Transition Elements: Colour, Stereoisomerism and Stability Constants

This guide covers subtopics 28.3, Colour of complexes, 28.4, Stereoisomerism in transition element complexes, and 28.5, Stability constants, Kstab, from Topic 28, Chemistry of transition elements, of Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. This is A Level content, continuing directly from Transition Elements: Properties, Complexes and Redox Chemistry.

Before studying this

This resource assumes ligands, complex formation, coordination number and ligand exchange from Transition Elements: Properties, Complexes and Redox Chemistry — read that page first. It also assumes equilibrium-constant expressions from Acids, Bases, Buffers and Partition Coefficients.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL CHEMISTRY 9701 — A Level, Topic 28

28.3 Colour of complexes — defining degenerate and non-degenerate d orbitals; describing the splitting of degenerate d orbitals into two non-degenerate sets in octahedral (two higher, three lower) and tetrahedral (three higher, two lower) complexes; explaining coloured compounds in terms of light absorbed as an electron is promoted between non-degenerate d orbitals; describing qualitatively how different ligands affect the splitting energy, frequency absorbed and observed colour; using copper(II) and cobalt(II) ligand exchange as examples of colour change.

28.4 Stereoisomerism in transition element complexes — describing geometrical (cis/trans) and optical isomerism in complexes, including those with bidentate ligands; deducing the overall polarity of such complexes.

28.5 Stability constants, Kstab — defining Kstab as the equilibrium constant for complex-ion formation; writing a Kstab expression; using Kstab in calculations; explaining ligand exchange in terms of Kstab values.

Why transition-metal complexes are coloured

In an isolated transition-metal ion, the five d orbitals all have the same energy — they are degenerate. When ligands bond to the metal, their electron density repels the d electrons unevenly, depending on each orbital’s shape and orientation relative to where the ligands sit. This splits the five d orbitals into two sets of different energy — non-degenerate — separated by an energy gap, ΔE.

• In an octahedral complex (six ligands along the x, y, z axes), the orbitals pointing directly at the ligands are repelled more, giving two higher-energy orbitals and three lower-energy orbitals.
• In a tetrahedral complex (four ligands), the geometry is reversed relative to the axes, giving three higher-energy orbitals and two lower-energy orbitals.

Colour arises because an electron in a lower-energy d orbital can absorb a photon and be promoted to a higher-energy d orbital, provided the ion has at least one d electron available to make that jump and at least one vacancy to jump into. The energy absorbed corresponds to a specific frequency (E = hf) in the visible spectrum; the colour observed is the complementary colour to the light absorbed (the colours the eye sees are the wavelengths not absorbed, transmitted or reflected instead) — for example, a complex absorbing mostly red-orange light appears blue-green.

Different ligands change ΔE, and therefore the frequency absorbed and the colour observed, because different ligands repel the d electrons to different extents. This is exactly why ligand exchange changes colour:

• [Cu(H₂O)₆]²⁺ (pale blue) → [Cu(NH₃)₄(H₂O)₂]²⁺ (deep blue): NH₃ produces a larger ΔE than H₂O, shifting the absorbed frequency and hence the observed colour.
• [Co(H₂O)₆]²⁺ (pink) → [CoCl₄]²⁻ (blue): here the geometry also changes (octahedral to tetrahedral), which on its own changes the splitting pattern (and typically reduces ΔE, since tetrahedral splitting is inherently smaller than octahedral splitting for comparable ligands), compounding the ligand-identity effect on colour.

(A complex with no d electrons, like Sc³⁺, or a full d sub-shell, like Zn²⁺, cannot undergo this electron promotion — there’s no gap to promote from, or no vacancy to promote into — which is exactly why scandium and zinc compounds are colourless and are excluded from the “transition element” definition.)

Stereoisomerism in complexes

Complexes can show the same two broad categories of stereoisomerism met in organic chemistry, now arising from three-dimensional arrangement around a central metal ion rather than a C=C double bond or a chiral carbon.

Geometrical (cis/trans) isomerism occurs where two arrangements of the same ligands around the metal aren’t interconvertible without breaking bonds:

• Square planar, e.g. [Pt(NH₃)₂Cl₂]: the two Cl (and two NH₃) ligands can be positioned next to each other (cis) or opposite each other (trans) — cisplatin, the cis isomer, is a well-known anti-cancer drug.
• Octahedral, e.g. [Co(NH₃)₄(H₂O)₂]²⁺: the two H₂O ligands can be adjacent (cis) or directly opposite (trans) on the octahedron.

Optical isomerism occurs where a complex and its mirror image are non-superimposable, especially common with bidentate ligands wrapping around an octahedral centre:

• [Ni(H₂NCH₂CH₂NH₂)₃]²⁺ (three bidentate “en” ligands, filling all six coordination positions) has no internal mirror plane and exists as a pair of non-superimposable mirror-image optical isomers.
• [Ni(H₂NCH₂CH₂NH₂)₂(H₂O)₂]²⁺ (two bidentate “en” ligands plus two water) can show both cis/trans geometrical isomerism and, in its cis form, optical isomerism — the trans form has a mirror plane and is not chiral.

Polarity follows directly from geometry: a symmetric arrangement (e.g. the trans isomer of a square planar or octahedral complex with two pairs of identical ligands) is non-polar, since bond dipoles cancel by symmetry; the corresponding cis isomer, lacking that symmetry, is polar.

Stability constants, Kstab

The stability constant, Kstab, is the equilibrium constant for the formation of a complex ion in solution from its constituent (usually aqueous) ions or molecules — a direct measure of how far the equilibrium lies towards the complex.

Worked example. Write the Kstab expression for the formation of [Cu(NH₃)₄]²⁺ from [Cu(H₂O)₄]²⁺ and NH₃.

[Cu(H₂O)₄]²⁺(aq) + 4NH₃(aq) ⇌ [Cu(NH₃)₄]²⁺(aq) + 4H₂O(l)

Kstab = [[Cu(NH₃)₄]²⁺] / ([[Cu(H₂O)₄]²⁺][NH₃]⁴)

(water, as the solvent, is omitted from the expression, exactly as a pure solid is omitted from Ksp).

A large Kstab means the equilibrium lies strongly towards the new complex — the new ligand binds much more strongly than the one it displaced. This is precisely why ligand exchange happens at all: adding excess NH₃ to [Cu(H₂O)₆]²⁺ drives the equilibrium towards [Cu(NH₃)₄(H₂O)₂]²⁺ because that complex has a substantially larger Kstab than the aqua complex — the new complex is simply more thermodynamically stable once enough of the new ligand is available.

Worked example. Kstab for [Cu(NH₃)₄]²⁺ formation (as above) is 1.2 × 10¹³ mol⁻⁴ dm¹². At equilibrium, [Cu(NH₃)₄²⁺] = 0.0500 mol dm⁻³ and [NH₃] = 0.100 mol dm⁻³. Calculate [[Cu(H₂O)₄]²⁺].

Rearranging: [[Cu(H₂O)₄]²⁺] = [[Cu(NH₃)₄]²⁺] / (Kstab × [NH₃]⁴)

[NH₃]⁴ = (0.100)⁴ = 1.00 × 10⁻⁴

[[Cu(H₂O)₄]²⁺] = 0.0500 / (1.2 × 10¹³ × 1.00 × 10⁻⁴) = 0.0500 / (1.2 × 10⁹) = 4.17 × 10⁻¹¹ mol dm⁻³

The vanishingly small concentration of the original aqua complex remaining confirms just how strongly the equilibrium has shifted towards the ammine complex — consistent with the large Kstab value.

Common mistakes

Assuming all coloured-compound explanations are the same as for main-group chemistry. Transition-metal colour is specifically about d-to-d electron promotion across a ligand-induced splitting gap — it has nothing to do with the flame-test or emission-spectrum explanations used elsewhere.

Forgetting the electron count requirement for colour. A d⁰ ion (like Sc³⁺) has nowhere to promote an electron from; a d¹⁰ ion (like Zn²⁺) has nowhere to promote an electron to — both give colourless compounds despite being d-block.

Missing that geometry alone (not just ligand identity) affects the size of ΔE. Tetrahedral splitting is inherently smaller than octahedral splitting for the same ligand, which is part of why a coordination-number change (like [Cu(H₂O)₆]²⁺ → [CuCl₄]²⁻) shifts colour even beyond the effect of the ligand itself changing.

Confusing which isomer is polar. It’s the asymmetric cis form that’s generally polar, and the more symmetric trans form that’s generally non-polar (bond dipoles cancelling by symmetry) — check the specific geometry rather than assuming.

Quick revision checklist

• d orbitals split by ligand field: octahedral 2 high + 3 low; tetrahedral 3 high + 2 low
• Colour: electron promoted across ΔE; observed colour is complementary to light absorbed
• No colour: d⁰ (nothing to promote) or d¹⁰ (nowhere to promote to)
• Different ligand or different geometry → different ΔE → different colour
• Cis/trans (geometrical) isomerism: square planar and octahedral complexes with paired ligands
• Optical isomerism: common with bidentate ligands filling an octahedral centre; non-superimposable mirror images
• Kstab = equilibrium constant for complex formation (solvent omitted); larger Kstab = more stable complex, drives ligand exchange

Related resources

• Transition Elements: Properties, Complexes and Redox Chemistry — ligands, complex formation and coordination number this page builds on
• Acids, Bases, Buffers and Partition Coefficients — equilibrium-constant expressions applied here to Kstab
• Optical Isomerism and Chirality — the organic-chemistry counterpart to optical isomerism in complexes
• Cambridge AS & A Level Chemistry hub

Written against Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. Always check the current syllabus for your examination year.