Geometric Isomers In Small Rings: Cis And Trans Cycloalkanes

Geometric Isomers: Cis vs Trans Cycloalkanes

In the last post, we mentioned that one of the consequences of the fact that carbon can form rings is that small rings (less than 8 carbons) are so rigid that they can’t be turned inside out. One of the important consequences of this, as we’ll see today, is that it leads to the formation of new types of isomers we haven’t seen before: geometric isomers (aka cis- and trans– isomers).

Table of Contents

1. Cycloalkanes And Constitutional Isomers
2. Substituents On Small Rings Are “Locked” In Place, Giving Rise To “Geometric Isomers” (Stereoisomers)
3. The Wedge-Dash Convention For Showing Stereochemistry In Flat Molecules
4. Molecules Are No Different Than Any Other 3-Dimensional Object You Encounter In Everyday Life
5. The cis– and trans– Naming Convention
6. More Examples of cis– and trans- Isomers In Cycloalkanes
7. Notes

1. Cycloalkanes And Constitutional Isomers

Remember isomers? [See post: Types of Isomers] If you’ve gone through the first few chapters covering alkanes, no doubt you have. The most familiar kind of isomer to us right now are constitutional isomers. These are molecules that have the same molecular formula, but different structural formula. In other words, different connectivity. A simple example is for C₄H₁₀, where we have n-butane (a straight chain of 4 carbons) and 2-methyl propane (with a longest chain of 3 carbons, and a methyl group attached to the middle carbon).

Of course an easy way to remember constitutional isomers is to tie them back to cats.

OK, let’s get back to the topic at hand. What do we understand so far about constitutional isomers and cyclic molecules?
Let’s take the example of “dimethylcyclopropane”. This is a cyclopropane with two methyl groups (CH₃) attached. Can you draw two constitutional isomers for dimethylcyclopropane? You should: here they are

Here, both molecules have the same molecular formula but different connectivities. That’s why specifying “1,1” or “1,2” is important – it avoids ambiguity.

An unambiguous name for a molecule is necessary in order to draw the structure perfectly from the name – just like an unambiguous address for your house is necessary to allow the postal service to deliver a letter to your door. Anything less and you get, “Return To Sender”.

2. Cycloalkanes Can Have Geometric Isomers (Stereoisomers)

Funny thing about that. If you try to make a model of 1,2-dimethylcyclopropane, you might notice something. There are actually two of them!  In one version, the two methyl groups are on the same face of the three-membered ring. In the other, they are on the opposite face. Since the three membered ring is rigid, we can’t interconvert the two without bustimicating the three membered ring.  

These molecules can’t be converted into each other without breaking the ring apart. The ring is too rigid. 
[Just like you can’t touch your left elbow with your left hand without breaking your forearm : – {   ]

This means that the orientation of the groups on C-1 and C-2 are locked in place. Therefore they are two different molecules.
In other words, they are isomers! That is, they have the same molecular formula (C₅H₁₀) but different structural formulae. (this is true for any two non-H substituents on C-1 and C-2 – not just methyl).

They will have different physical properties (e.g. boiling and melting points):

What kind of isomers are they exactly? They can’t be constitutional isomers, since they have the same connectivity. We’ll need a different name. Since these two isomers of 1,2-dimethylcyclopropane differ only in their orientation in space, we call them stereoisomers. For cases like this one where the groups are locked in place, we  also can use the phrase, “geometric isomers”, described by the terms “cis” and “trans” (more below)

3. The Wedge-Dash Convention Shows Us Which Groups Point Out Of The Page, And Which Point Into The Page

Let’s highlight this concept of stereoisomers with a cat example : – ) . Look at the white legs in each case. Same connectivity, but different arrangement in space.

Now: there’s actually a much more convenient way to draw stereoisomers than by using these 3-D perspective drawings. Except in certain cases (mostly bridged rings – that’s a little later in the chapter) in organic chem it’s usually much more convenient for us to draw the flat versions of molecules.

This presents a little problem. How do we give the illusion of showing three dimensions on a two-dimensional page?

We’re going to do two things. First of all, we’re going to draw these molecules from the perspective of looking straight on at them, rather than from the side. In other words, look at them such that the plane of the ring will be in the plane of the page.

Some groups will be pointing towards us, while others will point away.

So we’re going to take some inspiration from everyday life to give the effect of distance.

In this lovely picture of the Austrian alps, notice how the mountains close to us have well defined outlines and sharp contrast, whereas the mountains farther away are more faint.

We’re going to use a similar visual trick. With the ring in the plane of the page, groups that point towards us are going to have a dark solid line (“wedge”) whereas groups that point away from us will be denoted with a dashed line (“dash”).

This is what it will look like:
Here’s what the other one will look like:

4. Molecules Are No Different Than Any Other Three-Dimensional Object You Encounter In Everyday Life

Molecules are just like any other 3-D object.  Their structure is INDEPENDENT of the perspective you draw them from. Whether you choose to draw them from the top, the bottom, the side – they all represent the same three-dimensional object. By the way – we could also have chosen to look at it from the bottom instead. In that case the drawings would look like this

Regardless of whether we look at the molecule on the left from the top or the bottom, we’d get the same thing. Just like whether you photograph a propane tank from the top, the side, or the bottom, you’re still photographing the propane tank. One last illustration.

5. Geometric  Isomerism: “cis-” And “trans-” Isomerism In Cycloalkane Rings

One last point remains. How do we name these molecules so that it’s clear which version of 1,2-dimethylcyclopropane we’re referring to? In a pinch, a good scientist retreats to Latin for naming duties. For the case where the two groups are on the same side of the ring, we refer to it as ‘cis‘ (from the Latin, meaning, “same side of”.) For the case where the two groups are on the opposite side of the ring, we refer to it as “trans” (meaning “opposite side of'”). That gives us the following names (usually we italicize the cis and trans)

6. More Examples of Cis- And Trans- Isomers In Cycloalkanes

We can apply this to other groups (and rings) beside methyls and cyclopropane, of course. Note that in the absence of dashes/wedges, the structures drawn would be ambiguous.

In the next post, we’ll talk about another interesting consequence of ring size: a phenomenon known as strain. 

Notes

Note 1. Some of these structures (not all) are not even fully made unambiguous by the terms “cis” and “trans”. There’s an even deeper level of nomenclature we’ll need to describe, for example, trans-1,2-dimethylcyelopropane.

That’s the Cahn-Ingold-Prelog (CIP) system, as we’ll discuss shortly. [See Introduction to Assigning (R) and (S): The Cahn-Ingold-Prelog Rules]