Coordination Number

Introduction

Coordination number answers a geometric question: how many donor atoms bind directly to the central metal? It is not the number of ligands written in the formula, the metal's oxidation state or the magnitude of the complex ion's charge. For simple one-site ligands these counts can coincide by accident. Multidentate ligands reveal the difference immediately.

Core explanation

In [Ag(NH₃)₂]⁺, two ammonia molecules each donate through one nitrogen atom, so silver has coordination number two. In [Co(H₂O)₆]³⁺, six water ligands each donate through one oxygen atom, giving coordination number six. [CuCl₄]²⁻ has four chloride donor atoms and coordination number four. These familiar examples show the direct count for monodentate ligands.

Ethylenediamine, abbreviated en, has two nitrogen donor atoms connected within one molecule. If both bind to the same metal, en is bidentate. [Co(en)₃]³⁺ contains only three ligand molecules but six Co–N donor contacts, so coordination number is six. Likewise, an oxalate ligand may bind through two oxygen atoms. [Fe(C₂O₄)₃]³⁻ then has three bidentate ligands and coordination number six under the usual chelating arrangement. Its metal oxidation state is a separate +3 calculation.

Some ligands have more donor atoms. EDTA can bind through several oxygen and nitrogen donors and is often described as hexadentate in common complexes. Whether all potential donor atoms actually bind in a specific species must be checked; a ligand's maximum denticity is not an automatic count for every metal and geometry. Bridging ligands can attach to two or more different metal centers, so for a multinuclear complex count donor contacts separately at each center.

Coordination number influences possible geometry but does not uniquely fix it. Two-coordinate complexes are often linear. Six-coordinate complexes commonly have approximately octahedral arrangements, though distortions occur. Four-coordinate complexes may be tetrahedral or square planar, with metal electron configuration and ligand effects helping determine which. Counting four donor atoms alone cannot decide between those two shapes.

Chemical formula conventions can hide the contact pattern. If a ligand is ambidentate, like thiocyanate, it usually attaches through one of two possible donor atoms at a time in a simple mononuclear complex; it is not automatically bidentate. Conversely, a formula containing one polydentate ligand may create several contacts. Read the ligand's actual binding mode, not merely how many possible lone-pair atoms it contains.

A reliable count uses a contact table: list each ligand type, its number of molecules and its denticity in the given complex. Multiply and sum. For [Co(en)₂Cl₂]⁺, two en ligands give 2 × 2 = 4 contacts and two chloride ligands give 2 × 1 = 2, so coordination number is six. The ion has charge +1 and Co is +3 because two Cl⁻ contribute −2, but neither of those charge values alters the contact count.

Step-by-step reasoning

1. Identify the central metal and all ligands inside its bracket. 2. Determine the actual donor atoms used by each ligand. 3. Multiply ligand count by binding denticity for each kind. 4. Add the direct metal–donor contacts. 5. Consider geometry separately after the coordination number is known.

Visual explanation

Draw three en molecules as U-shaped links to Co. Each link has two N endpoints touching the metal, making six contacts. Place next to it a six-ammonia diagram to show how three ligand molecules and six ligand molecules can both give coordination number six.

Real-world analogy

Three extension cords can each have two plugs attached to a power hub, giving six connections, while six single-plug cords also make six. The number of cords differs from the number of direct connections. The analogy illustrates counting, not actual electrical or chemical bonding.

Real-world example

Chelating agents in water treatment may bind a metal through multiple donor atoms. The count of attached donor sites helps describe the resulting complex's geometry and stability more accurately than the count of ligand molecules alone.

Why?

Why does [Co(en)₃]³⁺ have coordination number six? Each en molecule supplies two directly attached nitrogen atoms, and three times two equals six separate donor contacts around the cobalt center.

Common misconception

“A ligand containing two potential donor atoms always contributes two to coordination number.” It contributes two only if both atoms actually bind that metal in the specified structure. Potential and actual denticity must not be confused.

Worked example

For [Co(en)₂Cl₂]⁺, each en uses two N atoms, contributing four contacts total. Each chloride uses one donor atom, contributing two more. Coordination number = 4 + 2 = 6. Charge balance gives Co(III), since x + 2(−1) = +1. The six and the +3 answer different questions.

Quick check

1. What is the coordination number of [Ag(NH₃)₂]⁺? Answer: Two, from two Ag–N contacts.

Exam focus

Draw or list direct donor contacts for mixed-ligand complexes. Report oxidation state and coordination number with distinct labels; a six-coordinate metal need not be in oxidation state +6.

Advanced insight

Coordination numbers beyond two, four and six are known, especially for large metal centers and specialised ligands. The usual shapes are common teaching patterns, not an exhaustive catalogue of every possible structure.

Summary

Coordination number counts donor atoms directly attached to a metal. Denticity tells how many contacts one ligand supplies. Geometry depends on both that count and electronic and steric conditions, so ligand count alone is insufficient.

Practice questions

1. What is the coordination number of [Co(en)₃]³⁺? Answer: Six. 2. How many ligands are in [Co(en)₃]³⁺? Answer: Three en molecules, distinct from its six donor contacts. 3. What geometries are common for coordination number four? Answer: Tetrahedral and square planar. 4. Can a bridging ligand contribute to coordination at more than one metal center? Answer: Yes. Count its contacts separately for each metal.