Specify the oxidation numbers of the metals in the following coordination entities: (i) [Co(H₂O)(CN)(en)₂]²⁺ (

Exercises · 5.5

Q. Specify the oxidation numbers of the metals in the following coordination entities:

(i)

[Co(H_2O)(CN)(en)_2]^{2+}

(ii)

[CoBr_2(en)_2]^{+}

(iii)

[PtCl_4]^{2-}

(iv)

K_3[Fe(CN)_6]

(v)

[Cr(NH_3)_3Cl_3]

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Concept understanding — Werner Coordination Theory

Werner Coordination Theory: The Idea That Changed Inorganic Chemistry

Imagine you're looking at a salt like cobalt(III) chloride. The formula is written as $\ce{CoCl3}$ , and when you dissolve it in water, you expect to find $\ce{Co^{3+}}$ and $\ce{Cl^-}$ ions. But something strange happens: when you add silver nitrate (which precipitates chloride ions), only some of the chlorine comes out as silver chloride. Not all of it. And the amount that precipitates depends on how you made the compound.

This was the puzzle that faced chemists in the late 1800s. Compounds like $\ce{CoCl3·6NH3}$ (orange-yellow) and $\ce{CoCl3·5NH3}$ (purple) had the same metal and the same ligands (ammonia), but different colours, different conductivities in solution, and different numbers of chloride ions that could be precipitated. The old ideas of fixed valency couldn't explain it.

Alfred Werner proposed a radical solution in 1893. He said: a metal ion has two kinds of valency.

The Core Intuition

Think of a metal ion like a king in a castle. The king has two types of relationships:

Primary valency (today: oxidation state) — this is the king's royal authority. It's fixed, non-directional, and satisfied by negative ions. For cobalt(III), this is +3. It's like the king's crown: it doesn't change.
Secondary valency (today: coordination number) — this is the king's personal bodyguard. The king can have a fixed number of guards (usually 4 or 6) who stand in specific positions around him. These guards can be neutral molecules (like ammonia) or negative ions (like chloride). The key: these guards are directly attached to the metal, forming a stable cluster called the coordination sphere.

The revolutionary idea: the chloride ions that act as bodyguards (inside the coordination sphere) do not behave like free ions. They don't precipitate with silver nitrate. They don't conduct electricity. They are "locked" to the metal.

The Precise Statement

Werner Coordination Theory (1893) Every metal atom has two types of valency : Primary valency (ionisable): corresponds to the oxidation state. It is satisfied by negative ions. These ions are outside the coordination sphere and behave as free ions in solution. Secondary valency (non-ionisable): corresponds to the coordination number. It is satisfied by neutral molecules or negative ions directly bonded to the metal. These are inside the coordination sphere and do not dissociate. The secondary valencies are directional — they point to fixed positions in space around the metal, giving the complex a definite geometry (e.g., octahedral for coordination number 6, square planar for 4). The primary valency is non-directional — it is just a number, not a spatial arrangement.

How It Explains the Puzzle

Take the compound $\ce{CoCl3·6NH3}$ (orange-yellow). Werner said:

Cobalt has primary valency +3 (needs three negative charges to satisfy it).
Cobalt has secondary valency 6 (can hold six ligands around it).
The six ammonia molecules satisfy all six secondary valencies. So the chloride ions cannot be inside the coordination sphere — they must be outside, as free ions.
Structure: $[\ce{Co(NH3)6}]\ce{Cl3}$ . All three chlorides precipitate with $\ce{AgNO3}$ .

Now take $\ce{CoCl3·5NH3}$ (purple):

Again, primary valency +3, secondary valency 6.
Five ammonia molecules satisfy five secondary valencies. One chloride ion must fill the sixth spot — it becomes a ligand inside the sphere.
The other two chlorides are outside as free ions.
Structure: $[\ce{Co(NH3)5Cl}]\ce{Cl2}$ . Only two chlorides precipitate.

Note

The number of free ions in solution determines the conductivity and the number of precipitable chlorides. Werner's theory predicted exactly these numbers — and experiments confirmed them.

The Geometry Insight …

Why this formula?

Werner Coordination Theory: Why the Key Formulas Hold

Werner Coordination Theory (1893) revolutionized inorganic chemistry by explaining how metal ions bind ligands. Let's build the reasoning from first principles — not just memorize formulas.

1. The Core Observation: Primary vs. Secondary Valence

Werner noticed that metal compounds had two types of bonding capacity:

Primary valence (now oxidation state): Satisfies the metal's charge — ionic in nature.
Secondary valence (now coordination number): Determines how many ligands attach — directional, spatial in nature.

Why this distinction?

Consider $\ce{CoCl3 \cdot 6 NH3}$ (one of Werner's classic compounds).

The compound is electrically neutral overall.
Adding $\ce{AgNO3}$ precipitates all 3 Cl⁻ as $\ce{AgCl}$ — meaning all chlorides are free ions.
Therefore, the $\ce{NH3}$ molecules must be directly bonded to $\ce{Co}$ , not the chlorides.

This forces the idea: Co has a fixed capacity for direct ligand attachment (secondary valence = 6 here), separate from its charge balance (primary valence = +3).

2. The Key Formula: Coordination Number = Number of Ligands Attached

Formula:

\text{Coordination number} = \text{number of donor atoms directly bonded to the metal}

Why this holds:

Werner's experiments showed that only a fixed number of ligands could be replaced without breaking the compound's identity.
For $\ce{CoCl3 \cdot 6 NH3}$ , adding acid doesn't remove $\ce{NH3}$ easily — they are coordinated.
The maximum number of such tightly bound ligands is the coordination number — a property of the metal ion, not the counterions.

Derivation from data:

If you have $\ce{[Co(NH3)6]Cl3}$ , conductivity measurements show 4 ions in solution ( $\ce{[Co(NH3)6]^{3+}}$ + 3 Cl⁻).

If you had $\ce{[Co(NH3)5Cl]Cl2}$ , conductivity shows 3 ions.

The number of chlorides inside the coordination sphere (non-precipitable) plus those outside must sum to the total chlorides. This gives the coordination number directly.

3. The Geometry Formula: Coordination Number Determines Shape

Werner proposed that secondary valences are directed in space — leading to specific geometries.

Coordination Number	Geometry	Why?
2	Linear	Minimizes repulsion between 2 ligands
4	Tetrahedral or Square planar	4 points in space — two arrangements possible
6	Octahedral	6 ligands at 90° angles — most symmetric

Why octahedral for 6?

6 ligands around a central atom must be placed to maximize separation.
The octahedron (6 vertices, all equidistant from center, 90° between adjacent bonds) is the only regular polyhedron with 6 vertices.
This explains why $\ce{[Co(NH3)6]^{3+}}$ is octahedral — no other arrangement gives equal bond angles and distances.

4. The Isomer Counting Formula: Why $2^n$ or $n!$ Appears

Werner used isomer counts to confirm geometry. For an octahedral complex $\ce{[Ma2b2c2]}$ :

Number of geometrical isomers = 5 (not 6, not 4)

Why this formula?

Place the two 'a' ligands: they can be cis (90°) or trans (180°).
For each, place 'b' and 'c' in remaining positions — but symmetry reduces duplicates. …

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Werner’s coordination theory tells us that the metal’s oxidation number is the charge left after removing all ligands (with their known charges) from the complex ion. For these five complexes, the oxidation numbers are: (i) Co = +3,

(ii) Co = +3,

(iii) Pt = +2,

(iv) Fe = +3,

(v) Cr = +3.

Werner’s theory is the foundation here. The key insight: a coordination compound has a central metal ion with a specific oxidation state, surrounded by ligands that are neutral or carry a fixed charge. The overall charge of the complex ion is the sum of the metal’s charge and the charges of all ligands. So to find the metal’s oxidation number, you simply set up an algebraic equation.

Let’s go through each one step by step.

(i) $[Co(H_2O)(CN)(en)_2]^{2+}$

Identify ligand charges.
- $H_2O$ (water) is a neutral ligand — charge = 0.
- $CN^-$ (cyanide) carries a charge of –1.
- $en$ (ethylenediamine, $NH_2CH_2CH_2NH_2$ ) is a neutral bidentate ligand — charge = 0. There are two of them.
Set up the equation.

Let the oxidation number of Co be $x$ . The complex ion has an overall charge of $+2$ .

x + (0) + (-1) + 2(0) = +2

Solve.

x - 1 = +2 \quad \Rightarrow \quad x = +3

Tip

Cyanide is almost always –1, and water and en are neutral — memorise these common ligand charges to speed things up.

(ii) $[CoBr_2(en)_2]^{+}$

Ligand charges.
- $Br^-$ (bromide) is –1. There are two of them.
- $en$ is neutral (0). Two of them.
Equation.

Let Co oxidation number be $x$ .

x + 2(-1) + 2(0) = +1

Solve.

x - 2 = +1 \quad \Rightarrow \quad x = +3

Watch out

A common mistake: forgetting that the charge on the complex ion itself must be included. Here the complex has a $+1$ charge, not zero.

(iii) $[PtCl_4]^{2-}$

Ligand charge.
- $Cl^-$ is –1. Four chlorides.
Equation.

Let Pt oxidation number be $x$ .

x + 4(-1) = -2

Solve.

x - 4 = -2 \quad \Rightarrow \quad x = +2

[ML_n]^{q}

(iv) $K_3[Fe(CN)_6]$

Handle the counterion first.

The compound is $K_3[Fe(CN)_6]$ . Potassium ( $K^+$ ) is always +1. Three potassium ions give a total positive charge of $+3$ . The whole compound is neutral, so the complex ion $[Fe(CN)_6]^{3-}$ must have a charge of –3.
Ligand charge. …

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Here are the common mistakes students make when assigning oxidation numbers in coordination compounds, specifically for the Werner Coordination Theory context, and how to avoid each.

Mistake 1: Forgetting the Overall Charge of the Complex Ion

The Error: Students often ignore the superscript charge on the square bracket (e.g., $[Co(H_2O)(CN)(en)_2]^{2+}$ ) and set the sum of oxidation numbers equal to zero instead of $+2$ .

How to Avoid:

Always write the charge balance equation first. Let $x$ = oxidation number of the metal. Sum of (oxidation numbers of all ligands) + $x$ = charge on the complex ion.
Example (i): $[Co(H_2O)(CN)(en)_2]^{2+}$ Ligands: $H_2O$ (0), $CN^-$ (-1), $en$ (0). Equation: $x + 0 + (-1) + 0 = +2 \implies x = +3$ .

Mistake 2: Assigning Wrong Charges to Neutral Ligands

The Error: Treating neutral molecules like $H_2O$ , $NH_3$ , or $en$ (ethylenediamine) as if they carry a charge.

How to Avoid:

Memorize the common neutral ligands: $H_2O$ , $NH_3$ , $CO$ , $en$ , $NO$ (nitrosyl, but careful — it can be neutral or charged depending on bonding).
Rule: If the ligand is a molecule (not an ion), its oxidation number is 0 unless specified otherwise.

Mistake 3: Forgetting the Charge of Anionic Ligands

The Error: Using the wrong charge for ligands like $CN^-$ , $Cl^-$ , $Br^-$ , or $OH^-$ .

How to Avoid:

Make a quick reference list:
- $CN^-$ : $-1$
- $Cl^-$ , $Br^-$ , $I^-$ : $-1$
- $OH^-$ : $-1$
- $O^{2-}$ : $-2$ (rare in simple complexes, but appears in oxo complexes)
Example (ii): $[CoBr_2(en)_2]^{+}$ $Br^-$ = $-1$ each, $en$ = $0$ . Equation: $x + 2(-1) + 0 = +1 \implies x = +3$ .

Mistake 4: Ignoring the Counter-Ion in Neutral Complexes

The Error: When the complex is part of a salt (e.g., $K_3[Fe(CN)_6]$ ), students forget to account for the charge of the counter-ions to find the charge on the complex ion.

How to Avoid:

Step 1: Find the charge on the complex ion using the counter-ions. $K_3[Fe(CN)_6]$ : $K^+$ has charge $+1$ , so $3 \times (+1) = +3$ . The salt is neutral, so the complex ion must be $[Fe(CN)_6]^{3-}$ .
Step 2: Now solve for $Fe$ : $x + 6(-1) = -3 \implies x = +3$ .

Mistake 5: Misidentifying the Charge of Ambidentate Ligands

The Error: Ligands like $CN^-$ can bind through C or N, but the charge remains $-1$ regardless. Students sometimes assign a different charge based on bonding mode.

How to Avoid:

The charge of a ligand is fixed by its formula, not by how it binds. $CN^-$ is always $-1$ , $NO_2^-$ is always $-1$ , $SCN^-$ is always $-1$ .

Mistake 6: Forgetting That the Sum Must Be an Integer …

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Q.Specify the oxidation numbers of the metals in the following coordination entities:

Concept understanding — Werner Coordination Theory

Werner Coordination Theory: The Idea That Changed Inorganic Chemistry

The Core Intuition

The Precise Statement

How It Explains the Puzzle

The Geometry Insight …

Why this formula?

Werner Coordination Theory: Why the Key Formulas Hold

1. The Core Observation: Primary vs. Secondary Valence

2. The Key Formula: Coordination Number = Number of Ligands Attached

3. The Geometry Formula: Coordination Number Determines Shape

4. The Isomer Counting Formula: Why $2^n$ or $n!$ Appears

(i) $[Co(H_2O)(CN)(en)_2]^{2+}$

(ii) $[CoBr_2(en)_2]^{+}$

(iii) $[PtCl_4]^{2-}$

(iv) $K_3[Fe(CN)_6]$

Method: Charge Balance Method

Steps:

(i) $[Co(H_2O)(CN)(en)_2]^{2+}$

(ii) $[CoBr_2(en)_2]^{+}$

(iii) $[PtCl_4]^{2-}$

(iv) $K_3[Fe(CN)_6]$

Mistake 1: Forgetting the Overall Charge of the Complex Ion

Mistake 2: Assigning Wrong Charges to Neutral Ligands

Mistake 3: Forgetting the Charge of Anionic Ligands

Mistake 4: Ignoring the Counter-Ion in Neutral Complexes

Mistake 5: Misidentifying the Charge of Ambidentate Ligands

Mistake 6: Forgetting That the Sum Must Be an Integer …

Q.Specify the oxidation numbers of the metals in the following coordination entities:

(i) [Co(H2O)(CN)(en)2]2+[Co(H_2O)(CN)(en)_2]^{2+}[Co(H2​O)(CN)(en)2​]2+

(ii) [CoBr2(en)2]+[CoBr_2(en)_2]^{+}[CoBr2​(en)2​]+

(iii) [PtCl4]2−[PtCl_4]^{2-}[PtCl4​]2−

(iv) K3[Fe(CN)6]K_3[Fe(CN)_6]K3​[Fe(CN)6​]

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(i) $[Co(H_2O)(CN)(en)_2]^{2+}$

(ii) $[CoBr_2(en)_2]^{+}$

(iii) $[PtCl_4]^{2-}$

(iv) $K_3[Fe(CN)_6]$

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