Many Isomers of C₄H₉Br Are Possible