28. Chemistry A2 of transition elements
- Syllabus
- 9701–2028–2029
- Section
- 28
- Level
- A2
A transition element is a d-block element that forms at least one stable ion with an incomplete d subshell.
| Element | Relevant stable ion | d configuration | Transition element? |
|---|---|---|---|
| Sc | Sc³⁺ | 3d⁰ | no: the d subshell is empty |
| Fe | Fe²⁺ or Fe³⁺ | 3d⁶ or 3d⁵ | yes: the d subshell is incomplete |
| Zn | Zn²⁺ | 3d¹⁰ | no: the d subshell is complete |
Classify the element by the electron configuration of its stable ion or ions, not by the neutral atom alone. Only one stable ion with a partly filled d subshell is required.
Being in the d block is necessary but is not sufficient under this definition: scandium and zinc are d-block elements but are not transition elements because their stable ions are d⁰ and d¹⁰ respectively.
| Orbital | Plane / axis | Electron-density shape | How to sketch it |
|---|---|---|---|
| 3dxy | xy plane | four lobes between the x and y axes | draw labelled x and y axes, then place one lobe in each quadrant between them |
| 3dz² | z axis and xy plane | two lobes along z plus a torus around the centre in the xy plane | draw a labelled vertical z axis, two opposing lobes on it, then a ring around the centre |
Put the nucleus at the origin and label the relevant axes. For 3dxy the axes pass between the lobes; for 3dz² the two main lobes lie on the z axis and the ring lies perpendicular to it.
An orbital sketch represents a region of electron probability density. It is not a path followed by an electron, and the 3dxy lobes must not be drawn on the x and y axes.
| Property | What it means here | Example |
|---|---|---|
| variable oxidation states | the same element forms stable species in more than one oxidation state | Fe²⁺ and Fe³⁺ |
| catalytic activity | the element or one of its compounds speeds a reaction and is regenerated | Fe in the Haber process |
| complex-ion formation | a central metal ion accepts lone pairs from ligands | [Cu(H₂O)₆]²⁺ |
| coloured compounds | many compounds absorb part of visible light and appear coloured | aqueous Cu²⁺ compounds are blue |
These behaviours arise because 3d and 4s levels are close enough in energy for several electron arrangements and bonding interactions to be accessible.
These are characteristic trends, not a claim that every compound of every transition element displays all four. Detailed explanations of colour and complex geometry belong to later objectives.
The 3d and 4s sublevels are close in energy. Different numbers of 4s and 3d electrons can therefore be removed or used in bonding without an impossibly large extra energy change, allowing several stable oxidation states.
| Species | Electron configuration | Oxidation state |
|---|---|---|
| Fe | [Ar] 3d⁶ 4s² | 0 |
| Fe²⁺ | [Ar] 3d⁶ | +2 |
| Fe³⁺ | [Ar] 3d⁵ | +3 |
When a first-row transition metal forms a positive ion, its 4s electrons are removed before its 3d electrons, even though 4s fills before 3d in the neutral atom.
Variable oxidation state is not caused by electrons having no energy cost. It reflects the relatively small energy differences among accessible 3d/4s arrangements, balanced by bonding and lattice or hydration stabilisation.
| Catalytic route | Role of the transition element | Result |
|---|---|---|
| oxidation-state cycling | changes reversibly between stable oxidation states by accepting and donating electrons, such as Fe²⁺ ⇌ Fe³⁺ | provides a lower-energy sequence of redox steps |
| ligand binding | accessible vacant d orbitals accept lone pairs to form temporary dative bonds with reactants | brings reactants together or weakens bonds before products leave |
In either route, the catalyst participates in intermediate steps but is regenerated by the end. The alternative pathway has a lower activation energy, so a larger fraction of collisions is successful at the same temperature.
A catalyst changes reaction rate, not the position of equilibrium or the overall enthalpy change. A proposed mechanism must show both how the catalyst participates and how it is regenerated.
A complex ion contains a central metal ion surrounded by ligands. Each ligand donates a lone pair into an energetically accessible vacant orbital on the metal ion, forming a dative covalent bond.
TiX3++6HX2O[Ti(HX2O)X6]X3+
| Part of [Ti(H₂O)₆]³⁺ | Electron-pair role |
|---|---|
| each H₂O ligand | donor: an oxygen lone pair is donated |
| Ti³⁺ central ion | acceptor: an accessible vacant orbital accepts the pair |
| six Ti–O links | dative bonds; both bonding electrons originally came from the ligand |
Water is a neutral ligand, so the complex charge is the Ti³⁺ charge plus six zeros: +3. Once a dative bond has formed, it behaves as a covalent bond; its name records the origin of the shared electron pair.
A complex ion is a bonded coordination entity, not merely a metal ion and nearby counter-ions. Counter-ions may balance its charge but are not ligands unless they donate a lone pair directly to the metal centre.
A ligand forms a complex by donating a lone pair into an accessible orbital on Cu²⁺ or Co²⁺. Ligand size, charge and number determine the product formula, charge, coordination number and geometry.
| Ligand around M²⁺ (M = Cu or Co) | Representative complex | Coordination / geometry |
|---|---|---|
| H₂O | [M(H₂O)₆]²⁺ | 6 / octahedral |
| NH₃ | [M(NH₃)₆]²⁺; Cu commonly [Cu(NH₃)₄(H₂O)₂]²⁺ in aqueous excess NH₃ | 6 / octahedral |
| OH⁻ with water | [M(H₂O)₄(OH)₂] | 6 / octahedral precipitate |
| Cl⁻ in concentrated chloride | [MCl₄]²⁻ | 4 / tetrahedral |
For each product, conserve the metal and ligands and add charges algebraically. Neutral H₂O/NH₃ retain the metal's +2 overall charge; two OH⁻ give a neutral complex; four Cl⁻ give an overall 2− charge.
Complex formation is coordinate bonding, not necessarily redox. Changing ligand or colour does not by itself change the metal oxidation state.
A ligand is a species containing a lone pair of electrons that forms a dative covalent bond to a central metal atom or ion. The donor atom is the ligand atom directly bonded to the metal.
| Ligand | Donor atom | Ligand charge |
|---|---|---|
| H₂O | O | 0 |
| NH₃ | N | 0 |
| Cl⁻ | Cl | −1 |
| CN⁻ | usually C in the standard cyanido complex | −1 |
A counter-ion outside the coordination sphere is not a ligand unless it directly donates a lone pair to the metal. In the dative bond, both bonding electrons originate from the ligand, not the metal.
| Term | Donor atoms used by one ligand | Required examples |
|---|---|---|
| monodentate | 1 | H₂O, NH₃, Cl⁻, CN⁻ |
| bidentate | 2 | 1,2-diaminoethane (en), H₂NCH₂CH₂NH₂; ethanedioate, C₂O₄²⁻ |
| polydentate | several | EDTA⁴⁻, commonly hexadentate |
Three bidentate en ligands provide six donor atoms, so [M(en)₃]ⁿ⁺ has coordination number 6 even though only three ligand molecules are present.
Denticity is neither ligand charge nor the number of ligand molecules in a formula. Count how many atoms of one ligand actually bind to the same metal centre.
A complex is a molecule or ion formed by a central metal atom or ion surrounded by one or more ligands. The metal–ligand links are dative covalent bonds.
| Formula feature | Meaning in [CoCl₄]²⁻ |
|---|---|
| central metal | Co |
| ligands inside brackets | four Cl⁻ |
| overall complex charge | 2− |
| ions outside brackets in a salt | counter-ions, not part of the complex |
A complex can be neutral or charged. Coordination number is based on directly bonded donor atoms and is not automatically the number of written ligand molecules when ligands are polydentate.
| Geometry | Coordination number | Characteristic bond angle(s) | Example |
|---|---|---|---|
| linear | 2 | 180° | [Ag(NH₃)₂]⁺ |
| square planar | 4 | 90° adjacent; 180° opposite | [PtCl₄]²⁻ |
| tetrahedral | 4 | 109.5° | [CoCl₄]²⁻ |
| octahedral | 6 | 90° adjacent; 180° opposite | [Co(H₂O)₆]²⁺ |
First count coordinated donor atoms, then use the identity of the stated complex: coordination number 4 can be either tetrahedral or square planar, so donor count alone does not decide between them.
Do not infer shape from the complex charge. Real complexes may be distorted, but use the named ideal geometry and its ideal angles unless the question supplies a distortion.
Coordination number is the number of dative covalent bonds from ligand donor atoms to the central metal atom or ion. Complex charge equals metal oxidation state plus the charges on all coordinated ligands.
| Step | Question to answer |
|---|---|
| 1 | What is the metal symbol and oxidation state? |
| 2 | What ligand and denticity are given? |
| 3 | How many ligand molecules supply the required coordination number? |
| 4 | What is metal charge + total ligand charge? |
| 5 | Put the whole coordination entity in brackets and write that charge outside. |
M²⁺ with coordination number 4 and four neutral NH₃ ligands gives [M(NH₃)₄]²⁺. M³⁺ with coordination number 4 and two bidentate C₂O₄²⁻ ligands gives [M(C₂O₄)₂]⁻ because +3 + 2(−2) = −1.
Oxidation state and overall complex charge are different quantities, and the number of ligand molecules is not the coordination number for bidentate or polydentate ligands.
[M(HX2O)X6]X2++2OHX−[M(HX2O)X4(OH)X2](s)+2HX2O(M=Cu,Co)
[Cu(HX2O)X6]X2++4NHX3[Cu(NHX3)X4(HX2O)X2]X2++4HX2O
[M(HX2O)X6]X2++4ClX−[MClX4]X2−+6HX2O(M=Cu,Co)
| Change | Cu(II) observation | Co(II) observation |
|---|---|---|
| hexaaqua + OH⁻ | blue solution → pale-blue precipitate | pink solution → blue precipitate |
| excess NH₃ | deep-blue ammine solution after the initial precipitate | ammine solution; subsequent air oxidation can alter the colour and oxidation state |
| concentrated Cl⁻ | blue/yellow species can appear green as an equilibrium mixture | pink → blue |
| add water after concentrated Cl⁻ | shifts back toward the hexaaqua complex | shifts back toward pink hexaaqua complex |
Exchange occurs when an entering ligand donates a lone pair and replaces one or more existing ligands. Larger Cl⁻ favours four-coordinate tetrahedral products, whereas small H₂O/NH₃ commonly give six-coordinate octahedral environments.
Keep ligand exchange separate from subsequent redox: Co(II) ammine species can be oxidised by air, but that oxidation is not itself the substitution step.
Ecell∘=Ereduction∘−Eoxidation∘
| Step | Action |
|---|---|
| 1 | write both data-book half-equations as reductions |
| 2 | choose the more positive E° half-equation to remain as reduction |
| 3 | reverse the other half-equation to give oxidation |
| 4 | calculate E°cell without multiplying E° values by stoichiometric coefficients |
| 5 | E°cell > 0 predicts feasibility in the written direction under standard conditions |
For Fe³⁺/Fe²⁺, +0.77 V, and Cu²⁺/Cu⁺, +0.15 V: Fe³⁺ is reduced and Cu⁺ is oxidised, so E°cell = 0.77 − 0.15 = +0.62 V.
A positive E°cell is a thermodynamic standard-condition prediction, not a guarantee of an observable rate. Activation energy, concentration and non-standard conditions can change what is observed.
2MnOX4X−+5CX2OX4X2−+16HX+2MnX2++10COX2+8HX2O
MnOX4X−+5FeX2++8HX+MnX2++5FeX3++4HX2O
2CuX2++4IX−2CuI(s)+IX2
| System | Electron / reacting ratio used in calculations | Key observation or follow-up |
|---|---|---|
| MnO₄⁻ : C₂O₄²⁻ in acid | 2 : 5 | Mn²⁺ product autocatalyses; warm reaction initially |
| MnO₄⁻ : Fe²⁺ in acid | 1 : 5 | first permanent pale pink marks slight MnO₄⁻ excess |
| Cu²⁺ : I⁻ | 1 : 2 overall | white CuI precipitate and I₂; I₂ + 2S₂O₃²⁻ → 2I⁻ + S₄O₆²⁻ |
Convert the known concentration and volume to moles, apply the coefficient ratio from the balanced equation, then convert the target moles to the requested concentration, mass or percentage. Track any aliquot or dilution factor separately.
The medium is part of the reaction: acidified permanganate gives Mn²⁺. For Cu²⁺/I⁻ include CuI precipitation, which consumes an additional iodide beyond the 2I⁻ oxidised to I₂.
| Stage | Check |
|---|---|
| choose | identify oxidant/reductant from oxidation states, E° data and stated conditions |
| balance | conserve atoms and charge in each half-equation; use H₂O/H⁺ in acid or convert appropriately for alkaline medium |
| combine | multiply half-equations to cancel electrons, but never multiply E° values |
| calculate | convert the given quantity to moles, apply the overall coefficient ratio, then answer in requested units |
| verify | recheck mass, charge, units, significant figures and any aliquot/dilution factor |
If X²⁺ + 2e⁻ → X and Y → Y³⁺ + 3e⁻, the least common electron count is 6. The combined ratio is 3X²⁺ : 2Y, giving 3X²⁺ + 2Y → 3X + 2Y³⁺.
Do not import a memorised ratio into an unfamiliar system. The balanced electron transfer determines the stoichiometry before any mass, concentration or titre calculation begins.
| Term | Meaning | Application to d orbitals |
|---|---|---|
| degenerate | equal in energy | the five d orbitals of an isolated gaseous metal ion are degenerate |
| non-degenerate | not equal in energy | surrounding ligands split the five d orbitals into two sets with different energies |
Equal energy does not mean equal shape or orientation. The five d orbitals can have different spatial orientations while remaining degenerate before the ligand field is applied.
Ligand-field splitting changes energies within the same d subshell; it does not create a new shell or change the principal quantum number.
| Geometry | Higher-energy set | Lower-energy set | Gap |
|---|---|---|---|
| octahedral | 2: dz², dx²−y² | 3: dxy, dxz, dyz | ΔE between the two sets |
| tetrahedral | 3: dxy, dxz, dyz | 2: dz², dx²−y² | ΔE between the two sets |
Orbitals directed more toward the approaching ligand lone pairs experience greater repulsion and lie higher in energy. Octahedral ligands approach along the axes; tetrahedral ligands approach between the axes, so the 2:3 ordering reverses.
A valid text-first energy diagram has energy increasing upward, two horizontal levels separated by a labelled ΔE, and the correct 2/3 degeneracy on each level for the stated geometry.
ΔE is an energy separation, not an extra orbital. Do not copy the octahedral 2-higher/3-lower arrangement into a tetrahedral complex.
ΔE=hf=λhc
A photon is absorbed when its energy matches ΔE. A d electron is promoted from the lower non-degenerate set to the higher set. Removing that frequency from white light leaves the transmitted or reflected complementary colour that the observer sees.
| If ΔE changes… | Absorbed frequency f | Absorbed wavelength λ | Observed colour |
|---|---|---|---|
| larger | higher | shorter | complement of the newly absorbed colour |
| smaller | lower | longer | complement of the newly absorbed colour |
The complex does not simply emit its displayed colour in this syllabus model. It selectively absorbs light for a d–d promotion, and the colour seen is complementary to the principal colour absorbed.
Different ligands interact differently with the metal's d orbitals. Therefore ligand identity can change ΔE; because ΔE = hf, this changes the absorbed frequency and wavelength, so the complementary colour observed changes.
| Ligand-field change | ΔE | Absorbed f | Absorbed λ | What must be concluded about observed colour? |
|---|---|---|---|---|
| stronger splitting | increases | increases | decreases | it changes to the complement of the higher-frequency absorbed light |
| weaker splitting | decreases | decreases | increases | it changes to the complement of the lower-frequency absorbed light |
For a fair ligand comparison, keep track of metal identity, oxidation state and geometry as well as ligand identity; each can affect the splitting. A ligand exchange can change colour while the metal remains Cu(II) or Co(II).
A ligand does not transfer its own colour to the complex. The colour follows from the new metal-centred energy gap and selective absorption.
| Metal(II) / ligand change | Starting species and colour | Product / observation |
|---|---|---|
| Cu²⁺, H₂O → OH⁻ | [Cu(H₂O)₆]²⁺, blue solution | [Cu(H₂O)₄(OH)₂], pale-blue precipitate |
| Cu²⁺, H₂O → excess NH₃ | blue hexaaqua solution; pale-blue precipitate first | [Cu(NH₃)₄(H₂O)₂]²⁺, deep-blue solution |
| Cu²⁺, H₂O ⇌ Cl⁻ | blue [Cu(H₂O)₆]²⁺ | yellow [CuCl₄]²⁻; an equilibrium mixture may look green |
| Co²⁺, H₂O → OH⁻ | [Co(H₂O)₆]²⁺, pink solution | [Co(H₂O)₄(OH)₂], blue precipitate |
| Co²⁺, H₂O → NH₃ | pink hexaaqua solution | ammine species; air oxidation can subsequently alter colour and oxidation state |
| Co²⁺, H₂O ⇌ Cl⁻ | pink [Co(H₂O)₆]²⁺ | blue [CoCl₄]²⁻ |
The incoming ligand changes the ligand field and sometimes coordination geometry, changing ΔE and the light absorbed. Adding water to concentrated chloride equilibria favours the hexaaqua complex and reverses the characteristic colour shift.
Identify the actual species and conditions before naming a colour. A precipitate is a distinct complex product, and any later oxidation of a Co(II) ammine is redox rather than ligand exchange alone.
Stereoisomers have the same metal–ligand connectivity but different three-dimensional arrangements. Geometrical isomers differ by whether matching ligands are adjacent (cis) or opposite (trans); optical isomers are non-superimposable mirror images called enantiomers.
| Complex and geometry | Geometrical isomerism | Optical isomerism | Structural test |
|---|---|---|---|
| square-planar [Pt(NH₃)₂Cl₂] | cis and trans | no | Cl ligands 90° apart or 180° apart |
| octahedral [Co(NH₃)₄(H₂O)₂]²⁺ | cis and trans | no | H₂O ligands 90° apart or 180° apart |
| octahedral [Ni(en)₃]²⁺ | no cis/trans pair | yes: two enantiomers | three en chelate rings form left- and right-handed arrangements |
| octahedral [Ni(en)₂(H₂O)₂]²⁺ | cis and trans | cis form has an optical pair | cis chelate arrangement lacks a mirror plane; trans form has symmetry |
Each en ligand, H₂NCH₂CH₂NH₂, uses two nitrogen donor atoms and therefore occupies two adjacent octahedral sites. Keep the two donor atoms joined as one chelate when constructing or comparing structures.
To test a proposed pair: keep the formula and metal–ligand bonds unchanged; place all six octahedral or four square-planar sites; mark cis/trans by 90°/180° separation; for optical isomers reflect the entire chelate arrangement and check that no rotation superimposes it.
A different viewpoint or a freely rotated drawing is not a new stereoisomer. Optical activity requires non-superimposable mirror images, not merely the presence of a bidentate ligand.
Assign each metal–donor bond a dipole direction, place those vectors in the actual three-dimensional geometry, and add them. Equal opposite vectors cancel; any non-zero resultant means the complex has an overall dipole and is polar.
| Complex arrangement | Symmetry / vector result | Overall polarity |
|---|---|---|
| cis-[Pt(NH₃)₂Cl₂] | unlike bond-dipole pairs are adjacent, so they do not cancel | polar |
| trans-[Pt(NH₃)₂Cl₂] | each ligand type lies in an equal opposite pair | non-polar |
| cis-[Co(NH₃)₄(H₂O)₂]²⁺ | the two distinct H₂O directions are adjacent; resultant remains | polar |
| trans-[Co(NH₃)₄(H₂O)₂]²⁺ | opposite matching directions cancel | non-polar |
| cis-[Ni(en)₂(H₂O)₂]²⁺ optical pair | each mirror image has the same non-zero dipole magnitude, reflected in direction | polar |
| trans-[Ni(en)₂(H₂O)₂]²⁺ | symmetric opposite contributions cancel | non-polar |
| either enantiomer of [Ni(en)₃]²⁺ | three identical chelates retain a symmetric zero vector sum | non-polar |
Polarity, ionic charge and chirality answer different questions. Charge is the algebraic total on the complex; polarity is a vector resultant; chirality asks whether the mirror image is superimposable. One does not determine either of the others.
Do not apply the shortcut ‘cis polar, trans non-polar’ without inspecting all ligands and the full geometry. It works for the named matched-pair examples because of their symmetry, not as a universal naming rule.
MXz+(solv)+nL[MLXn]Xq
The stability constant, Kstab, is the equilibrium constant for forming a complex ion in a specified solvent from its constituent metal ion and ligand ions or molecules.
A larger Kstab means the formation equilibrium lies further toward the complex under the stated conditions, so the complex is thermodynamically more stable relative to the separated constituents used in that definition.
Kstab is not a rate constant. A complex can have a large formation constant yet exchange ligands slowly or quickly; equilibrium stability and kinetic inertness are different ideas.
Kstab=[M][L]n[MLn]
[Cu(HX2O)X6]X2++4NHX3[Cu(NHX3)X4(HX2O)X2]X2++4HX2O
Kstab=[Cu(HX2O)X6X2+][NHX3]4[Cu(NHX3)X4(HX2O)X2X2+]
Write the balanced formation equation first. Put the complex concentration in the numerator and each dissolved constituent concentration in the denominator, raised to its stoichiometric coefficient. Omit H₂O when water is the solvent because its activity is effectively constant.
Derive units from the final expression rather than memorising one unit. In the copper example, one concentration divided by five concentration factors gives (mol dm⁻³)⁻⁴ = dm¹² mol⁻⁴.
A coefficient becomes a power, not a multiplier in front of a concentration. Do not include [H₂O] merely because water appears in the balanced aqueous exchange equation.
[Cu(HX2O)X5Cl]X++ClX−[Cu(HX2O)X4ClX2]+HX2O
| concentration / mol dm⁻³ | [Cu(H₂O)₅Cl]⁺ | Cl⁻ | [Cu(H₂O)₄Cl₂] |
|---|---|---|---|
| initial | 0.15 | 0.15 | 0 |
| change | −0.10 | −0.10 | +0.10 |
| equilibrium | 0.05 | 0.05 | 0.10 |
Kstab=(0.05)(0.05)0.10=40 dm3 mol−1
Use the balanced coefficients to construct concentration changes, calculate every equilibrium concentration, write the expression with water omitted, substitute equilibrium—not initial—values, then derive units and interpret the magnitude.
Here Kstab = 40, so products are favoured for this step under the stated conditions, although appreciable reactant remains. A large value does not mean the equilibrium goes literally to completion.
If the supplied amounts and equilibrium value do not fit a simple one-to-one change, follow the actual stoichiometric coefficients. Reject any calculated equilibrium concentration that is negative or exceeds what atom balance permits.
MLXa+bLX′MLXb′+aL
Kexchange=Kstab(MLa)Kstab(MLb′),logKexchange=logKstab,new−logKstab,old
The ratio applies when the two overall Kstab values use the same free metal reference and consistent standard-state convention. If Kexchange is much greater than 1, the new complex is favoured under comparable ligand activities.
| Co(II) ligand environment | log₁₀ Kstab | Relative conclusion |
|---|---|---|
| chloride complex | 5.6 | less stable in this comparison |
| ammonia complex | 13.1 | more stable in this comparison |
| exchange | 13.1 − 5.6 = 7.5 | Kexchange ≈ 10⁷⋅⁵ ≈ 3.2 × 10⁷, favouring the ammonia complex |
Adding sufficient NH₃ therefore favours replacement of chloride by ammonia because formation of the ammine complex has the larger Kstab. The actual equilibrium mixture still depends on incoming and outgoing ligand concentrations through the reaction quotient.
Do not rank equilibrium concentrations from Kstab alone when ligand concentrations differ greatly. Kstab compares intrinsic equilibrium tendency under its definition; composition also reflects the amounts and activities present.