Isomerism — structural (chain, position, functional, metamerism, tautomerism) and stereo (geometrical - cis-trans - E-Z,: Foundations

This page unpacks every symbol, term, and drawing convention the parent note quietly assumed. Read it top to bottom — each item is built only from the items above it.

0. What is a "molecular formula"? (the starting brick)

The picture: imagine emptying a molecule into a bucket and counting.

$C_{4} H_{10}$ means 4 carbon atoms and 10 hydrogen atoms in the bucket.
A subscript is a count: the little $10$ in $H_{10}$ says "ten H atoms".
No subscript = one atom (we don't write $C_{1}$ ).

Figure s01 — same bucket, two builds. A butter-yellow "atom bucket" labelled 4 C, 10 H feeds an arrow into two different carbon skeletons: a straight four-carbon chain (n-butane) and a three-carbon chain with a branch (isobutane). The caption box on the right reads "same tally, different map = isomers", showing that an identical formula can produce two separable compounds.

Figure — Isomerism — structural (chain, position, functional, metamerism, tautomerism) and stereo (geometrical - cis-trans - E-Z,

1. The bond — a shared pair of electrons drawn as a line

$C - H$ : a line between C and H = one shared pair.
Carbon always draws exactly 4 lines total (its 4 bonds).

The picture: a single bond is a rope you can spin around; a double bond is like two ropes side by side, which lock the two atoms so they cannot twist relative to each other. Hold that image — the whole idea of cis/trans lives on it.

$C = O$ is called a carbonyl group (a C double-bonded to O).
The extra "second rope" is called the π (pi) bond; the first rope is the σ (sigma) bond. You don't need the full theory yet — just: single = 1 rope (σ), double = σ + π = 2 ropes, and π forbids twisting.

Figure s02 — one rope spins, two ropes lock. On the left, a single C–C bond (one line) with a curved lavender arrow showing free rotation — labelled "conformations". On the right, a C=C bond (two parallel lines) with a red X over a would-be rotation arrow — labelled "cis / trans locked". The picture is the core reason geometric isomers exist.

Recall Why do we care that σ spins but π locks?

Rotation about a σ bond ::: gives conformations (interconvert freely, not separable). Rotation about a π bond ::: is forbidden, so cis/trans become genuinely different, separable molecules.

2. Connectivity vs arrangement — the split that names everything

The picture: connectivity is the subway map (which station connects to which); arrangement is which platform you stand on at a station. Same map, different platform.

3. The functional group — the reactive "handle"

Group	Drawn as	Family name
hydroxyl	$- O H$	alcohol
ether oxygen	$- O -$ (O between two carbons)	ether
carbonyl at chain end	$- C H O$	aldehyde
carbonyl inside chain	$- C (= O) -$	ketone

$α$ (alpha) is the Greek letter we use to label the carbon directly next to a functional group. An α-carbon sits one bond away from the $C = O$ ; an α-hydrogen is an H attached to that α-carbon.
Why this label matters: tautomerism needs an α-H to shuttle — the parent's "no α-H ⇒ no tautomerism" is exactly this. See Acidity of Alpha-Hydrogens for why that α-H is loosenable.

4. The proton and the arrows — how atoms and electrons "move"

The picture: $⇌$ is a see-saw that keeps rocking — the molecule flickers between two real forms (this is exactly tautomerism). $\leftrightarrow$ is a camera double-exposure of one thing. $\to$ is a slide you go down once.

5. Wedges and dashes — how to draw 3D on flat paper

To talk about arrangement, we need a way to show depth on a 2D page. All three bond styles below are drawn for you in the figure — match each symbol to its picture.

Figure s03 — wedge/dash and mirror images. Two tetrahedral carbons drawn as "tripods": each has a plain line (in-plane), a filled lavender wedge (bond toward you) and a hatched bond (away from you), carrying groups OH, H, Br. A coral dashed vertical line between them marks a mirror; the right carbon is the left one flipped. Because you cannot slide one onto the other, they are enantiomers.

The picture: a carbon with four bonds is a tripod on a table — three legs you can see, one pointing straight at your eye. Wedge/dash is how we photograph that tripod. Newman Projections is a second camera angle for the same 3D truth.

6. Priority — ranking atoms to break every tie

Cis/trans by eye works for simple cases, but the rigorous E/Z and R/S systems need an unambiguous ranking of groups. This ranking system is named after its three inventors — Cahn, Ingold and Prelog — so it is called the CIP system (Cahn–Ingold–Prelog priority).

Quick order from atomic number: $Br > Cl > F > O > N > C > H$ .

7. cis / trans — same side or opposite side of the lock

Now that a double bond "locks" (Section 1) and groups have a defined layout, we can name the two frozen arrangements.

Works only when each double-bond carbon carries two different groups (otherwise "same side" is meaningless — swapping identical groups changes nothing).

Figure s04 — same-side vs opposite-side, on a double bond and on a ring. Top row: a C=C with two reference groups both above the bond (cis) and then one above / one below (trans). Bottom row: a flat triangular ring (cyclopropane) with two methyls drawn as up-wedges on the same face (cis) versus one up-wedge and one down-dash (trans). Both rows show the identical "same face vs opposite face" logic.

8. E / Z — cis/trans made rigorous with CIP

"Same side" is ambiguous when the groups aren't obviously similar. E/Z fixes this by ranking with CIP priority (Section 6).

9. The chiral centre — the four-different-groups carbon

Optical isomers need a specific structural feature. Here is exactly what makes one.

The test in practice:

Count the four groups on the carbon. If any two are identical, it is not a chiral centre (swapping the identical pair gives the same molecule back).
Example ✅: $C H F C l B r$ — the four groups $H, F, C l, B r$ are all different → chiral.
Example ❌: $C H_{2} C l B r$ — two H's are identical → not chiral.

10. R / S — naming the two mirror images with CIP

cis/trans got a rigorous label (E/Z); the two enantiomers get theirs (R/S) — again from CIP priority.

The prerequisite map

Equipment checklist

Recall Self-test: are you ready for the topic?

A subscript in $C_{4} H_{10}$ means ::: the count of that atom (4 carbons, 10 hydrogens). A single line between two atoms represents ::: one shared pair of electrons — a single (σ) bond. Why carbon draws exactly 4 lines ::: it shares 4 electron pairs to reach a full octet of 8 shared electrons. The " $=$ " double bond forbids ::: free twisting/rotation of the two carbons (the π "rope" locks it). Connectivity vs arrangement ::: connectivity = which atom bonds to which (the map); arrangement = where groups point in 3D. An α-hydrogen is ::: an H on the carbon directly next to a functional group (e.g. next to C=O). $⇌$ versus $\to$ ::: two-way equilibrium (both directions, a balance) versus a one-way reaction. The resonance arrow $\leftrightarrow$ means ::: one molecule, two electron-pictures, no atom moved (NOT an equilibrium). A solid wedge bond points ::: toward you, out of the page. A dashed/hatched wedge bond points ::: away from you, behind the page. Superimposable means ::: one can be slid/rotated onto the other so every atom matches; if not, they are enantiomers. cis versus trans ::: cis = reference groups on the same side of the double bond/ring face; trans = on opposite sides/faces. What CIP stands for ::: Cahn–Ingold–Prelog, the priority-ranking system. The duplicate-atom rule handles ::: double/triple bonds — each doubly-bonded atom gains a phantom copy of its partner for ranking. Z versus E ::: Z = two higher-CIP-priority groups on the same side; E = on opposite sides. A chiral centre is ::: a carbon bonded to four different groups (any two identical → not chiral). To assign R/S ::: point lowest priority away, trace 1→2→3; clockwise = R, anticlockwise = S. CIP priority ranks groups by ::: atomic number (higher = higher priority), deciding at the first point of difference. A racemic mixture's optical rotation is ::: zero — the equal-and-opposite twists of the two enantiomers cancel. $2^{n}$ for n chiral centres means ::: the maximum number of stereoisomers (fewer if a meso/symmetry is present).