The topic of this lecture will be some special cases of both chiral and achiral molecules. For this lecture, it's important to remember what makes a molecule chiral. Chirality requires two things. First, There must be left and right-handed forms of something. Those are mirror images of one another.
Secondly, chirality requires that these left and right-handed forms are non-superimposable. They can't be the same. Remembering these two requirements, is important for the following discussion. These requirements of chirality mean that having chiral centers does not make something chiral.
Conversely, not having chiral centers does not automatically make a molecule achiral. Chirality purely requires that there be left and right-handed forms that are non-superimposable. Now let's look at some examples of these special cases. The first case we're going to look at are traditionally mobile systems.
of saying that molecules can change conformation, which we already know. Most organic molecules are conformationally mobile. This is important to the discussion of chirality, however, because a molecule cannot be chiral if it is in equilibrium with a structure or conformation that is achiral. Remember that the easiest way to determine if a molecule is achiral is to look for a plane of symmetry. Therefore, we should consider the most symmetric conformation of a molecule to determine if it is chiral.
Let's look at some examples. examples. We'll start with cis-1,2-dibromylcyclohexane.
The most symmetrical conformation we can draw this molecule in is the flat hexagonal cyclohexane ring. When we draw the molecule in this way, it's fairly easy to see that this molecule has an internal mirror plane of symmetry, right down the middle. But we know that cyclohexane rings typically adopt a chair conformation to allow the angles to be 109.5.
Having substituents in a cis-1,2-biz... position means that one of the substituents will be axial and one will be equatorial. We can draw a mirror image of this molecule that looks like this.
Take a moment to pause the video and make these two molecules with your modeling kit. If you do so, what you will see is that these two are non-superimposable images. However, they can interconvert through a ring flip. So if you've made these two molecules, do a ring flip with one of them, and you should see that they will, in fact, overlap.
overlap, they are superimposable. This means that this molecule is achiral. Even though in its most common conformation, which is the chair conformation, it would appear to have non-superimposable mirror images, we can determine that this molecule is achiral by looking at it in its most symmetrical conformation, which is in the flat hexagonal cyclohexane that we drew first.
Cis-1,2-dibromocyclohexane is an example of a molecule that has chiral centers but is achiral. Now let's look at some molecules that don't have chiral centers but are still chiral. There are two main classes of molecules that do not contain chiral centers but are still chiral.
The first of these are called conformational enantiomers. Conformational enantiomers are mirror image isomers that cannot interconvert due to steric or ring strain. An example of a conformational enantiomer are substituted biphenyl rings.
Let's look at an example. This is an example of a substituted biphenyl ring. This compound cannot exist in the conformation in which I've drawn it, because the bulky bromine groups and the bulky iodine groups would be bumping into each other's van der Waals radii. Steric strain prevents this molecule from adopting this conformation. Instead, it must have the two phenyl rings at right angles to one another.
Where the left airing is in the plane, of the screen and the right airing is perpendicular to it with the bromine pointing away from us and the iodine pointing towards us. This molecule in this conformation has no internal mirror plane of symmetry. We can draw a mirror image and it is non-superimposable. If you make these two molecules with your modeling kit you will see that they're non-superimposable.
Because they cannot interconvert, neither one of these molecules can rotate around the bond between the two aryne rings due to the steric strain, they do not interconvert and there's no plane of symmetry. These are a case of conformational enantiomers. These molecules have no chiral centers, but they are chiral. Another class of molecules that do not contain chiral centers but are still chiral are called allenes.
Allenes are compounds that contain two carbon-carbon double bonds. one after another. The simplest example of an alene is propadiene. The carbon in the middle is sp-hybridized, leaving two unhybridized p-orbitals for the two pi bonds.
This carbon is linear. The carbons on either end are sp2-hybridized and are trigonal planar. The two unhybridized p-orbitals So the center carbon must be perpendicular to one another, which means that the planes of the two trigonal planar carbons on either end must also be perpendicular to each other to allow for the proper orbital overlap. The center carbon has two unhybridized p orbitals that are perpendicular to one another. One p orbital is going up and down and the other is going into and out of the screen.
The carbon on one side of the central carbon will have p orbitals that go up and down to overlap with the central carbon's p orbital that goes up and down. And the carbon on the other side will have an unhybridized p orbital that goes into and out of the screen. The sp2 orbitals on either side of the central carbon are going to be perpendicular to the unhybridized p orbital. unhybridized p-orbital of each carbon.
So on the right carbon, the two carbon-hydrogen bonds will be going into and out of the screen, and on the leftmost carbon, they'll be in the plane of the screen. The actual three-dimensional representation of an allene then looks like this. If you make this molecule with your modeling kit, you should be able to see how the plane of the carbon and the hydrogens on the right are perpendicular to the plane of the carbon and the hydrogens on the left. Propadiene has a plane of symmetry, and therefore it's... is achiral, but when we get to more complicated allenes, such as penta-2,3-diene, the plane of symmetry no longer exists.
Let's draw this molecule out in three dimensions. This is one possible three-dimensional representation of penta-2,3-diene. This molecule has no plane of symmetry.
If we draw its mirror image, we can see that this mirror image is not superimposable over the original molecule. You may find it helpful to make the models of these two molecules in order to see that they are. are non-superimposable mirror images. Having non-superimposable mirror images is the definition of chirality. So even though neither of these molecules contain a chiral center, they are chiral.