28.2 Chemical properties of first-row transition elements

Learning objectives

28.2.1Ligand reactions forming complexes• Describe/explain: the reactions of transition elements with ligands to form complexes, incl. complexes of copper(II) and cobalt(II) ions with water and ammonia molecules and hydroxide and chloride ions 28.2.2Terms: ligand as a species that contains• Define: ligand as a species that contains a lone pair of electrons that forms a dative covalent bond to a central metal atom / ion 28.2.3Terms• Use terms:: (a) monodentate ligand e.g. H2O, NH3, Cl – and CN–; (b) bidentate ligand e.g. 1,2-diaminoethane, en, H2NCH2CH2NH2, and the ethanedioate ion, C2O4; 2–; (c) polydentate ligand including as an example EDTA4–28.2.4Complex ions• Define: complex as a molecule or ion formed by a central metal atom / ion surrounded by one or more ligands 28.2.5Shapes of transition metal complexes• Describe the geometry (shape and bond angles) of transition element complexes which are linear, square planar, tetrahedral or octahedral 28.2.6Coordination number and complex formula• The ligand and its coordination number or geometry: (a) state what is meant by coordination number; (b) predict the formula and charge of a complex ion, given the metal ion, its charge or oxidation state,28.2.7Ligand exchange reactions• Explain qualitatively that ligand exchange can occur, incl. complexes of copper( II) ions and cobalt(II) ions with water and ammonia molecules and hydroxide and chloride ions 28.2.8Predict, using E• Predict, using E ⦵ values, the feasibility of redox reactions involving transition elements and their ions 28.2.9Transition metal redox calculations• Describe the reactions of, and perform calculations involving:: (a) MnO 4 – / C2O4; 2– in acid solution given suitable data; (b) MnO 4 – / Fe2+ in acid solution given suitable data; (c) Cu 2+ / I– given suitable data 28.2.10Calculations: other redox systems• Calculate: other redox systems given suitable data

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.

$\ce{[M(H2O)6]^2+ + 2OH- -> [M(H2O)4(OH)2](s) + 2H2O}\quad(M=Cu,Co)$

$\ce{[Cu(H2O)6]^2+ + 4NH3 <=> [Cu(NH3)4(H2O)2]^2+ + 4H2O}$

$\ce{[M(H2O)6]^2+ + 4Cl- <=> [MCl4]^2- + 6H2O}\quad(M=Cu,Co)$

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.

$E^\circ_{cell}=E^\circ_{reduction}-E^\circ_{oxidation}$

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.

$\ce{2MnO4- + 5C2O4^2- + 16H+ -> 2Mn^2+ + 10CO2 + 8H2O}$

$\ce{MnO4- + 5Fe^2+ + 8H+ -> Mn^2+ + 5Fe^3+ + 4H2O}$

$\ce{2Cu^2+ + 4I- -> 2CuI(s) + I2}$

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.

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—28.3 Colour of complexesRead

28.2 Chemical properties of first-row transition elements

Learning objectives

Cu(II) and Co(II) form predictable complexes with common ligands

A ligand donates a lone pair to a central metal atom or ion

Denticity counts donor atoms used by one ligand

A complex is a metal centre surrounded by coordinated ligands

Complex geometry links coordination sites to characteristic bond angles

Coordination number and charge construct a complex formula

Ligand exchange replaces coordinated species without necessarily causing redox

A positive E°cell predicts a feasible standard redox direction

Three required redox systems have fixed half-equation mole ratios

Unfamiliar redox calculations use one conservation workflow

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