Chemistry · Chemistry of the elements · Year 1

Complex compounds and ligands

Why does copper sulfate turn deep blue when ammonia is added, and how did Werner explain it?

The situation

The iron in haemoglobin makes our blood red, magnesium sits in the chlorophyll of leaves, and cobalt in vitamin B₁₂; the anticancer drug cisplatin is a platinum compound, and the EDTA in water softeners and washing powders “traps” calcium ions. All of these are complex compounds. In the laboratory, if ammonia is dripped into a pale blue solution of copper sulfate, a blue precipitate forms first, then it dissolves and the solution turns deep blue. In 1893 A. Werner explained why cobalt ammines of similar composition give different amounts of AgCl with silver nitrate. How are the ligands arranged around the metal, where do colour and magnetism come from, and how stable is a complex?

Topic

Coordination compounds: Werner, crystal field, stability. Haemoglobin (Fe), chlorophyll (Mg), vitamin B₁₂ (Co), the cancer drug cisplatin and EDTA in a water softener — all coordination compounds. In the laboratory, blue CuSO₄…

Key ideas

Coordination number and isomerism
Crystal field Δ and spin
Stability constant

Formulas

β_{n} = K_{1} K_{2} \dots K_{n} = \frac{[{ML}_{n}]}{[M] {[L]}^{n}}, K_{inst} = 1 / β_{n}

Stepwise and overall stability constants; the instability constant is the reciprocal.

CFSE = (- 0.4 n_{t_{2 g}} + 0.6 n_{e_{g}}) Δ_{o} + p P

Crystal field stabilisation energy (octahedron); $P$ is the pairing energy, $p$ is the number of extra pairs.

Δ_{t} \approx \frac{4}{9} Δ_{o}

For the same metal and ligands, the tetrahedral field is weaker than the octahedral one — tetrahedral complexes are almost always high spin.

μ = \sqrt{n (n + 2)} μ_{B}, EAN = Z - o.d. + 2 \cdot KS

Spin-only magnetic moment; Sidgwick rule: noble-gas configuration (36, 54, 86).

A = ε l c

Beer–Lambert law: absorbance is proportional to concentration.

Theory

Werner's theory: the central atom and ligands

A complex compound is a particle made of a central atom (ion) and the ligands (addends) surrounding it; they form the inner sphere, written in square brackets: [Co(NH₃)₆]³⁺. The ions outside the brackets form the outer sphere and separate in solution as free ions. The number of donor atoms bonded directly to the central atom is the coordination number (CN: 2, 4 and 6 are the most common). The number of donor atoms through which a ligand binds is its denticity: NH₃ and Cl⁻ are monodentate, ethylenediamine (en) is bidentate, EDTA is hexadentate. The bond is donor–acceptor: an electron pair of the ligand passes into an empty orbital of the metal. A. Werner (1893) explained why the compounds CoCl₃·6NH₃, ·5NH₃ and ·4NH₃ give 3, 2 and 1 mol of AgCl with AgNO₃: part of the Cl⁻ is bonded in the inner sphere. The Werner–Miolati series — molar conductivity matches the number of ions: [Pt(NH₃)₆]Cl₄ (5 ions) ≈ 523, [Pt(NH₃)₂Cl₄] (neutral) ≈ 0 Ω⁻¹·cm²·mol⁻¹. Jørgensen's “chain” theory could not explain such a sequence. IUPAC nomenclature: first the ligands in alphabetical order, with number prefixes (di-, tri-, tetra-, hexa-; bis-, tris- for complex ligands), anionic ligands with the ending -o (chloro, cyano), then the central atom and its oxidation state: [Co(NH₃)₅Cl]Cl₂ — pentaamminechlorocobalt(III) chloride; in a complex anion the metal name gets the ending -ate: K₄[Fe(CN)₆] — potassium hexacyanoferrate(II).

Types of complex compounds and isomerism

Types: ammines and amines ([Cu(NH₃)₄]²⁺), hydrates and aqua complexes ([Co(H₂O)₆]²⁺), carbonyls (Ni(CO)₄, Fe(CO)₅), acido complexes ([Fe(CN)₆]⁴⁻, [PtCl₆]²⁻), chelates (ring-forming en, EDTA), inner complex compounds — a chelate that is neutral (copper glycinate, nickel dimethylglyoximate), π-complexes (Zeise's salt K[PtCl₃(C₂H₄)]), metallocenes — “sandwich” compounds (ferrocene), polynuclear and cluster compounds (metal–metal bond), clathrates (gas molecules in the cavities of a crystal lattice). Isomerism: geometric — cis/trans ([Pt(NH₃)₂Cl₂], [Co(NH₃)₄Cl₂]⁺), fac/mer; optical — Δ and Λ ([Co(en)₃]³⁺, the mirror image cannot be superimposed); hydrate — [Cr(H₂O)₆]Cl₃ (violet), [CrCl(H₂O)₅]Cl₂·H₂O, [CrCl₂(H₂O)₄]Cl·2H₂O (green); ionisation — [Co(NH₃)₅Br]SO₄ and [Co(NH₃)₅SO₄]Br; linkage — nitro (Co–NO₂) and nitrito (Co–ONO); coordination — [Co(NH₃)₆][Cr(CN)₆] and [Cr(NH₃)₆][Co(CN)₆]; ligand isomerism (the ligand itself is an isomer); conformational — the δ/λ forms of the en ring; coordination polymers — a ligand links two metals. Werner found only two isomers of [Co(NH₃)₄Cl₂]⁺ (green “praseo” and violet “violeo”, 1907) — this proved that the structure is octahedral: a hexagon or a prism would give three.

Chemical bonding: Kossel, Lewis, Sidgwick and valence bonds

The Kossel approach treats a complex as an electrostatic attraction of ions; Lewis treats the ligand as an electron-pair donor (Lewis base) and the metal as an acceptor. Sidgwick rule (EAN): the effective atomic number of the central atom = Z − oxidation state + electrons received from the ligands; in many stable complexes it equals that of a noble gas: [Fe(CN)₆]⁴⁻ 26 − 2 + 12 = 36 (Kr), Ni(CO)₄ 28 + 8 = 36, ferrocene 36. For carbonyls the rule (the 18-electron rule) works well, but [Cu(NH₃)₄]²⁺ (35), [Ag(NH₃)₂]⁺ (50) or cisplatin (84) do not obey it. Valence bond theory (Pauling): the ligand pairs occupy hybrid orbitals of the metal — sp (linear), sp³ (tetrahedral), dsp² (square planar), d²sp³ (inner orbital, low-spin octahedron: [Co(NH₃)₆]³⁺, [Fe(CN)₆]⁴⁻), sp³d² (outer orbital, high spin: [CoF₆]³⁻). Symmetry: octahedron $O_{h}$ , tetrahedron $T_{d}$ , square $D_{4 h}$ , tris-chelate $D_{3}$ ; symmetry determines the splitting of the orbitals (the symmetry elements are in the “The molecule: orbitals and symmetry” experiment). VB theory cannot explain colour and spectra — crystal field theory does that.

Crystal field: Δ, spin, colour and magnetism

Ligands, as negative charges (or dipoles), do not repel the d-orbitals equally. In an octahedron the $d_{z^{2}}$ and $d_{x^{2} - y^{2}}$ ( $e_{g}$ ) orbitals, which point at the ligands, are raised (+0.6Δo), while $d_{x y}, d_{x z}, d_{y z}$ ( $t_{2 g}$ ), which lie between the ligands, are lowered (−0.4Δo). In a tetrahedron it is the other way round and weaker: Δt ≈ 4/9 Δo. Spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO — Δ increases along the series of ligands; it also increases as the charge of the central ion rises and from 3d → 4d → 5d. High and low spin: in d⁴–d⁷ an electron either goes up to $e_{g}$ or pairs up; if Δo < P — high spin ([Fe(H₂O)₆]²⁺, 4 unpaired e⁻), if Δo > P — low spin ([Fe(CN)₆]⁴⁻, diamagnetic). Colour: an electron jumps from $t_{2 g}$ to $e_{g}$ and absorbs a photon whose energy equals Δ; we see the complementary colour of the absorbed one: [Ti(H₂O)₆]³⁺ (d¹) absorbs 20 300 cm⁻¹ ≈ 243 kJ/mol, ≈ 490–500 nm (green-blue) — the solution is violet. In an octahedron with a centre of symmetry, d–d transitions are “forbidden” (Laporte rule) and weak (ε ≈ 1–100); a tetrahedron has no centre of symmetry — [CoCl₄]²⁻ has ε ≈ 600, so it is deep blue. Magnetic properties: substances with unpaired electrons are paramagnetic (drawn into a field), those with all electrons paired are diamagnetic (slightly repelled); Fe, Co, Ni are ferromagnetic: the spins in domains are parallel, and above the Curie point (Fe 770 °C, Ni 358 °C) they become paramagnetic. Paramagnetic molar susceptibility obeys Curie's law ( $χ_{M} \propto μ^{2} / T$ ); it is measured with a Gouy balance. Nuclear spins are the basis of NMR spectroscopy. Jahn–Teller effect: in d⁹ Cu²⁺ the $e_{g}$ level is filled unevenly — the octahedron elongates.

Equilibrium in solution, the chelate effect and importance in analysis

A complex forms step by step: Cu²⁺ + NH₃ ⇌ [Cu(NH₃)]²⁺ ( $K_{1}$ ), … ( $K_{4}$ ); for Cu²⁺–NH₃, lg $K$ = 4.31; 3.67; 3.04; 2.30, lg β₄ = 13.32 (Bjerrum). Usually $K_{1} > K_{2} > K_{3} > K_{4}$ : free space decreases, and there is a statistical factor. The formation function $\overline{n}$ is the average number of ligands bound to one metal (Bjerrum's method). Thermodynamics: $Δ G^{\circ} = - R T \ln β$ . Chelate effect: lg β([Ni(en)₃]²⁺) = 18.28 ≫ lg β([Ni(NH₃)₆]²⁺) = 8.61; in the complexes of Cd²⁺ with 4 CH₃NH₂ and with 2 en, ΔH is almost the same (−57.3 and −56.5 kJ/mol), and the difference comes from entropy — one en displaces two water molecules. The macrocyclic effect — a ring-shaped ligand (porphyrin, corrin, cyclam) is even more stable than its open-chain analogue: haemoglobin, chlorophyll, B₁₂. Irving–Williams series: Mn²⁺ < Fe²⁺ < Co²⁺ < Ni²⁺ < Cu²⁺ > Zn²⁺ (lg $K_{1}$ (en): 2.73 … 10.55 … 5.71) — CFSE and the Jahn–Teller stabilisation of Cu²⁺. Effect of pH: a ligand is protonated in acid (NH₄⁺, H₄Y) — the complex breaks down; for EDTA the conditional constant is lg K′ = lg K + lg α(Y⁴⁻): CaY²⁻ is titrated at pH ≥ 8–10 (lg K′ ≥ 8). In analysis: complexometry (water hardness with EDTA), Ni²⁺ — red precipitate with dimethylglyoxime, Fe³⁺ — photometry with thiocyanate or phenanthroline, Cu²⁺ — by the colour of the ammine.

Synthesis, methods of study, safety and the model

Synthesis: [Cu(NH₃)₄]SO₄·H₂O — add ammonia and then ethanol to a copper sulfate solution and crystallise (the complex is poorly soluble in alcohol); cobalt(III) ammines are obtained by oxidising a Co(II) salt with air or H₂O₂ in the presence of NH₄Cl and NH₃: $4 CoCl_{2} + 4 NH_{4} Cl + 20 NH_{3} + O_{2} \overset{}{\to} 4 [Co (NH_{3})_{6}] Cl_{3} + 2 H_{2} O$ — the ligand changes the potential: E°(Co³⁺/Co²⁺) = +1.92 V, but E°([Co(NH₃)₆]³⁺/[Co(NH₃)₆]²⁺) = +0.11 V, so air easily oxidises the Co(II) ammine (redox with complexes, lab work 20). Template synthesis — a macrocycle is assembled around a metal ion (phthalocyanines). Kinetic stability: labile complexes exchange a ligand instantly (water exchange on Cu²⁺ ~10⁹ s⁻¹), inert ones take hours (Cr³⁺ ~10⁻⁶ s⁻¹, low-spin Co³⁺); do not confuse this with thermodynamic stability. Methods of study: X-ray structure (diffraction) analysis — positions of atoms; IR — C≡N, C≡O, N–H vibrations and the nitro/nitrito difference; UV-visible spectrum — Δ and colour; NMR — diamagnetic complexes; EPR — unpaired electrons (Cu²⁺); conductometry — number of ions; magnetic balance — μ. Laboratory work (1–8): complexes with ammonia (inorganic) and with en and EDTA (organic ligands), their colour and solubility — [Cu(NH₃)₄]SO₄·H₂O dissolves well in water and poorly in ethanol; many ammines, when heated, lose their ligand and decompose without melting, so the decomposition temperature is recorded instead of the melting point (L3); checking Beer's law in a spectrophotometer, the dependence of complex formation on pH and time (the labile Cu²⁺ ammine forms instantly, while inert Cr³⁺ gives a violet complex with EDTA over hours at room temperature and in minutes on boiling — the absorbance is recorded against time). Safety: work with concentrated ammonia in a fume cupboard; cobalt and nickel salts are allergens and suspected carcinogens; cyanides are extremely toxic — do not acidify (HCN is released); AgNO₃ stains the skin black. Model: Δ and the absorption bands are taken from the literature (with approximate widths), and the colour is calculated from them through the CIE curves; for ions other than d¹ the number and positions of the bands depend on the Tanabe–Sugano diagram, so the single Δ in the picture is a simplification. Cu–NH₃ equilibrium: 25 °C, activities = concentrations, the precipitate is taken to be Cu(OH)₂ (in practice basic sulfate also precipitates); Gouy balance model: 1.00 mmol of salt, 5 cm tube, B = 0.5 T, 20 °C.

Did you know?

In 1913 Alfred Werner received the Nobel Prize in Chemistry for coordination theory — he was the first inorganic chemist to win this prize.
Cisplatin was first made by M. Peyrone in 1844, and its anticancer action was discovered by chance in 1965 by B. Rosenberg: bacteria stopped dividing in a medium through which current was passed with platinum electrodes.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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