Oxidation Number & Coordination Number

CHENomenclature & Numbers

Before any bonding analysis you must pin down the metal's oxidation number and its coordination number from the formula. These two quantities drive hybridisation, geometry, magnetism and naming, so the arithmetic must be automatic.

Oxidation number

x = (\text{charge on complex ion}) - \sum(\text{charges of ligands})

x

= oxidation number of the central metal

Coordination number

\text{CN} = \sum_i (n_i \times d_i)

n_i

= number of ligands of type

i

;

d_i

= denticity (donor atoms per ligand)

Oxidation number of the metal $=$ overall charge on the complex ion $-$ (sum of ligand charges); set up $x + (\text{ligand charges}) = \text{net charge}$ and solve for $x$ .
Common ligand charges: neutral $0$ ( $H_2O$ , $NH_3$ , CO, en); $-1$ ( $Cl^-$ , $CN^-$ , $OH^-$ , $NO_2^-$ ); $-2$ (oxalato $C_2O_4^{2-}$ ).
Coordination number $=$ number of ligand donor atoms (sigma bonds to the metal), NOT the number of ligands; chelating ligands contribute more than one.
Bidentate ligands (en, oxalato) each occupy 2 coordination sites; EDTA occupies 6 — so $[Co(en)_2Cl_2]^+$ has coordination number $6$ , not $4$ .
Counter-ions outside the square brackets are NOT counted in the coordination sphere: in $[Cr(NH_3)_4Cl_2]Cl$ only the two inner $Cl$ count, giving CN $= 6$ and oxidation state $+3$ .
Worked checks: $[Fe(C_2O_4)_3]^{3-} \rightarrow$ Fe is $+3$ , CN $= 6$ ; $[Mn(CN)_6]^{4-} \rightarrow$ Mn is $+2$ , CN $= 6$ ; $[Fe(CO)_5] \rightarrow$ Fe is $0$ , CN $= 5$ .
For a neutral complex the net charge is zero, so the metal's oxidation number simply balances the ligand charges; in $[Ni(CO)_4]$ all ligands are neutral, so Ni is $0$ .
Denticity terms: monodentate (1 donor: $NH_3$ , $Cl^-$ ), bidentate (2: en, $C_2O_4^{2-}$ , glycinato), polydentate/hexadentate (EDTA, 6 donors); coordination number sums these donor atoms.
Most common coordination numbers are 6 (octahedral) and 4 (tetrahedral or square planar); 2 (linear) is rarer, as in $[Ag(NH_3)_2]^+$ and $[CuCl_2]^-$ .
To find the oxidation number when the complex is written with its counter-ions, first separate the coordination sphere (inside the brackets) from the counter-ions and use the bracketed charge.
Charges of ambidentate ligands are the same whichever end binds: $NO_2^-$ and $ONO^-$ are both $-1$ ; $SCN^-$ and $NCS^-$ are both $-1$ — the donor atom does not change the charge.
Coordination number is a property of the metal, independent of geometry: CN 4 can be tetrahedral or square planar, and CN 6 is octahedral; the number alone does not fix the shape.

Where the marks go

Equating coordination number with the number of ligands — bidentate/polydentate ligands raise CN above the ligand count (en counts as 2, EDTA as 6).
Including counter-ions (the species outside the brackets) when computing the oxidation number or coordination number.
Giving a ligand the wrong charge: $NH_3$ , $H_2O$ , CO and en are neutral (0), while $CN^-$ , $Cl^-$ , $OH^-$ , $NO_2^-$ are $-1$ and oxalato is $-2$ .
Forgetting that CN counts donor atoms (sigma bonds), so an octahedral complex always has CN 6 regardless of ligand type — a polydentate ligand contributes several of those bonds.
Assuming CN 4 implies tetrahedral geometry — CN fixes the number of bonds, not the shape (square-planar complexes are also CN 4).

How the board asks it

Numericalthe oxidation-number balance $x + (\text{ligand charges}) = \text{net charge}$
Calculate the oxidation number of the central metal atom and state the coordination number in $[Cr(NH_3)_4Cl_2]Cl$ and in $K_4[Fe(CN)_6]$ .
Identify / classifycommon ligand charges and counter-ion exclusion from the coordination sphere
For $[Pt(NH_3)_2Cl_2]$ and $[Ag(NH_3)_2]Cl$ , identify in each case the oxidation state of the metal, the coordination number, and the species acting as counter-ion.
Give reasonschelating ligands contribute more than one donor atom
Account for the fact that $[Co(en)_2Cl_2]^+$ has a coordination number of $6$ and not $4$ , even though it contains only four ligands.
Define / statecoordination number as the count of donor atoms sigma-bonded to the metal
Define the term coordination number of a central metal atom, and state the coordination number of cobalt in $[Co(en)_2Cl_2]^+$ .
Assertion–Reasoncoordination number is independent of geometry
Assertion: A complex with coordination number $4$ must be tetrahedral. Reason: The coordination number fixes the number of metal-ligand bonds but not the geometry. State whether the assertion and reason are true and whether the reason correctly explains the assertion.

Practise this topic

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Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.