Descriptive, Organic, and Nuclear Chemistry

This is Unit Twelve of Chemistry, Part Three: transition metals and coordination compounds. Parts One and Two read the periodic table's two edges — the reactive metals and the nonmetals — and closed on a capstone predicting an element's chemistry from position alone. This part turns to the block in the middle, where that approach stops being sufficient. Transition metals are defined by partially filled d orbitals, and the consequences of those orbitals are what this part is about: multiple oxidation states rather than one, compounds built by accepting electron pairs from surrounding molecules, more kinds of isomerism than a simple formula can distinguish, and colour. The single idea holding the second half together is that ligands change the energies of a metal's d orbitals, and how much they change them decides both how the electrons arrange themselves and what colour the compound is. By the end you will be able to say what defines a transition metal and why group twelve falls outside the strict definition; determine a ligand's denticity by counting the right thing; name a coordination compound and find the metal's oxidation state from its charge; say what decides whether a complex is high-spin or low-spin; and say why some complexes are coloured and others are not.

Three entries. A definition that rests on orbital occupancy rather than position, and which excludes one group people usually include. Then two trends about oxidation states that look similar and answer different questions — one runs across a period, the other down a group.

Partially filled d.

Chem 2372 Transition Metals Defined by Partially Filled d Orbitals

A transition metal has, or readily forms ions with, a partially filled set of d orbitals — which among the d-block covers groups three through eleven. Iron qualifies: its configuration leaves the d orbitals partly filled. Group twelve does not, on the strict definition. It fills its d orbitals completely and loses only s electrons when it ionises, which places it with the representative metals despite being grouped informally with the rest.

Most in the middle.

Chem 2375 Multiple Oxidation States Peak Mid-First-Series

Across the first transition series the number of available oxidation states rises toward the middle and falls off at both ends, because later members hold their d electrons more stably. Manganese, near the middle, runs from two plus through seven plus — far more than scandium or copper at the ends. Having one fixed oxidation state is not what transition metal means; this variability is the group's defining signature.

Further down, higher up.

Chem 2378 Heavier d-Block Series Favor Higher Oxidation States

Second and third series elements are more stable in higher oxidation states than their first-series counterparts, because larger atomic radii make the outer electrons easier to remove. Molybdenum and tungsten sit below chromium and are largely limited to six plus in solution, where chromium favours the more stable three plus. This is a trend down a group, and the previous entry's was a trend across a period — they answer different questions.

Four entries building the central object of this part. A coordination compound is a Lewis acid–base adduct, which is Unit Ten's framework applied to a metal ion: the metal accepts electron pairs, the surrounding molecules donate them. Then what the number of those donors decides about shape, how to count them properly, and the naming procedure — which is worth more than it looks, because working out the name is how you work out the metal's oxidation state.

Donated, not shared equally.

Chem 2381 Coordination Compounds as Lewis Acid-Base Adducts

A coordination compound forms when a central metal ion acts as a Lewis acid and accepts electron pairs donated by ligands acting as Lewis bases. In the hexaamminecobalt ion, six ammonia molecules each donate a nitrogen lone pair to the cobalt centre. These are genuine bonds — the term coordinate covalent describes where the electrons came from originally, not any weakness in the bond itself.

Count the donors.

Chem 2384 Coordination Number Sets Complex Geometry

A complex's coordination number is the count of donor atoms bonded to the central metal, and it sets the geometry: two gives linear, four gives tetrahedral or square planar, six gives octahedral. The diamminesilver ion is linear; the hexaaquacobalt ion is octahedral. Unlike VSEPR, nonbonding d electrons do not distort the shape here — coordination number alone predicts how the donor atoms arrange.

One donor, or several.

Chem 2387 Monodentate vs. Polydentate Ligands

A monodentate ligand bonds through a single donor atom; a polydentate, or chelating, ligand bonds through two or more donor atoms at once. Chloride is monodentate. Ethylenediamine has two donor nitrogens and is bidentate. What settles denticity is the number of donor atoms and not the size of the molecule — a large ligand with one donor atom is monodentate however many atoms it contains.

The name gives the oxidation state.

Chem 2390 Naming a Coordination Compound

Name the ligands alphabetically with multiplying prefixes, then the metal, then a Roman numeral for its oxidation state — and add the suffix -ate to the metal's name if the complex is an anion. The oxidation state comes from balancing: the ligand charges inside the brackets against the coordination sphere's overall charge. In tetraaquadichlorochromium chloride, the sphere carries one plus, four waters are neutral and two chlorides are one minus each, so chromium is three plus. The chloride sitting outside the brackets plays no part in that balance — including it gives an oxidation state the complex's charge will not support.

Two entries on complexes that share a formula and are nonetheless different compounds. The first kind you can tell apart by looking — the isomers differ in colour and polarity. The second kind you cannot: the two forms are nearly identical in every ordinary physical property and differ only in how they interact with polarised light and with other handed molecules.

Adjacent, or opposite.

Chem 2394 Geometric Isomerism in Complexes

Geometric isomers carry the same ligands on the same metal and differ in how those ligands are arranged: cis places like ligands adjacent, trans places them opposite. A tetraamminedichlorocobalt ion has its two chlorides adjacent in the cis form and across the octahedron in the trans. These are different compounds with different properties — different colour, different polarity — not one compound drawn two ways.

Left hand, right hand.

Chem 2397 Optical Isomerism (Enantiomers)

Optical isomers, or enantiomers, are nonsuperimposable mirror images — related as a left hand is to a right hand. The tris-ethylenediamine cobalt ion exists as such a pair. Unlike geometric isomers they share nearly identical melting point, boiling point and solubility, so ordinary measurements will not separate them; what distinguishes them is their interaction with polarised light and with other chiral molecules.

Four entries, and this is the mechanism the second half of the part rests on. When ligands approach a metal ion, they raise the energies of the d orbitals pointing at them more than the ones pointing between them, so a set that was all one energy separates into two levels. How wide that separation is depends on the ligand — and the width decides how the electrons distribute themselves. The registered twin here names the two possible outcomes.

Pointing at, or between.

Chem 2400 Crystal Field Splitting in an Octahedral Complex

In an octahedral complex, the ligands' electron pairs raise the two d orbitals that point directly at them above the three that point between them — the crystal field splitting. Iron's five equal-energy d orbitals separate into a higher pair and a lower trio once ligands coordinate around it. The orbitals do not merge or disappear: what changes is their energies, not how many there are.

Which ligand, and how much.

Chem 2403 The Spectrochemical Series: Weak- vs. Strong-Field Ligands

The spectrochemical series ranks ligands by how large a crystal field splitting they produce, from weak-field ligands that separate the levels slightly to strong-field ligands that separate them widely. Cyanide is strong-field and produces a much larger splitting than iodide, which is weak-field. A ligand's place in that ranking follows from its own electronic character, not from the identity or charge of the metal it happens to bond to.

Spread out first.

Chem 2406 Twin: The High-Spin Complex

A high-spin complex forms when the splitting is small enough that electrons occupy every d orbital singly before any of them pair up, which maximises the number of unpaired electrons. The hexaaquairon two-plus ion, with water as a weak-field ligand, is high-spin and carries four unpaired electrons out of six. High-spin is not a description of the metal — the same ion is high-spin with one ligand and low-spin with another, because the ligand sets the splitting.

Pair up instead.

Chem 2409 Twin: The Low-Spin Complex

A low-spin complex forms when the splitting is large enough that pairing two electrons in a lower orbital costs less energy than promoting one to the upper level — which minimises unpaired electrons. The hexacyanoferrate two-minus ion, with strong-field cyanide, is low-spin and carries none unpaired out of six. The comparison that shows what is varying is the same metal with a different ligand, not a different metal.

Two entries closing the part. Transition metal complexes are the coloured compounds of inorganic chemistry, and the splitting from the previous topic is why — the gap between those two d levels is exactly the sort of energy that visible light carries. Then the capstone, which takes one complex and answers four separate questions about it from a single fact: which ligand it has.

A jump the size of visible light.

Chem 2412 Complex Color from d-d Electron Transitions

A complex is coloured when an electron absorbs visible light to jump between d orbitals, and the colour you see is complementary to the light absorbed — a complex absorbing mostly red appears green, as many chromium three-plus complexes do. A metal ion with an empty or a completely filled d subshell has no such transition available, so scandium three-plus and zinc two-plus complexes are colourless.

Four answers, one ligand.

Chem 2417 Capstone: Full Analysis of a Coordination Complex

Hexacyanoferrate three-minus. Balancing charge, six cyanides at one minus each against a sphere at three minus makes iron three plus, and because the complex is an anion the name takes the -ate ending. No geometric isomerism is possible, because all six ligands are identical and cis-trans needs at least two different ligand types. Cyanide is strong-field, so a large splitting is predicted; iron three plus has five d electrons, and a large splitting favours pairing them low rather than promoting one, predicting a low-spin complex with one unpaired electron. That same large gap shifts absorption toward higher-energy light. One honest qualification: this particular ion's intense colour also involves charge-transfer absorption beyond the simple d–d picture, so colour follows the splitting direction more loosely than the other three answers do. And none of this makes iron three plus low-spin in general — swapping cyanide for fluoride around the same centre would predict high-spin.

Five things to carry out of this part. A transition metal is one with, or readily forming ions with, a partially filled set of d orbitals — groups three through eleven of the d-block. Group twelve falls outside the strict definition, because it fills its d orbitals completely and loses only s electrons on ionising, whatever the informal grouping suggests. A ligand's denticity is set by how many donor atoms it bonds through, not by how large the molecule is: chloride is monodentate, ethylenediamine with two donor nitrogens is bidentate, and a large ligand with a single donor atom is still monodentate. Naming a coordination compound gives you the metal's oxidation state as a by-product, because you get it by balancing the charges of the ligands inside the brackets against the coordination sphere's overall charge — and anything written outside those brackets plays no part in that balance. Whether a complex is high-spin or low-spin is decided by the size of the crystal field splitting relative to the cost of pairing electrons, and the splitting size is set by the ligand rather than the metal: a small splitting spreads electrons out singly and gives high spin, a large one pairs them low and gives low spin, and the same metal ion gives either answer depending on what surrounds it. And a complex is coloured when an electron can absorb visible light to jump between those split d levels, which is why a metal ion with an empty or a full d subshell has no transition available and its complexes are colourless. Part Four takes up organic chemistry.