Foundations — Isomerism — structural (linkage, ionization, coordination, hydrate) and stereo (geometrical, optical)

Before you can read a single isomerism example, you must be fluent in the notation the parent note throws at you: the square brackets, the superscript charges, the little symbols like $en$, $py$, ${\Delta }_o$. This page builds each one from nothing. We go slowly and in order — every symbol is earned before it is used.

1. The central metal and the idea of "attaching"

Picture a single metal atom that has lost a few electrons, so it carries a positive charge. That missing-electron atom is hungry: it has empty slots that would love to be filled with electron pairs from nearby molecules.

The little superscript, as in $C{o}^{3+}$, just says "this cobalt has lost 3 electrons, so it is 3-plus charged." Charge is bookkeeping: we must keep track of it because the whole complex must balance out to a sensible total charge.

Look at the figure: the burnt-orange ball in the middle is the metal, with six empty parking spaces drawn as dotted sockets. This is the stage on which all isomerism happens.

2. Ligands — the things that attach

A lone pair is simply two electrons sitting on an atom that are not being used in a bond — they are free to be offered to the metal. That offering is the "attach".

The parent note uses several ligand shorthands. Here they all are, decoded:

3. Denticity — how many hands a ligand has

See Ambidentate vs Polydentate Ligands for the full family. This matters because a two-toothed ligand takes up two adjacent parking spaces — and "adjacent" is exactly the geometric fact that later creates optical isomers.

The teal claw in the figure is one $en$ molecule bridging two neighbouring sockets. A single monodentate $N{H}_3$ (plum) fills just one. Notice: $en$ can only span two spaces that are side-by-side, never two opposite spaces — remember this, it returns in the chirality story.

4. The coordination sphere — the square brackets

Now the most important piece of notation in the whole chapter.

So in $[Co(N{H}_3{)}_{5}Br]S{O}_4$:

• Inside the fence: $Co$, five $N{H}_3$, one $Br$ — all bonded to cobalt.
• Outside the fence: $S{O}_4^{2-}$ — a free sulphate ion, floating nearby to balance charge.

Inside vs outside is the whole game for ionization and hydrate isomerism: those isomers move a piece across the fence.

The figure draws the fence explicitly: bonded ligands inside the orange box, the free counter-ion drifting outside. A test with $AgN{O}_3$ or $BaC{l}_2$ only "sees" the free ion outside — that is why counting the free ion tells you the structure.

5. Two atoms with lone pairs — the ambidentate idea

WHY the topic needs this: it is the cause of linkage isomerism. Same ligand, same formula, but flip which atom faces the metal → a genuinely different compound with a different colour.

6. Geometry words — cis, trans, fac, mer

The metal's parking spaces sit at fixed angles in space. For six ligands they point to the corners of an octahedron (see Coordination Number and Geometry).

These are pure geometry: no chemistry yet, just where things point. But "where" is exactly what distinguishes geometrical isomers.

Left octahedron: the two orange ligands are adjacent — cis. Right octahedron: the two orange ligands are on opposite poles — trans. Same formula $M{A}_4{B}_2$, different picture, different compound.

7. Mirror images and symmetry — the chirality tools

Your two hands are the model: same fingers, mirror images, but no way to overlay them. See Chirality in Organic Chemistry. This is the machinery behind optical isomerism.

The Greek letters $\Delta$ (delta) and $\Lambda$ (lambda) that appear in $[Co(en{)}_3{]}^{3+}$ are just names for the two mirror-image twists — like calling one hand "left" and the other "right". Do not fear them: $\Delta$ = one handedness, $\Lambda$ = the other.

8. Why colour changes — ${\Delta }_o$ in one line

The parent note says N and O give "different ${\Delta }_o$." Here is the symbol demystified.

You do not need to compute it here — just know that swapping which atom binds (nitro vs nitrito) or which ligand sits where changes this gap, and that is why isomers have different colours.

9. How it all feeds the topic

Equipment checklist