Determine the coordination number of the central metal ion in each of the following: (a) $[ ext{Co}( ext{NH}_3)_6] ext{Cl}_3$, (b) $[ ext{Ni}( ext{CO})_4]$, (c) $[ ext{PtCl}_4]^{2-}$.

Question

Determine the coordination number of the central metal ion in each of the following: (a) $[	ext{Co}(	ext{NH}_3)_6]	ext{Cl}_3$, (b) $[	ext{Ni}(	ext{CO})_4]$, (c) $[	ext{PtCl}_4]^{2-}$.

Accepted Answer

Concept understanding — Coordination Number

Coordination Number: The "How Many Neighbours" Rule

Imagine you are standing in a crowded room. The people closest to you — the ones you could touch without moving your feet — are your immediate neighbours. Now imagine that same idea, but inside a crystal. Atoms or ions don't float around randomly; they pack together in repeating patterns. The coordination number (CN) is simply the count of those immediate neighbours that touch a given atom or ion.

It answers one question: How many nearest neighbours does this particle have?

The Intuition: Packing and Touching

Think of stacking oranges at a fruit market. If you arrange them in a single flat layer, each orange touches six others around it (like a honeycomb). That's a coordination number of 6 for that layer. But if you stack a second layer on top, each orange now also touches three oranges above and three below — so the total nearest neighbours become 12. The coordination number changes depending on how the oranges are stacked.

In a crystal, the coordination number is determined by two things:

The size of the atoms/ions (can a smaller ion fit more neighbours around it?)
The geometry of the arrangement (cubic, hexagonal, etc.)

A higher coordination number means the atom is more tightly surrounded — it's "more crowded" in a sense, but also more stable energetically.

The Precise Definition

Coordination Number (CN) = The number of nearest-neighbour atoms or ions that are in direct contact with a given atom or ion in a crystal lattice.

"Nearest neighbour" means the shortest distance between centres of two particles in the lattice. These neighbours are touching — not just close, but physically adjacent.

Common Examples You Must Know

Crystal Structure	Coordination Number	Arrangement
Simple Cubic (SC)	6	One atom at each corner of a cube; neighbours are left, right, front, back, top, bottom
Body-Centred Cubic (BCC)	8	Atom at centre touches all 8 corner atoms
Face-Centred Cubic (FCC)	12	Atom at a face centre touches 4 atoms in its own face, 4 in the adjacent face, and 4 more
Hexagonal Close-Packed (HCP)	12	Similar to FCC — each atom touches 6 in its own layer, 3 above, 3 below
NaCl (rock salt)	6 (for each ion)	Each Na⁺ is surrounded by 6 Cl⁻ ions (octahedral)
CsCl	8 (for each ion)	Each Cs⁺ is surrounded by 8 Cl⁻ ions (cubic)

Watch out

Do not confuse coordination number with the number of atoms per unit cell. For example, in BCC, the unit cell contains 2 atoms, but the coordination number is 8. These are different concepts.

Why Does It Matter?

Coordination number directly affects physical properties:

Melting point: Higher CN usually means stronger bonding → higher melting point.
Density: Tighter packing (higher CN) often means denser material.
Ionic compounds: The CN tells you how ions arrange themselves to balance charges. For example, in NaCl, each Na⁺ has 6 Cl⁻ neighbours because the size ratio allows it.

Tip

To find CN from a diagram: pick one atom, count only the atoms that touch it directly. Ignore second-nearest neighbours — they are farther away and don't count.

A Quick Check for Yourself

Take a simple cubic lattice. Draw a cube with atoms at all eight corners. Pick one corner atom. How many other corner atoms touch it directly? Not the ones across the face diagonal (those are farther), not the one across the body diagonal (even farther). Only the three along the edges — but each edge is shared, so the total is 6. That's your CN.

If you got 6, you've understood the idea. If you got something else, trace the touching distances again.

Coordination number is not a formula to memorise — it is a count you derive from the geometry. Once you see the pattern, you can find it for any structure.

Coordination number is a key NCERT/CBSE Class 12 Chemistry solid state concept, and "coordination number in SCC BCC FCC and ionic crystals" is a commonly searched revision query around board exams. It's also a frequent important-question topic in JEE Main and NEET when discussing NaCl and CsCl-type ionic structures.

The coordination number equals the total number of donor atoms bonded to the central metal. All three complexes here contain only monodentate ligands, so the coordination number simply equals the number of ligand molecules/ions present. (a) $[\text{Co}(\text{NH}_3)_6]^{3+}$ has six separate $\text{NH}_3$ molecules, each donating through its single nitrogen atom: $\text{CN} = 6$ . (b) $[\text{Ni}(\text{CO})_4]$ has four $\text{CO}$ molecules, each donating through its single carbon atom: $\text{CN} = 4$ . (c) $[\text{PtCl}_4]^{2-}$ has four $\text{Cl}^-$ ions, each donating through its single chloride: $\text{CN} = 4$ . [!ANSWER] (a) $\text{CN} = 6$ ; (b) $\text{CN} = 4$ ; (c) $\text{CN} = 4$ .

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2023Set F1 markMCQ
$Q. The coordination number of a metal crystallizing in a hexagonal close packed structure is$
(a) 5
(b) 4
(c) 8
(d) 12
›Reveal solutionSolution

Both hcp and ccp are close-packed with coordination number 12.

In a close-packed structure each sphere is surrounded by 6 spheres in its own layer, 3 in the layer above and 3 in the layer below, giving 6 + 3 + 3 = 12 nearest neighbours. Therefore the coordination number of a metal crystallising in a hexagonal close-packed (hcp) structure is 12 (the same as for cubic close packing).

✓Final answer
$(D) 12.$
CBSE 2022Set HE2181 markMCQ
$Q. Which compound has 8:8 coordination number?$
(a) MgO
(b) Al2O3
(c) CsCl
(d) NaCl
›Reveal solutionSolution
CsCl crystallises in a body-centred-cubic-type arrangement where each ion touches 8 oppositely charged ions, giving 8:8 coordination; NaCl, MgO and Al2O3 do not.

The coordination number in an ionic solid depends mainly on the radius ratio (r+/r-) of the cation to the anion, since it is the packing geometry that keeps oppositely charged ions in contact while like-charged ions stay apart.

NaCl and MgO both adopt the rock-salt structure: each cation is surrounded by 6 anions and each anion by 6 cations (6:6 coordination), because their radius ratio falls in the 0.414-0.732 range (octahedral holes).

Al2O3 (corundum-type) has a more complex structure with Al3+ in octahedral sites, again not 8:8.

CsCl has a larger cation (Cs+) relative to Cl-, giving a radius ratio close to 1 (>0.732), which favours a cubic (body-centred) arrangement: one Cs+ sits at the body centre of a cube of 8 Cl- ions at the corners (and vice versa when you swap the reference ion). Every Cs+ therefore touches 8 Cl- ions, and every Cl- touches 8 Cs+ ions — 8:8 coordination.

✓Final answer
$(C) CsCl — its structure gives 8:8 coordination, unlike the 6:6 coordination of NaCl/MgO.$
CBSE 2022Set ANNUAL1 mark
$Q. A compound formed by elements A and B has the A atoms forming a ccp lattice and the B atoms occupy half of the tetrahedral voids. What is the co-ordination number of B atoms in the crystal ?$
›Reveal solutionSolution

B sits inside the tetrahedral voids of A's ccp lattice, so B is surrounded by 4 A atoms — coordination number 4.

In a cubic close packed (ccp/fcc) arrangement of A atoms, two kinds of voids are created between the layers: octahedral voids (surrounded by 6 nearest atoms) and tetrahedral voids (surrounded by 4 nearest atoms, arranged at the corners of a tetrahedron around the void). A ccp lattice of N atoms generates N octahedral voids and 2N tetrahedral voids.

Here the B atoms occupy tetrahedral voids, so geometrically each B atom touches exactly 4 surrounding A atoms — its coordination number is 4. (As a side note, since only half of the 2N tetrahedral voids are filled, the number of B atoms = N = number of A atoms, giving the overall formula AB, with A itself having a coordination number of 4 towards B by the same reciprocal geometric argument.)

✓Final answer
$Coordination number of B = 4 (tetrahedral coordination).$
CBSE 2019Set HE1 markMCQ
$Q. If the coordination number of cesium ion Cs+ in Cesium chloride is 8, then the coordination number of chloride ion will be -$
(a) 8
(b) 4
(c) 6
(d) 12
›Reveal solutionSolution

In CsCl, Cs⁺ and Cl⁻ occupy a body-centred-cubic-type arrangement in which each ion is surrounded by 8 ions of the other kind, so the coordination number of Cl⁻ is also 8.

CsCl crystallises with Cl⁻ ions at the eight corners of a cube and the Cs⁺ ion at the body centre (equivalently, either ion can be taken at the corners with the other at the centre). Each corner ion is simultaneously shared by 8 such cubes, and the ion at the body centre touches all 8 corner ions.

Because the structure is symmetric with respect to the two ions (it is NOT a true bcc lattice of identical atoms, but the geometric relationship is the same), the number of nearest neighbours of Cl⁻ is exactly the same as the number of nearest neighbours of Cs⁺.

Given: coordination number of Cs⁺ = 8.

Therefore: coordination number of Cl⁻ = 8 as well.

✓Final answer
$(a) 8.$
CBSE 2018Set ANNUAL1 mark
$Q. What is the co-ordination number of particles present in FCC crystal structure ?$
›Reveal solutionSolution

In a face-centred cubic (FCC/ccp) lattice, each particle touches 12 nearest neighbours, giving a co-ordination number of 12.

In an FCC unit cell, lattice points lie at the 8 corners and at the centre of each of the 6 faces. Consider any one particle, say the one at a face-centre: it touches 4 corner particles in its own layer, 4 particles in the layer directly above, and 4 particles in the layer directly below — a total of 4 + 4 + 4 = 12 nearest neighbours.

This close-packed arrangement (ccp/fcc) has the maximum possible packing efficiency (74%) for identical spheres, and correspondingly the highest co-ordination number of 12 among the common cubic structures (compare: simple cubic = 6, body-centred cubic = 8).

✓Final answer
$Co-ordination number in FCC = 12.$
CBSE 2018Set ANNUAL1 markMCQ
$Q. The co-ordination number of a metal crystallizing in hexagonal close packed (hcp) structure is -$
(a) 12
(b) 8
(c) 4
(d) 6
›Reveal solutionSolution

hcp is a close-packed structure → coordination number 12.

Both hcp and ccp are close-packed with maximum packing; each sphere is surrounded by 6 neighbours in the same layer + 3 above + 3 below = 12 nearest neighbours.

✓Final answer
$(a) 12.$
CBSE 2016Set ANNUAL1 mark
$^+$
›Reveal solutionSolution

NaCl adopts a face-centred cubic (rock-salt) lattice in which both ions have coordination number 6.

In crystalline NaCl, Cl $^-$ ions occupy an fcc lattice and Na $^+$ ions occupy all the octahedral voids of that lattice (or vice versa — the two sub-lattices are equivalent, each fcc, interpenetrating). Every Na $^+$ ion is surrounded by 6 nearest-neighbour Cl $^-$ ions positioned octahedrally around it, and by symmetry every Cl $^-$ ion is likewise surrounded by 6 nearest-neighbour Na $^+$ ions. So the structure is described as (6:6) coordination.

✓Final answer
$^+$

Q.Determine the coordination number of the central metal ion in each of the following:

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