'Curly arrows'

What do 'curly arrows' represent?

The correct use of curly arrows causes real problems – both to students (and teachers) and examiners. The main reason why students fail to score marks is that they use the arrows completely wrongly but even when arguably they have been used correctly students can still fail to score marks depending on how examiners interpret the markscheme. What I hope to show is how students can use them correctly so that they can be certain to get full marks. I have included a slide presentation you can use to illustrate the main points to students.
 

Definition

One of the main problems is the definition of what a ‘curly arrow’ actually means. The best definition and the one used by the IB can be found on the website hosted by Aberdeen University and this is supported by the Royal Society of Chemistry.

“Curly arrows are the notation used by organic chemists to indicate the movement of electrons when bonds are made, broken, or moved.

A ‘curly arrow’ represents the movement of an electron pair from its original position to a new one. The tail of the arrow shows where the electron pair has come from, and the head of the arrow shows where the electron pair is going to.”

Common errors made by students

1. Showing the arrow the wrong way round. Typically when showing the electrophilic addition reaction of H—Br with an alkene the arrow comes from the H—Br to the alkene – not the other way round.

2. Starting the arrow in the wrong place. This is often seen when the hydroxide ion is used as the nucleophile in a nucleophilic substitution reaction with a halogenoalkanes. The arrow must start either from the negative charge on the hydroxide ion or even better from a non-bonding pair of electrons on the hydroxide ion. It will be penalised if it is shown originating from the hydrogen atom.

3. Finishing the arrow in the wrong place. There is some disagreement with some examiners here who have been brought up to draw the arrow going directly to the carbon atom in a nucleophilic substitution reaction. From the definition the arrow should end up where the bond will be formed which will be between the carbon atom and the HO– group when it is bonded.

The above three errors are all due to students misunderstanding what a ‘curly arrow’ represents. There is a further problem which is best represented by an actual IB question and two different answers given by two students. The question was:

This initial information in the introduction to the question could be criticised as in part (II) it show the ‘curly arrow’ going right to the carbon atom instead of where the electron pair should end up which is in the middle of the line between C and O in the product. However, as some teachers and text books do use this approach, it would not be penalised if a student had done this in a written answer.

The question then went on:

The markscheme actually had four marking points so if a student scored any three of them they would get the full three marks.

These marking points were:

1. Showing a curly arrow from the O or the non-bonding pair on the O or the negative charge on the O on the OHion towards the C of C—Br.

2. A correct representation of the transition state showing partial bonds and a negative charge.

3. Curly arrow from the C—Br bond to the bromine to form Br-.

4. Correct products.

Now let’s look at a genuine student answer.

I personally think that the student got three of the four points correct (they missed the curly arrow from the C—Br bond) so I would have awarded full marks if I had been in charge of the paper. I accept that the reaction arrows should have a full arrow head but I would not penalise for ‘half-heads’. However it seems clear to me that the student understands the chemistry.

However several examiners argued that the first curly arrow is going to the wrong place as it would be repelled by the existing pair of electrons in the C—Br bond and the two partial bonds are too close in the transition state as they should be 180o apart. I can see their logic but I disagree. For the first point the arrow is shown going to exactly where it will end up in the product and in the transition state it depends on how the three-dimensional shape is represented in two-dimensions. This latter point is, I think, the root cause of many ‘curly arrow’ problems. I think it is best to train your students to show the mechanism in the normally accepted three-dimensional representation and in fact this is specifically mentioned in sub-topic 20.1: Types of organic reactions in the AHL programme. That way there can be no doubt about the fact that the nucleophile is attacking the carbon from the opposite side of its bond to the halogen and that the five-membered transition state has a trigonal bipyramid shape. I enclose the diagram on page 226 of the 2nd Edition of my Chemistry Course Companion to show this.

Further points

You might wish to go on and add some TOK as Paul Walden, (1863-1957) a Latvian chemist reasoned that if an SN2 mechanism took place with a secondary halogenoalkane then the product would rotate the plane of light in the opposite direction to the halogenoalkane reactant. This was indeed found to be the case and provides good evidence to support our picture of chemistry at the molecular level.

You should also teach your HL students that organic chemists use a 'curly arrows' with a 'half-head' (fish hook) to represent the movement of a single electron as this is detailed in the "Guidance" section of sub-topic 20.1. Fish hooks are used when explaining free radical mechanisms, for example the homolytic fission of a chlorine molecule by ultraviolet light to form two chlorine radicals.

If you want some more examples then Oxford University have produced a useful Website which contains a tutorial and also has a fun section where you (or your students) can test your skills at drawing the arrows in the correct places.

The following slide presentation can be used to illustrate the above points.

  

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