Animated Solution for Chemistry - Organic Chemistry: The number of stereoisomers possible for a compound of the molecular formula ${\text{CH}}_3-\text{CH}=\text{CH}-\text{CH(OH)}-\text{Me}$ is

When tackling stereoisomerism, the very first step is to visualize the molecule. We are given the compound ${\text{CH}}_3-\text{CH}=\text{CH}-\text{CH(OH)}-{\text{CH}}_3$, which is systematically named pent-3-en-2-ol. By drawing out its expanded structural formula, we can clearly see the carbon backbone, the position of the double bond, and the crucial hydroxyl ($-\text{OH}$) group attached to the second carbon.

To find the total number of stereoisomers, we must embark on a hunt for stereocenters (denoted by $n$). A stereocenter is any point in a molecule where interchanging two groups produces a new stereoisomer.

First, let's look for chiral carbons. A carbon atom is chiral if it is $s{p}^3$ hybridized and bonded to four completely different groups. If we inspect ${\text{C}}_2$, we see it is attached to a methyl group ($-{\text{CH}}_3$), a hydrogen atom ($-\text{H}$), a hydroxyl group ($-\text{OH}$), and the rest of the alkenyl chain ($-\text{CH}=\text{CH}-{\text{CH}}_3$). Since all four groups are distinct, ${\text{C}}_2$ is indeed a chiral center. This gives us our first stereocenter ($n_1=1$).

Next, we examine the double bond between ${\text{C}}_3$ and ${\text{C}}_4$. For a double bond to act as a stereocenter, it must be capable of showing geometrical isomerism (cis-trans or E/Z). This requires that each carbon of the double bond is attached to two different groups. ${\text{C}}_3$ is attached to a hydrogen and the $-\text{CH(OH)}{\text{CH}}_3$ group. ${\text{C}}_4$ is attached to a hydrogen and a $-{\text{CH}}_3$ group. Because both carbons meet the criteria, the double bond is our second stereocenter ($n_2=1$).

Before we calculate the total isomers, we must perform a critical check: Is the molecule symmetrical?

If we attempt to draw a plane of symmetry through the center of the molecule, we immediately notice a mismatch. The left side of the molecule contains a hydroxyl group, while the right side does not. The molecule is completely unsymmetrical. This is great news because it means we don't have to worry about meso compounds (which are optically inactive due to internal symmetry).

For an unsymmetrical molecule, the formula to calculate the maximum number of stereoisomers is beautifully simple:

Since we found a total of 2 stereocenters ($n=1+1=2$), we just plug this into our formula:

These 4 unique stereoisomers arise from the independent combinations of the configurations at each stereocenter. The chiral center can be either R or S, and the double bond can be either cis or trans. Therefore, the four specific isomers are: (2R, cis), (2S, cis), (2R, trans), and (2S, trans).