Transition Metals and Coordination Compounds

Transition metals are characterized by accessible d orbitals, variable oxidation states, colored compounds, magnetic behavior, and complex-ion formation. Coordination chemistry treats metal ions as Lewis acids surrounded by ligands that donate electron pairs.

In the Ebbing and Gammon sequence this topic sits near periodic trends in transition elements, chemistry of selected transition elements, complex formation, coordination compound naming, isomerism, valence bond theory of complexes, and crystal field theory. That placement matters because general chemistry is cumulative: a later calculation usually reuses earlier ideas about measurement, atomic structure, bonding, molecular motion, or equilibrium. The aim of this page is to turn the chapter-level ideas into a working reference that can be used for problem solving without copying the textbook's wording or examples.

Definitions

The following definitions give the vocabulary and notation used in this page. Treat them as operational definitions: each one says what can be counted, measured, compared, or conserved in a chemical argument.

Transition element forms at least one ion with partially filled d subshell.
Coordination compound contains a complex ion or neutral complex with ligands bound to a metal center.
Ligand is a Lewis base that donates an electron pair to a metal.
Coordination number is the number of donor atoms attached to the metal.
Chelating ligand binds through more than one donor atom.
Oxidation state is formal charge assigned to the metal after ligand charges are counted.
Crystal field splitting is energy separation of d orbitals caused by ligand environment.
High-spin and low-spin complexes differ in electron pairing depending on splitting energy and pairing energy.

Definitions in chemistry often connect a symbolic representation to a physical sample. A formula such as $\mathrm{H_2O}$ names a substance, gives the atomic ratio inside one molecule, and supplies the molar mass used in a macroscopic calculation. A state symbol such as $\mathrm{(aq)}$ is not cosmetic; it says the species is dispersed in water and may be treated as ions when writing a net ionic equation. In the same way, constants such as $R$ , $K_w$ , $F$ , or $N_A$ are compact definitions of the measurement system being used.

Key results

The central results are:

Complex charge equals metal oxidation state plus ligand charges.
Common neutral ligands include $\mathrm{H_2O}$ and $\mathrm{NH_3}$ ; common anionic ligands include $\mathrm{Cl^-}$ and $\mathrm{CN^-}$ .
Octahedral complexes split d orbitals into lower $t_{2g}$ and higher $e_g$ sets.
Tetrahedral splitting is smaller than octahedral splitting for comparable ligands.
Unpaired d electrons often produce paramagnetism.
Absorption of visible light across d-orbital splitting can produce observed color.

Coordination compounds combine acid-base bonding, geometry, naming, and electronic structure. The same metal ion can change color, magnetism, and reactivity when ligands change because ligand field strength changes d-orbital splitting and electron pairing.

A good way to use these results is to state the chemical model first, then substitute numbers second. For transition metals and coordination compounds, the model usually answers questions such as what particles are present, what is conserved, which process is idealized, and which measurement is being interpreted. Once that sentence is clear, the algebra becomes a bookkeeping problem rather than a search for a memorized pattern.

Units are part of the result, not decoration. Whenever a formula contains an empirical constant, a tabulated value, or a ratio of measured quantities, the units tell you whether the expression has been used in the intended form. This is especially important in general chemistry because several equations have nearly identical algebra but different meanings: pressure can be a measured state variable, an equilibrium correction, or a colligative effect; energy can be heat flow, enthalpy, internal energy, or free energy.

The strongest check is an independent chemical interpretation. Ask whether the sign agrees with direction, whether a concentration can be negative, whether a mole ratio follows the balanced equation, whether an equilibrium shift opposes the stress, and whether a microscopic description explains the macroscopic number. These checks connect transition metals and coordination compounds to neighboring topics instead of leaving it as an isolated technique.

A second check is to compare the limiting cases. If a reactant amount goes to zero, a product amount cannot remain large. If temperature rises in a gas sample at fixed volume, pressure should not fall in an ideal model. If an acid is diluted, hydronium concentration should normally decrease unless a coupled equilibrium supplies more. Limiting cases often reveal algebra that has been rearranged correctly but applied to the wrong chemical situation.

Finally, keep symbolic and particulate representations side by side. A balanced equation, an equilibrium expression, an orbital diagram, or a polymer repeat unit is a compact symbol for a population of particles. Translating that symbol into words forces you to say what is reacting, what is being counted, and what is being held constant. That translation is usually the difference between a calculation that can be adapted to a new problem and one that only imitates a worked example.

Visual

Octahedral crystal field sketch:

higher energy:        eg     dz2, dx2-y2
                     ----

lower energy:       t2g     dxy, dxz, dyz
                  --------

Geometry	Coordination number	Common examples	Isomerism
Linear	2	some $d^{10}$ metal ions	limited
Tetrahedral	4	$\mathrm{[ZnCl_4]^{2-}}$	optical possible
Square planar	4	many $d^8$ complexes	cis/trans
Octahedral	6	$\mathrm{[Co(NH_3)_6]^{3+}}$	cis/trans, fac/mer, optical

Worked example 1: Oxidation state and name of a coordination compound

Problem. Find the oxidation state of cobalt and name $\mathrm{[Co(NH_3)_5Cl]Cl_2}$ .

Method.

The two chloride ions outside the brackets indicate the complex ion has charge $+2$ .
Inside the complex, ammonia ligands are neutral and the coordinated chloride ligand is $-1$ .
Let cobalt oxidation state be $x$ .
Charge equation inside brackets: $x+5(0)+(-1)=+2$ .
Solve: $x=+3$ .
Name ligands alphabetically ignoring prefixes: ammine before chloro.
The cation is pentaamminechlorocobalt(III), followed by chloride.

Checked answer. Cobalt is +3; the compound is pentaamminechlorocobalt(III) chloride. The complex cation at +2 balances two external chloride anions.

The important habit is to identify the conserved quantity before reaching for an equation. In this example the units, coefficients, charges, or particles chosen in the first step control every later step. The final numerical answer is not accepted merely because it came from a formula; it is checked against the chemical picture. If the magnitude, sign, units, or limiting condition contradicts that picture, the calculation has to be restarted from the definition rather than patched at the end.

Worked example 2: Unpaired electrons in a high-spin octahedral complex

Problem. Predict the number of unpaired electrons for high-spin octahedral $\mathrm{Fe^{3+}}$ .

Method.

Neutral Fe is $\mathrm{[Ar]4s^2 3d^6}$ .
For $\mathrm{Fe^{3+}}$ , remove two 4s electrons and one 3d electron: $\mathrm{[Ar]3d^5}$ .
A high-spin octahedral complex places electrons singly before pairing as much as possible.
Five d electrons occupy the five d-related positions with parallel spins under the high-spin description.
Thus all five are unpaired.

Checked answer. High-spin octahedral $\mathrm{Fe^{3+}}$ has 5 unpaired electrons. A $d^5$ high-spin ion is maximally unpaired.

The important habit is to identify the conserved quantity before reaching for an equation. In this example the units, coefficients, charges, or particles chosen in the first step control every later step. The final numerical answer is not accepted merely because it came from a formula; it is checked against the chemical picture. If the magnitude, sign, units, or limiting condition contradicts that picture, the calculation has to be restarted from the definition rather than patched at the end.

Code

The snippet below is intentionally small, but it is runnable and mirrors the calculation style used in the worked examples. It keeps units visible in variable names so that the computation remains auditable.

def metal_oxidation_state(complex_charge, ligand_charges):
    return complex_charge - sum(ligand_charges)

co_state = metal_oxidation_state(+2, [0, 0, 0, 0, 0, -1])

def high_spin_d5_unpaired():
    electrons = 5
    orbitals = 5
    return min(electrons, orbitals)

print(co_state, high_spin_d5_unpaired())

Common pitfalls

Counting counterions as ligands. Avoid it by separating species inside and outside brackets.
Forgetting neutral ligand charges. Avoid it by memorizing common ligands such as ammine and aqua as neutral.
Naming ligands in formula order only. Avoid it by using alphabetical ligand names in coordination nomenclature.
Assuming all four-coordinate complexes are tetrahedral. Avoid it by checking metal electron count and ligand field for square planar cases.
Ignoring spin state in magnetic predictions. Avoid it by distinguishing high-spin and low-spin octahedral complexes.
Treating color as pigment only. Avoid it by linking observed color to absorbed wavelengths and d-orbital splitting.

Definitions​

Key results​

Visual​

Worked example 1: Oxidation state and name of a coordination compound​

Worked example 2: Unpaired electrons in a high-spin octahedral complex​

Code​

Common pitfalls​

Connections​