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A complex ion is a central metal ion — almost always a transition-metal cation — surrounded by a small group of attached species called ligands, each donating a lone pair of electrons into an empty orbital on the metal to form a dative covalent (coordinate) bond. The geometry, charge, colour, and reactivity of the complex are determined by the identity of the metal, its oxidation state, and the number, type, and arrangement of the ligands. This lesson develops the language and structural reasoning used for the rest of the AQA inorganic syllabus: how to recognise monodentate, bidentate, and polydentate ligands; how to assign coordination numbers; how to predict the shape of a complex (octahedral, tetrahedral, square planar, linear); how to compute the overall charge from the metal oxidation state and the ligand charges; how to name complexes using IUPAC rules; how to identify cis-trans (geometric) and optical (mirror-image) isomers; and why polydentate chelating ligands produce extraordinarily stable complexes — the chelate effect — with consequences from analytical chemistry to biology and medicine.
Spec mapping (AQA 7405): This lesson anchors §3.2.5 (transition metals — complex formation and shapes), the second of seven lessons in this course. It cross-references L4 (transition metals, electron configurations, variable oxidation states) for the d-block context, L6 (ligand substitution) for the kinetic and equilibrium behaviour of complexes once formed, L7 (colour and the spectrochemical series) for the optical consequences of ligand-field strength, and L8 (reactions of aqueous metal ions with bases and ammonia) for the practical chemistry built directly on these structures. It draws on §3.1.3 lesson 1 (dative covalent bonding origin — the lone-pair-into-empty-orbital model first met in NH₄⁺ and H₃O⁺) and connects forward to §3.3.7 (optical isomerism), originally introduced for chiral organic molecules but extended here to chiral chelate complexes. Refer to the official AQA specification document for the exact wording of each section.
Assessment objectives: AO1 — define complex ion, ligand, monodentate, bidentate, multidentate (polydentate), coordination number, and chelate; recall the four standard shapes and their bond angles; recall the named monodentate, bidentate, and hexadentate ligands on the specification. AO2 — predict the shape of an unfamiliar complex from its coordination number and ligand identity; calculate the overall charge of a complex from the metal oxidation state and the sum of ligand charges; name complexes using IUPAC conventions (Latin-stem -ate for anionic complexes, alphabetical ligand listing, Greek vs bis/tris prefixes); draw cis-trans isomers of square-planar and octahedral complexes. AO3 — identify the presence of optical isomerism in tris(bidentate) octahedral chelates; explain the chelate effect in entropy terms; rationalise the choice of cis- over trans-[Pt(NH₃)₂Cl₂] as a clinical drug.
A complex ion consists of a central metal ion, almost always from the d-block, bonded to a defined number of surrounding ligands. Each bond between metal and ligand is a dative covalent (or coordinate) bond — a covalent bond in which both electrons originate from the same atom, namely a lone pair on the ligand. The metal ion supplies an empty orbital (a vacant d, s, or p orbital, or more rigorously a hybridised acceptor orbital) into which that lone pair is donated.
Complex ion: a species comprising a central metal cation surrounded by ligands joined to it by dative covalent (coordinate) bonds.
Ligand: an atom, ion, or molecule that possesses at least one lone pair of electrons, which it donates to the central metal ion to form a coordinate bond. Ligands are electron-pair donors — they behave as Lewis bases — while the metal ion is an electron-pair acceptor — a Lewis acid.
The origin of the dative bond is identical to the model first met for NH₄⁺ (where N donates a lone pair to H⁺) and for the hydronium ion H₃O⁺ (where O donates a lone pair to H⁺). The only difference is that here the acceptor is a transition-metal cation, and several ligands typically attach to one metal simultaneously, producing a discrete polyatomic ion or molecule.
Key Point: Once formed, all the M-L bonds in a complex are chemically equivalent — the "dative" label refers only to the origin of the electrons, not to any lasting difference in bond character. The Cu-N bonds in [Cu(NH₃)₄(H₂O)₂]²⁺ are indistinguishable in length and strength from one another.
The coordination number is the total number of dative bonds formed between the central metal ion and its ligands. Crucially, it is not always equal to the number of ligands — when polydentate ligands are present, each ligand forms more than one bond, and the coordination number can exceed the ligand count.
All three of the above examples give octahedral complexes — the shape is set by the coordination number, not directly by the ligand count.
A monodentate ligand forms a single dative bond per metal — it has exactly one donor atom in use. The Greek root "mono-dentate" means "one-toothed".
| Ligand | Formula | Donor atom | Charge |
|---|---|---|---|
| Water | H₂O | O | 0 |
| Ammonia | NH₃ | N | 0 |
| Chloride | Cl⁻ | Cl | −1 |
| Hydroxide | OH⁻ | O | −1 |
| Cyanide | CN⁻ | C | −1 |
| Thiocyanate | SCN⁻ | N or S | −1 |
| Carbon monoxide | CO | C | 0 |
H₂O, NH₃, and Cl⁻ are the three monodentate ligands you must know cold for AQA — they appear in every Paper 2 complex-chemistry question. CN⁻ and OH⁻ feature in named reactions; CO is encountered in haemoglobin/carbonyl poisoning contexts.
A bidentate ligand has two donor atoms, both of which simultaneously bond to the same metal centre, forming a five- or six-membered "chelate ring" that includes the metal.
| Ligand | Formula | Donor atoms |
|---|---|---|
| 1,2-diaminoethane (ethylenediamine, "en") | H₂N-CH₂-CH₂-NH₂ | Both N atoms |
| Ethanedioate (oxalate, "ox") | ⁻O₂C-CO₂⁻ (C₂O₄²⁻) | Two O atoms (one from each carboxylate) |
| Glycinate | H₂N-CH₂-CO₂⁻ | N and O |
When written as a coordination-sphere member, a bidentate ligand "wraps around" the metal: in [Ni(en)₃]²⁺, each of the three en molecules occupies two adjacent coordination sites, producing six bonds in total and an octahedral geometry.
A polydentate ligand has three or more donor atoms able to bind a single metal centre. The most important examples for AQA are:
Key Definition: Chelation is the formation of a complex containing a polydentate ligand. The resulting complex is called a chelate. The word derives from the Greek chele, meaning crab's claw — an image evoked by the way a bidentate ligand "grips" the metal between two donor atoms.
The coordination number, together with steric considerations and electronic preferences of the metal, determines the geometry of the complex.
Six ligand donor atoms occupy the corners of a regular octahedron about the metal, all M-L bond angles equal to 90° between adjacent ligands and 180° between trans ligands. Octahedral geometry is by far the most common shape in transition-metal chemistry — most first-row aqua complexes adopt it.
Representative examples:
Note: Six monodentate ligands, three bidentate ligands, or one hexadentate ligand all give coordination number 6 and (almost always) octahedral geometry.
Four ligands at the corners of a regular tetrahedron, all bond angles 109.5°. Tetrahedral geometry is favoured when the ligands are large (most often Cl⁻), because four bulky ligands cannot fit around a small metal centre in a square planar arrangement. Many tetrahedral complexes are deeply coloured anions.
Four ligands at the corners of a square, with the metal at the centre. All four M-L bond angles between adjacent ligands are 90°. Square-planar geometry is the strong electronic preference of d⁸ metals — particularly Ni(II), Pd(II), Pt(II), and Au(III) — and appears whenever those metals form four-coordinate complexes.
Two ligands collinear with the metal, bond angle 180°. Linear geometry is characteristic of d¹⁰ Ag(I) and Cu(I), and of Au(I).
Summary: AQA expects you to recognise four shapes — octahedral (CN 6), tetrahedral (CN 4, large ligands), square planar (CN 4, d⁸ metals), and linear (CN 2). The shape is generally a direct consequence of the coordination number; square planar vs tetrahedral for CN 4 is decided by the metal's electron configuration and ligand size.
The overall charge on a complex equals the algebraic sum of the metal's oxidation state and the charges of all the ligands:
Q(complex) = (oxidation state of metal) + Σ(ligand charges)
Most named ligands carry recognisable charges: neutral (H₂O, NH₃, CO, en), −1 (OH⁻, Cl⁻, CN⁻, glycinate), −2 (oxalate, carbonate as a ligand), −4 (EDTA⁴⁻).
Worked example 1. [Fe(CN)₆]³⁻ — Fe is in oxidation state +3; six CN⁻ contribute 6 × (−1) = −6. Net: +3 + (−6) = −3. ✓
Worked example 2. [Cu(NH₃)₄(H₂O)₂]²⁺ — Cu is +2; four NH₃ contribute 0; two H₂O contribute 0. Net: +2 + 0 + 0 = +2. ✓
Worked example 3. [CrCl₂(H₂O)₄]⁺ — given the +1 overall charge, four neutral aqua ligands and two chloride at −1 each (total −2), the metal oxidation state must satisfy x + 0 + (−2) = +1, so Cr is +3. ✓
Worked example 4. [Co(en)₃]³⁺ — Co +3; three neutral en contribute 0. Net: +3. ✓
Worked example 5. Given the [CaEDTA]²⁻ formula and EDTA = −4, the metal must be in oxidation state +2: +2 + (−4) = −2. ✓ Consistent with Ca²⁺.
Exam Tip: AQA often gives you the overall charge and the ligand list and asks for the metal's oxidation state, or vice versa. The arithmetic is straightforward once you know the ligand charges by heart — commit at minimum H₂O, NH₃ (neutral), Cl⁻, OH⁻, CN⁻ (−1), C₂O₄²⁻ (−2), and EDTA⁴⁻ to memory.
A complex name is built in a fixed order:
| Complex | IUPAC name |
|---|---|
| [Cu(H₂O)₆]²⁺ | hexaaquacopper(II) ion |
| [CoCl₄]²⁻ | tetrachloridocobaltate(II) ion |
| [Cr(NH₃)₆]³⁺ | hexaamminechromium(III) ion |
| [Fe(CN)₆]³⁻ | hexacyanidoferrate(III) ion |
| [Ag(NH₃)₂]⁺ | diamminesilver(I) ion |
| [Cu(NH₃)₄(H₂O)₂]²⁺ | tetraamminediaquacopper(II) ion |
| [Pt(NH₃)₂Cl₂] | diamminedichloridoplatinum(II) (neutral) |
| [Ni(en)₃]²⁺ | tris(1,2-diaminoethane)nickel(II) ion |
Exam Tip: Three very common naming errors: (1) writing amine instead of ammine — amine with one m refers to an organic R-NH₂ group, ammine with two m's is the ligand name for NH₃ on a metal. (2) Forgetting the -ate / Latin-stem change when the complex is anionic — cobalt(II) in a cation, cobaltate(II) in an anion. (3) Listing ligands in formula order rather than alphabetical order — ammine comes before aqua in [Cu(NH₃)₄(H₂O)₂]²⁺, so the name is tetraamminediaqua…, not diaquatetraammine….
A given molecular formula can correspond to more than one distinct three-dimensional arrangement of ligands. AQA examines two types: cis-trans (geometric) isomerism and optical (mirror-image) isomerism.
When a square-planar or octahedral complex contains two different types of ligand in defined positions, two distinct geometric arrangements are possible:
Square planar. The textbook example is [Pt(NH₃)₂Cl₂], diamminedichloridoplatinum(II). In the cis isomer, the two NH₃ ligands are on adjacent corners of the square and the two Cl⁻ on the other two adjacent corners. In the trans isomer, the NH₃ ligands are on opposite corners, with Cl⁻ between them.
The clinical importance: cisplatin (the cis isomer) is a major anti-cancer drug, used since 1978 to treat testicular, ovarian, bladder, head-and-neck, and several other cancers. The trans isomer is essentially biologically inactive. The molecular basis is that cis-platin binds DNA by forming intrastrand cross-links between adjacent guanine bases — a geometry only possible because the two chloride leaving groups are adjacent in cis-Pt(II). Trans-platin cannot reach two adjacent bases simultaneously and instead forms different, less lethal DNA adducts that the cell repairs more easily.
Octahedral. A complex of formula [M(L)₄(L')₂] (four of one ligand, two of another, in an octahedron) has cis and trans isomers: cis with the two L' ligands at adjacent (90°) positions, trans with them at opposite (180°) positions. Example: cis- and trans-[CrCl₂(H₂O)₄]⁺.
A complex is optically active — exists as a pair of non-superimposable mirror-image enantiomers — when it lacks a plane of symmetry. For octahedral complexes the classic case is one containing three bidentate ligands, such as [Co(en)₃]³⁺ or [Ni(en)₃]²⁺. The three "propeller blades" of bidentate ligand can be arranged in a right-handed (Δ, delta) or left-handed (Λ, lambda) twist — two mirror images that cannot be superimposed by rotation. The two enantiomers rotate plane-polarised light in equal and opposite directions.
This is the same concept of chirality met in §3.3.7 for organic compounds (e.g. amino acids around a chiral carbon), here applied to a chiral metal centre rather than a chiral carbon.
Polydentate ligands form complexes with metals that are dramatically more thermodynamically stable than complexes of the same metal with the equivalent number of monodentate ligands of the same donor-atom type. This is the chelate effect, and its origin is overwhelmingly entropic rather than enthalpic.
Compare the two equilibria, in each case displacing six aqua ligands from [Ni(H₂O)₆]²⁺:
[Ni(H₂O)₆]²⁺ + 6 NH₃ ⇌ [Ni(NH₃)₆]²⁺ + 6 H₂O (six monodentate ligands)
[Ni(H₂O)₆]²⁺ + 3 en ⇌ [Ni(en)₃]²⁺ + 6 H₂O (three bidentate ligands)
[Ni(H₂O)₆]²⁺ + EDTA⁴⁻ ⇌ [Ni(EDTA)]²⁻ + 6 H₂O (one hexadentate ligand)
The Ni-N bond enthalpies are very similar in all three cases — the bonding differences are small. But:
Because ΔG = ΔH − TΔS, the entropy-favoured chelation reaction has a much more negative ΔG and therefore a much larger equilibrium constant — typically by several orders of magnitude. For Ni²⁺, the stepwise stability constant for [Ni(en)₃]²⁺ is roughly 10¹⁰ times larger than for [Ni(NH₃)₆]²⁺; the constant for [Ni(EDTA)]²⁻ is roughly 10¹⁸ times larger again.
Key Point: The chelate effect is the entropy advantage that polydentate ligands enjoy because binding one chelate releases multiple solvent molecules into the bulk, increasing the disorder of the system.
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