When predicting the number of possible
cis-trans isomers for alkenes a given carbon skeleton,
the first step is to predict the number of alkenes that are possible for that carbon skeleton.
the second step is to choose the isomers that have two different groups at each doubly-bonded carbon
When deciding the number of possible alkenes remember that
to have a
double bond between adjacent carbons, they must both bear a
hydrogen in the saturated compound.
there may be
fewer than the
maximum number due to
symmetry of the
carbon skeleton.
Linear carbon chains are symmetrical about their center.
For a four carbon chain this means that the two end carbons are equivalent and the two middle carbons are equivalent.
Therefore the double bond can be between two blue carbons or a blue and a red carbon.
The carbon skeletons for the two straight chain C
4 alkenes is shown below.
.
But-2-ene can exist as cis-trans isomers because it has two different groups at each doubly bonded carbon.
Branched compounds have fewer isomers if two or more branches attached to the same carbon are equivalent.
There is only one C
4 branched alkene isomer because introducing a double bond between any of the red carbons and the central carbon gives the SAME compound (2-methylpropene). Put another way, there is only one type of pair of adjacent carbons (red and black).
This alkene cannot exist as
cis-trans isomers because the two groups at both carbons are the same.
The five-carbon skeleton below has only three double bond isomers because a double bond to either of the red carbons gives the same compound (2-methylbut-1-ene). There are three different pairs of adjacent carbons (red and black, black and blue, blue and gold).
None of these alkenes have two different groups on both doubly-bonded carbons. Hence none of these exist as cis-trans isomers.