Chirality and R/S configuration

A concrete case

Two bottles of butan-2-ol

Carbon 2 of butan-2-ol, ${\mathrm{CH}}_3\mathrm{CH}\left(\mathrm{OH}\right){\mathrm{CH}}_2{\mathrm{CH}}_3$CH3​CH(OH)CH2​CH3​, carries four different groups: an $\mathrm{H}$H, an $\mathrm{OH}$OH, a ${\mathrm{CH}}_3$CH3​ and a ${\mathrm{CH}}_2{\mathrm{CH}}_3$CH2​CH3​. Build it with a model kit, then build its mirror image. Turn the second model any way you like. Two groups always end up swapped, and the models never match.

The two forms are two compounds, and they can be bottled separately. They boil at the same temperature and have the same density. One difference shows up in a polarimeter. Measured as the pure liquid at $20 °\mathrm{C}$20 ∘C, one form turns plane-polarized light to the left, with a specific rotation of about $-13.5$−13.5. The other turns it to the right by the same amount, about $+13.5$+13.5.

The labels R and S say which bottle is which. They come from the atomic numbers of the four atoms bonded to carbon 2. Oxygen is $8$8, the two carbons are $6$6 and hydrogen is $1$1. The rest of this lesson turns those numbers into a letter.

The rule

Stereocenters, chirality and enantiomers

A stereocenter is a carbon bonded to four different groups. Swapping any two of its groups gives the mirror-image arrangement, which no rotation turns back into the original.

An object that cannot be laid over its own mirror image is chiral, from the Greek word for hand. A molecule with one stereocenter is always chiral. Its two mirror-image forms are enantiomers.

A carbon with two identical groups is not a stereocenter. The carbon of ${\mathrm{CH}}_2{\mathrm{Cl}}_2$CH2​Cl2​ carries two $\mathrm{H}$H and two $\mathrm{Cl}$Cl, and the middle carbon of propan-2-ol carries two ${\mathrm{CH}}_3$CH3​ groups. Each molecule matches its mirror image, so it is achiral.

Wedges and hashes

A flat page has to show a three-dimensional arrangement. Plain lines lie in the page, a solid wedge points toward you and a hashed wedge points away, with the narrow end on the stereocenter. A hydrogen that is not drawn points roughly opposite the wedge. A drawing with no wedge at a stereocenter does not say which enantiomer it is, and Chalk does not guess.

To see one, use the Draw (2R)-butan-2-ol button at the end of this lesson. The Skeletal tool draws carbon 2 with three plain or wedged lines to its $\mathrm{OH}$OH, ${\mathrm{CH}}_3$CH3​ and ${\mathrm{CH}}_2{\mathrm{CH}}_3$CH2​CH3​ groups, and the hydrogen left out.

Ranking the four groups

The Cahn–Ingold–Prelog (CIP) rules rank the four groups from $1$1, highest priority, to $4$4, lowest.

First compare the atoms bonded directly to the stereocenter. The higher the atomic number, the higher the rank, so the order runs iodine, bromine, chlorine, sulfur, fluorine, oxygen, nitrogen, carbon, hydrogen.

If two groups start with the same atom, list the three atoms attached to each, highest first, and compare the lists term by term. The first difference decides. $–{\mathrm{CH}}_2{\mathrm{CH}}_3$–CH2​CH3​ carries (C, H, H) and $–{\mathrm{CH}}_3$–CH3​ carries (H, H, H), so ethyl outranks methyl. If the lists tie too, move one more bond outward.

A double bond counts as two single bonds to the same atom. The carbon of $–\mathrm{CHO}$–CHO therefore carries (oxygen, oxygen, H) and outranks $–{\mathrm{CH}}_2\mathrm{OH}$–CH2​OH, which carries (oxygen, H, H). Of two isotopes of one element, the heavier ranks higher.

Reading R or S

Turn the molecule so group 4, usually hydrogen, points away from you. Then trace the path $1\to 2\to 3$1→2→3 around the other three groups. Clockwise is R, from the Latin rectus, right. Counterclockwise is S, from sinister, left.

The letter goes in parentheses at the front of the name, with the number of its carbon, as in (2R)-butan-2-ol. With one stereocenter the number is often left out, as in (R)-butan-2-ol.

Why it works

Why there are exactly two arrangements

Hold group 4 pointing straight away from you. The other three groups now sit in a ring around the carbon, like numbers on a clock face. Three groups can be placed in a ring in $3!=6$3!=6 orders. Each order looks the same as two others after a turn of the ring, so only $6÷3=2$6÷3=2 truly different arrangements are left. One runs $1\to 2\to 3$1→2→3 clockwise and the other counterclockwise.

The same count explains the swap rule. Exchanging any two groups reverses the direction around the ring, so it turns R into S.

The ranking by atomic number is a convention. Nothing physical makes oxygen first. The rules exist so that every chemist, given the same structure, reaches the same letter, and a bottle labeled (R) means the same thing in every lab.

The method

Assigning R or S in five steps

1. Find each stereocenter. Check every carbon with four single bonds for four different groups, counting an undrawn hydrogen.

2. Rank the four groups by the atomic number of the bonded atom.

3. Break each tie by listing the atoms one bond further out, highest first, and comparing at the first difference. Count a double bond as two bonds to the same atom.

4. Find group 4. If it points away from you, trace $1\to 2\to 3$1→2→3 as drawn. If it points toward you, trace the path and reverse the letter.

5. If group 4 lies in the page, swap it with the group that points away from you. Read the swapped drawing, then reverse the letter, since one swap inverts it.

Where it breaks

Where it breaks

R and S do not tell you the sign of rotation. (R)-Butan-2-ol turns polarized light to the left, and nothing in the priority rules predicts that. The sign of rotation has to be measured.

R and S are also not D and L. The D and L labels compare a molecule with glyceraldehyde. Most L-amino acids are S, but L-cysteine is R, because the sulfur in its side chain changes the ranking.

A stereocenter does not guarantee a chiral molecule. A molecule with two stereocenters can contain a mirror plane and be achiral, as meso compounds are. Some molecules with no stereocenter are chiral, such as certain allenes.

The ranking can stop short. Chalk applies the first two CIP rules, atomic number and mass. When they do not separate two groups, Chalk says the ranking is not settled and shows no R or S there.

Check your answer

Check your answer

Swap and reread. Exchange any two groups in your drawing and assign the center again. You must get the opposite letter, because one swap inverts the arrangement.

Check the view. Before you trust the direction of the path, confirm where group 4 points. A clockwise path with the hydrogen on a solid wedge is S, not R.

Compare with a known case. L-alanine, the form in proteins, is S. A drawing of L-alanine that gives you R has a slip in the ranking or the view.

Chalk reads the drawing for you. Draw the structure and choose Analyze → Stereochemistry. Chalk puts R or S beside each center and lists the ranking that gave it. A name with its letter, entered under Analyze → Target, has the letter checked as well. If the drawing shows the other enantiomer, Chalk says, for example, “The name says (2S), but the drawing shows (2R): the name is this structure’s mirror image.”