Coordination Compounds Formula Sheet — JEE Main Chemistry

Every key Coordination Compounds formula, definition and theorem for JEE Main Chemistry in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 12 sub-topics

Introduction to coordination compounds
Werner's theory
Ligands
Coordination number
Denticity
Chelation
IUPAC nomenclature of mononuclear coordination compounds
Isomerism
Bonding: Valence bond approach
Basic ideas of Crystal field theory
Colour and magnetic properties
Importance of coordination compounds

Werner's Theory & Key Terms

Coordination compound: A compound containing a

coordination entity

— a central metal atom/ion bonded to a fixed number of ions or neutral molecules (ligands) that

retains its identity

even in solution, e.g.

K_{4} [Fe (CN)_{6}]

gives

K^{+}

and

[Fe (CN)_{6}]^{4 -}

, not free

F e^{2 +}

and

C N^{-}

Annotated structure of hexaamminecobalt(III) chloride: a central Co atom bonded to six NH3 ligands inside the coordination sphere (square brackets, charge 3+), with three chloride counter ions outside; coordination number 6, oxidation number of cobalt +3. — Anatomy of $[Co (N H_{3})_{6}] C l_{3}$ : $Co$ and its six $N H_{3}$ ligands form the complex ion $[Co (N H_{3})_{6}]^{3 +}$ (the coordination sphere, written inside $[]$ ); the three $C l^{-}$ outside are counter ions. CN $= 6$ , oxidation number of Co $= + 3$ .

★ Remember · Werner's two valences

Primary valence

= oxidation number; ionisable, satisfied by

anions

(the counter ions).

Secondary valence

= coordination number; non-ionisable,

fixed and directional

, satisfied by ligands inside the square bracket.

🎯 Exam · Double salt vs complex

double salt

(e.g. Mohr's salt

FeS O_{4} \cdot (N H_{4})_{2} S O_{4} \cdot 6 H_{2} O

, alum) dissociates

completely

into simple ions in water. A

complex

keeps its coordination ion intact — that is the key difference.

Core vocabulary

▸ $Central atom$ accepts electron pairs ⇒ a $Lewis acid$ ; the ligand is the donor (Lewis base).
▸ $Coordination number (CN)$ = number of ligand donor atoms σ-bonded to the metal (π bonds not counted).
▸ $Coordination sphere$ = metal + ligands inside $[]$ ; ions outside are $counter ions$ .
▸ $Oxidation number$ = charge on metal if every ligand (with its shared pair) is removed; shown as a Roman numeral.
▸ $Shape$ is fixed by CN: CN $2 \to$ linear, CN $4 \to$ tetrahedral or square planar, CN $6 \to$ octahedral (the commonest).

Homoleptic vs heteroleptic

▸ $Homoleptic$ : one kind of ligand, e.g. $[Co (N H_{3})_{6}]^{3 +}$ .
▸ $Heteroleptic$ : more than one kind, e.g. $[Co (N H_{3})_{4} C l_{2}]^{+}$ — these can show geometrical isomerism (Page 4).

🚫 Examiner Trap · Examiner traps

(1)

Primary valence

=

oxidation number (ionisable, anions outside);

secondary valence

=

coordination number (fixed, directional, ligands inside

[]

). (2) A

double salt

dissociates fully; a

complex

keeps its ion intact. (3) CN counts

σ

-bonded

donor atoms

(

π

not counted). (4) Central atom

=

Lewis acid (acceptor), ligand

=

Lewis base (donor).

Ligands, Denticity & Chelation

Ligand & denticity: A

ligand

is an ion/molecule that donates a lone pair to the central atom.

Denticity

is the number of donor atoms a single ligand actually uses to bind the metal.

Unidentate

C l^{-}, H_{2} O, N H_{3}, C N^{-}

— 1 donor

Didentate

en,

C_{2} O_{4}^{2 -}

(ox) — 2 donors

Hexadentate

EDT A^{4 -}

— 2 N

+

4 O donors

🎯 Exam · Ambidentate ligands

Can attach through

either

of two donor atoms:

N O_{2}^{-}

binds via N (

nitrito-N

- N O_{2}

) or via O (

nitrito-O

- ONO

);

SC N^{-}

via S (

thiocyanato

) or N (

isothiocyanato

- NCS

). They cause linkage isomerism (Page 4).

★ Remember · Chelate effect

A di-/polydentate ligand that grips the metal through two or more donor atoms forms a

ring

(a chelate). Chelate complexes are

more stable

than similar ones with unidentate ligands — e.g.

[Ni (en)_{3}]^{2 +}

is more stable than

[Ni (N H_{3})_{6}]^{2 +}

Counting coordination number

▸CN counts $donor atoms$ , not ligands: in $[Fe (C_{2} O_{4})_{3}]^{3 -}$ and $[Co (en)_{3}]^{3 +}$ , CN $= 6$ (each didentate ligand donates twice).
▸ $[PtC l_{6}]^{2 -}$ : CN $= 6$ ; $[Ni (N H_{3})_{4}]^{2 +}$ : CN $= 4$ .
▸5- and 6-membered chelate rings are the most stable.

🚫 Examiner Trap · Examiner traps

(1) CN counts

donor atoms

, not ligands:

[Co (en)_{3}]^{3 +}

has CN

= 6

(en is didentate). (2)

Ambidentate

ligands bind via either of two atoms (NO

_{2}^{-}

: N

=

nitrito-N, O

=

nitrito-O; SCN

^{-}

: S vs N). (3)

Chelate effect

: ring-forming polydentate ligands give extra stability. (4) 5- and 6-membered chelate rings are the most stable.

IUPAC Nomenclature

Writing the formula

▸ $Central atom first$ , then ligands in $alphabetical$ order (charge does not matter).
▸Enclose the whole entity in square brackets; polyatomic/abbreviated ligands in parentheses, e.g. $[Co (en)_{2} C l_{2}]^{+}$ .
▸Net charge is written as a right superscript outside the bracket.

Naming the complex

▸ $Cation named first$ (whether complex or simple), then the anion.
▸Within the entity, $ligands alphabetical before the metal$ (reverse of the formula order).
▸Anionic ligands end in $-o / -ido$ ( $C l^{-} =$ chlorido, $C N^{-} =$ cyanido, $O H^{-} =$ hydroxido); neutral: $H_{2} O =$ aqua, $N H_{3} =$ ammine, $CO =$ carbonyl, $NO =$ nitrosyl.
▸Oxidation number of the metal in $Roman numerals$ in parentheses, no space.

🎯 Exam · Prefixes & anionic complexes

Use

di, tri, tetra

for simple ligands;

bis, tris, tetrakis

(with the ligand in parentheses) when the ligand name already contains di/tri, e.g. bis(ethane-1,2-diamine). If the

complex ion is an anion

, the metal ends in

-ate

: ferrate (Fe), cuprate (Cu), cobaltate, zincate, argentate, aluminate.

[Cr (N H_{3})_{3} (H_{2} O)_{3}] C l_{3}

triamminetriaquachromium(III) chloride

[Co (en)_{3}]_{2} (S O_{4})_{3}

tris(ethane-1,2-diamine)cobalt(III) sulphate

K_{3} [Fe (C_{2} O_{4})_{3}]

potassium trioxalatoferrate(III)

[Ni (CO)_{4}]

tetracarbonylnickel(0)

⚠️ Watch out · Common slips

Order ligands alphabetically by ligand

name

, ignoring the multiplying prefix (di-/tri-). Never write the number of cations/anions for an ionic compound — 'cobalt(III) sulphate', not 'dicobalt tris-sulphate'.

🚫 Examiner Trap · Examiner traps

(1) FORMULA: central atom first, ligands alphabetical; NAME: ligands alphabetical

before

the metal (opposite order). (2) Anionic ligands end

-o/-ido

(chlorido, cyanido); if the complex ION is an anion the metal ends

-ate

(ferrate, cuprate). (3) Use bis/tris/tetrakis when the ligand name already has di/tri (en). (4) Alphabetise by ligand NAME, ignoring the multiplier prefix.

Isomerism in Coordination Compounds

Stereoisomers of complexes: cis/trans square-planar pairs and non-superimposable optical isomers.

★ Remember · Geometrical (cis / trans, fac / mer)

Arises in heteroleptic complexes. Square-planar

[M X_{2} L_{2}]

and octahedral

[M X_{2} L_{4}]

show

cis

(adjacent) and

trans

(opposite).

[M a_{3} b_{3}]

shows

fac

(3 on one face) and

mer

(3 on a meridian).

Tetrahedral

complexes show

no

geometrical isomerism.

🎯 Exam · Optical (d / l enantiomers)

Non-superimposable

mirror images

that rotate plane-polarised light — d (right) and l (left). Common in octahedral chelates:

[Co (en)_{3}]^{3 +}

is chiral; for

[PtC l_{2} (en)_{2}]^{2 +}

only the

cis

isomer is optically active (trans has a plane of symmetry).

Structural isomerism: Isomers with the

same formula but different bonds/connectivity

— four standard types in coordination chemistry.

Ionisation

[Co (N H_{3})_{5} S O_{4}] Br

[Co (N H_{3})_{5} Br] S O_{4}

Linkage

- N O_{2}

(yellow) /

- ONO

(red), ambidentate

Coordination

[Co (N H_{3})_{6}] [Cr (CN)_{6}]

[Cr (N H_{3})_{6}] [Co (CN)_{6}]

Solvate / hydrate

[Cr (H_{2} O)_{6}] C l_{3}

[Cr (H_{2} O)_{5} Cl] C l_{2} \cdot H_{2} O

How to tell them apart

▸ $Ionisation$ : counter ion and a ligand swap ⇒ different ions in solution (test with $BaC l_{2}$ / $AgN O_{3}$ ).
▸ $Linkage$ : same ambidentate ligand, different donor atom.
▸ $Solvate$ : water inside the sphere vs free in the lattice.

🚫 Examiner Trap · Examiner traps

(1)

Tetrahedral

complexes show NO geometrical isomerism. (2) cis/trans for

[M X_{2} L_{2}]

(sq planar) and

[M X_{2} L_{4}]

; fac/mer for

[M a_{3} b_{3}]

. (3) Optical: only the

cis

isomer of

[PtC l_{2} (en)_{2}]^{2 +}

is active (trans has a symmetry plane). (4) Ionisation isomers give DIFFERENT ions in solution (test with AgN

O_{3}

/BaC

l_{2}

Valence Bond Theory (VBT)

VBT of complexes: The metal ion provides

hybrid orbitals

(mixing

(n - 1) d

, ns, np, nd) of a definite geometry; each accepts a

lone pair

from a ligand to form a coordinate bond. The hybridisation fixes the shape.

Orbital box diagrams contrasting the inner-orbital low-spin d2sp3 hexaamminecobalt(III) ion with the outer-orbital high-spin sp3d2 hexafluorocobaltate(III) ion, plus a table mapping coordination number and hybridisation to geometry — Inner ( $d^{2} s p^{3}$ ) vs outer ( $s p^{3} d^{2}$ ) orbital octahedral complexes.

CN	Hybridisation	Geometry	Example
4	$s p^{3}$	tetrahedral	$[NiC l_{4}]^{2 -}$ , $[Ni (CO)_{4}]$
4	$dsp^{2}$	square planar	$[Ni (CN)_{4}]^{2 -}$ , $[PtC l_{4}]^{2 -}$
5	$s p^{3} d$	trig. bipyramidal	$[Fe (CO)_{5}]$
6	$d^{2} s p^{3}$ / $s p^{3} d^{2}$	octahedral	inner / outer orbital

🎯 Exam · Inner vs outer orbital

Inner orbital

(

d^{2} s p^{3}

, uses inner

(n - 1) d

): strong-field ligand pairs electrons ⇒

low spin

, e.g.

[Co (N H_{3})_{6}]^{3 +}

(diamagnetic).

Outer orbital

(

s p^{3} d^{2}

, uses outer nd): weak-field ligand keeps electrons unpaired ⇒

high spin

, e.g.

[Co F_{6}]^{3 -}

(4 unpaired).

Spin-only magnetic moment

μ = n (n + 2) BM

n =

unpaired electrons. Measured

μ

reveals the hybridisation and geometry.

Standard CN-4 cases

▸ $[NiC l_{4}]^{2 -}$ : $s p^{3}$ , $tetrahedral$ , paramagnetic (2 unpaired).
▸ $[Ni (CN)_{4}]^{2 -}$ : $dsp^{2}$ , $square planar$ , diamagnetic (strong-field $C N^{-}$ pairs the $d^{8}$ ).
▸ $[Ni (CO)_{4}]$ : $s p^{3}$ , tetrahedral, diamagnetic (Ni in zero state, $3 d^{10}$ ).

⚠️ Watch out · Limitations of VBT

It does

not

explain colour, give quantitative magnetic data, predict tetrahedral vs square-planar reliably, or distinguish strong- and weak-field ligands — that needs Crystal Field Theory (Page 6).

🚫 Examiner Trap · Examiner traps

(1)

Inner-orbital

d^{2} s p^{3}

(uses

(n - 1) d

)

=

low spin;

outer-orbital

s p^{3} d^{2}

(uses nd)

=

high spin. (2)

μ = n (n + 2)

counts unpaired electrons. (3)

[NiC l_{4}]^{2 -}

s p^{3}

tetrahedral (paramagnetic) but

[Ni (CN)_{4}]^{2 -}

dsp^{2}

square planar (diamagnetic). (4) VBT can't explain colour or strong/weak-field — use CFT.

Crystal Field Theory (CFT)

Crystal Field Theory: An

electrostatic

model: ligands are point negative charges/dipoles. Their field lifts the degeneracy of the five d orbitals — orbitals pointing

at

the ligands are raised, those pointing

between

them are lowered.

Octahedral

e_{g} ↑ + \frac{3}{5} Δ_{o}

t_{2 g} ↓ - \frac{2}{5} Δ_{o}

Tetrahedral

inverted (e low,

t_{2}

high),

Δ_{t} = \frac{4}{9} Δ_{o}

★ Remember · Spectrochemical series

Ligands by increasing field strength:

I^{-} < B r^{-} < SC N^{-} < C l^{-} < F^{-} < O H^{-} < C_{2} O_{4}^{2 -} < H_{2} O < N H_{3} < en < C N^{-} < CO

. Left = weak-field; right = strong-field.

d6 electron filling under a weak field giving high spin t2g4 eg2 with 4 unpaired electrons versus a strong field giving low spin t2g6 with zero unpaired, plus a colour wheel showing observed colour as the complement of the absorbed light — $d^{6}$ high-spin vs low-spin filling; colour as the complement of absorbed light.

🎯 Exam · High spin vs low spin

Compare

Δ_{o}

with the pairing energy P. If

Δ_{o} < P

(weak field) the 4th d electron enters

e_{g}

⇒

high spin

. If

Δ_{o} > P

(strong field) it pairs in

t_{2 g}

⇒

low spin

. Tetrahedral

Δ_{t}

is small, so tetrahedral complexes are

almost always high spin

Worked spin counts (

d^{6}

, octahedral)

▸Weak field ( $[Co F_{6}]^{3 -}$ , $[Fe (H_{2} O)_{6}]^{2 +}$ ): $t_{2 g}^{4} e_{g}^{2}$ , 4 unpaired ⇒ paramagnetic.
▸Strong field ( $[Co (N H_{3})_{6}]^{3 +}$ , $[Fe (CN)_{6}]^{4 -}$ ): $t_{2 g}^{6} e_{g}^{0}$ , 0 unpaired ⇒ diamagnetic.

🚫 Examiner Trap · Examiner traps

(1) Octahedral:

e_{g}

UP (

+ \frac{3}{5} Δ_{o}

t_{2 g}

DOWN; tetrahedral is INVERTED with

Δ_{t} = \frac{4}{9} Δ_{o}

(small). (2) High vs low spin: compare

Δ_{o}

with pairing energy P — strong field (

Δ_{o} > P

)

=

low spin. (3) Tetrahedral complexes are

almost always high spin

. (4) Spectrochemical series: CO/CN

^{-}

/en strong, I

^{-}

/Br

^{-}

weak — memorise the order.

Colour, Carbonyls, Stability & Applications

Colour of complexes: A partially filled d ion absorbs visible light to promote an electron

t_{2 g} \to e_{g}

(

d-d transition

); the complex shows the

complementary

colour.

[Ti (H_{2} O)_{6}]^{3 +}

(

d^{1}

) absorbs ~498 nm and looks violet;

d^{0}

d^{10}

ions are colourless.

🎯 Exam · Ligand changes the colour

A stronger-field ligand widens

Δ_{o}

, shifting absorption:

[Ni (H_{2} O)_{6}]^{2 +}

(green) →

[Ni (H_{2} O)_{2} (en)_{2}]^{2 +}

(blue/purple) →

[Ni (en)_{3}]^{2 +}

(violet) as

H_{2} O

is replaced by en.

Synergic bonding in metal carbonyls: sigma donation CrightarrowM plus pi back-donation MrightarrowCO. — Synergic bonding in metal carbonyls: $σ$ donation C $\to$ M plus $π$ back-donation M $\to$ CO.

Carbonyl	Shape
$[Ni (CO)_{4}]$	tetrahedral
$[Fe (CO)_{5}]$	trig. bipyramidal
$[Cr (CO)_{6}]$	octahedral
$[M n_{2} (CO)_{10}]$	Mn–Mn bond
$[C o_{2} (CO)_{8}]$	2 bridging CO

★ Remember · Synergic bonding in carbonyls

Two reinforcing parts: a

σ

-bond (C lone pair

\to

empty metal orbital) and a

π

back-bond (filled metal d

\to

empty CO

π^{*}

). They strengthen M–C and weaken C–O. Metal is in a

low/zero

oxidation state, e.g.

[Ni (CO)_{4}]

[Fe (CO)_{5}]

[Cr (CO)_{6}]

Stability (formation) constant

M + 4 L ⇌ M L_{4}, β_{4} = \frac{[ M L _{4} ]}{[ M ] [ L ] ^{4}} = K_{1} K_{2} K_{3} K_{4}

Larger

β

⇒ more stable complex; instability constant

= 1/ β

What raises stability

▸ $Higher metal charge$ , smaller size, and stronger-field ligands.
▸The $chelate effect$ : ring-forming polydentate ligands give very large $β$ .
▸Stepwise constants usually decrease: $K_{1} > K_{2} > K_{3} > K_{4}$ .

Applications

▸ $Analysis$ : EDTA, DMG (dimethylglyoxime) for estimating metal ions; $N a_{2} EDTA$ for water hardness ( $C a^{2 +} /M g^{2 +}$ ).
▸ $Extraction$ : gold/silver via $[Au (CN)_{2}]^{-}$ ; $purification$ : Mond process, $[Ni (CO)_{4}]$ .
▸ $Biology$ : chlorophyll (Mg), haemoglobin (Fe), vitamin $B_{12}$ (Co); medicine: cisplatin.

🚫 Examiner Trap · Examiner traps

(1) Colour is from a

t_{2 g} \to e_{g}

d-d transition

; the observed colour is the COMPLEMENT of the absorbed;

d^{0}

d^{10}

are colourless. (2) Stronger-field ligand

\Rightarrow

larger

Δ_{o}

\Rightarrow

absorbs shorter

λ

. (3)

Synergic

M–CO:

σ

\to

+

π

back-bond (M

\to

π^{*}

); metal in low/zero state. (4)

β_{n} = K_{1} K_{2} \dots K_{n}

; chelates give very large

β

(more stable).

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Frequently Asked Questions

What are the most important Coordination Compounds formulas for JEE Main?

This Coordination Compounds formula sheet covers all the high-yield Chemistry formulas, definitions and theorems you need for JEE Main, across Introduction to coordination compounds, Werner's theory, Ligands, Coordination number, Denticity — each shown with the key result and, where useful, a worked example.

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How should I revise Coordination Compounds formulas?

Blurt the Coordination Compounds formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

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