One mole of $CrCl_3 \cdot 6H_2O$ compound reacts with excess $AgNO_3$ solution to yield two moles of $AgCl$ (s). The structural formula of the compound is (A) $[Cr(H_2O)_5Cl]Cl_2 \cdot H_2O$ (B) $[Cr(H_2O)_3Cl_3] \cdot 3H_2O$ (C) $[Cr(H_2O)_4Cl_2]Cl \cdot 2H_2O$ (D) $[Cr(H_2O)_6]Cl_3$

One mole of CrCl₃ · 6H₂O compound reacts with excess Ag — CBSE Class 12 Chemistry 2020 PYQ

Question

CrCl_3 \cdot 6H_2O

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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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The key idea is that only chloride ions outside the coordination sphere (ionisable chlorides) precipitate with $AgNO_3$ . Since 1 mole of the complex gives 2 moles of $AgCl$ , there must be 2 ionisable Cl⁻ ions outside the coordination sphere. The correct option is (A) $[Cr(H_2O)_5Cl]Cl_2 \cdot H_2O$ .

Why Werner Coordination Theory is the key

Before we touch a single calculation, let's understand the principle. Alfred Werner showed that in coordination compounds, some groups are directly bonded to the central metal ion (inside the coordination sphere, written in square brackets), while others are outside the sphere as counter-ions.

Here's the critical exam point: Only the chloride ions outside the coordination sphere are free to precipitate with $AgNO_3$ as $AgCl$ . Chloride ions inside the sphere are covalently bonded to chromium and do not dissociate in solution.

So the problem reduces to a simple count: how many chlorides are outside the brackets?

Step-by-step reasoning

1. Identify the total composition

The formula $CrCl_3 \cdot 6H_2O$ tells us we have:

1 Cr atom
3 Cl atoms
6 H₂O molecules

Every option must contain exactly these atoms — just arranged differently between inside and outside the coordination sphere.

2. Interpret the experimental result

1 mole of compound + excess $AgNO_3$ → 2 moles of $AgCl$ (s)

This means exactly 2 chloride ions from each formula unit are free to react. These are the ionisable chlorides — the ones outside the square brackets.

3. Apply the logic to each option

Let’s count the outside chlorides for each choice:

(A) $[Cr(H_2O)_5Cl]Cl_2 \cdot H_2O$

Inside: 1 Cl. Outside: 2 Cl. → 2 ionisable Cl⁻ ✓
(B) $[Cr(H_2O)_3Cl_3] \cdot 3H_2O$

Inside: 3 Cl. Outside: 0 Cl. → 0 ionisable Cl⁻ ✗
(C) $[Cr(H_2O)_4Cl_2]Cl \cdot 2H_2O$

Inside: 2 Cl. Outside: 1 Cl. → 1 ionisable Cl⁻ ✗
(D) $[Cr(H_2O)_6]Cl_3$ …

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

Showing the 12 most recent of 66 on this concept.

CBSE 2026Set 56/3/11 markMCQ
$Q. According to Werner's theory, the primary valencies of the central metal atom : (A) are satisfied by neutral molecules or negative ions. (B) are equal to its coordination number. (C) are satisfied by negative ions. (D) are non-ionisable.$
›Reveal solutionSolution
Werner’s theory distinguishes primary valencies (ionisable, satisfied only by negative ions, equal to oxidation state) from secondary valencies (non-ionisable, satisfied by neutral molecules or negative ions, equal to coordination number). The correct answer is (C).

Werner’s Coordination Theory was a breakthrough because it explained why compounds like $\ce{CoCl3·6NH3}$ (which we now write as $\ce{[Co(NH3)6]Cl3}$ ) behave so differently from simple salts. The key insight: a metal ion has two kinds of bonding capacity — not just one.

Primary valency (now called oxidation state) is the metal’s ionic bonding capacity. It is satisfied only by negative ions (anions), because it arises from the metal’s need to neutralise its positive charge. These bonds are ionisable — they break apart in solution, giving the familiar conductivity and precipitation tests.

Secondary valency (now called coordination number) is the metal’s ability to bind ligands directly. It is satisfied by neutral molecules (like $\ce{NH3}$ ) or negative ions (like $\ce{Cl-}$ ). These bonds are non-ionisable — they stay attached to the metal even in solution.

Now let’s apply this to the options.

Option (A): “Primary valencies are satisfied by neutral molecules or negative ions.”

This is false. Primary valencies are satisfied only by negative ions. Neutral molecules satisfy secondary valencies. For example, in $\ce{[Co(NH3)6]Cl3}$ , the three $\ce{Cl-}$ ions satisfy the primary valency (Co³⁺ needs three negative charges), while six $\ce{NH3}$ molecules satisfy the secondary valency.

Option (B): “Primary valencies are equal to its coordination number.”

This is false. Primary valency equals the oxidation state of the metal. Coordination number equals the secondary valency. They are often different. In $\ce{[Co(NH3)6]Cl3}$ , primary valency = 3, coordination number = 6.

Option (C): “Primary valencies are satisfied by negative ions.” …
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CBSE 2026Set 56/1/11 markMCQ
$[Co(NH_3)_5(NO_2)]^{2+}$
›Reveal solutionSolution
In Werner’s coordination theory, secondary valency equals the coordination number — the number of ligand donor atoms directly bonded to the metal. For $[Co(NH_3)_5(NO_2)]^{2+}$ , there are 5 NH₃ molecules (each donating one N) and one NO₂⁻ ligand (also donating one N), giving a total of 6 donor atoms. So the secondary valency is 6.

Werner’s coordination theory is the foundation here. He proposed that metal ions have two kinds of valency: primary (ionisable, corresponding to oxidation state) and secondary (non-ionisable, corresponding to coordination number). The secondary valency is simply the number of ligand donor atoms directly attached to the central metal ion — in other words, the coordination number.

For the complex $[Co(NH_3)_5(NO_2)]^{2+}$ , we need to count how many atoms are actually bonded to cobalt.

Identify the ligands and their denticity.

NH₃ (ammine) is a monodentate ligand — it binds through the lone pair on nitrogen. Each NH₃ contributes one donor atom.

NO₂⁻ (nitrito or nitro, depending on binding mode) is also monodentate when it binds through nitrogen (the more common nitro form) or through oxygen. In either case, it uses one donor atom per ligand. The problem doesn’t specify the linkage isomer, but that doesn’t change the count — it’s still one donor atom.

Count the total number of donor atoms.

Five NH₃ ligands: $5 \times 1 = 5$ donor atoms.

One NO₂⁻ ligand: $1 \times 1 = 1$ donor atom.

Total = $5 + 1 = 6$ donor atoms.

Relate this to secondary valency.

Werner defined secondary valency as the number of groups directly coordinated to the metal — exactly the coordination number. So here, secondary valency = 6. …
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CBSE 2026Set DZ1 markMCQ
$K_3[Co(C_2O_4)_3]$
(a) 3
(b) 4
(c) 5
(d) 6
›Reveal solutionSolution

Oxalate is a bidentate ligand; three of them occupy six coordination sites, so the coordination number of Co is 6 — option (d).

The coordination number is the number of ligand donor atoms directly bonded to the central metal ion (not the number of ligand molecules).

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q. What is the coordination number of Cobalt in [Co(en)3]Cl3 ?$
(a) 6
(b) 5
(c) 4
(d) 3
›Reveal solutionSolution

Each 'en' ligand is bidentate, so [Co(en)3]Cl3 has coordination number 6.

In $[Co(en)_3]Cl_3$ , ethylenediamine (en, $H_2NCH_2CH_2NH_2$ ) acts as a bidentate ligand — it has two nitrogen donor atoms, each with a lone pair, that can simultaneously coordinate to the central metal ion, forming a five-membered chelate ring with cobalt.

Since there are three 'en' ligands attached to the cobalt centre, and each contributes 2 donor atoms, the total number of coordinate bonds (and hence the coordination number) is:

$3 \times 2 = 6$

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q. Ambidentate ligand is$
(a) H2O
(b) NH3
(c) NO2-
(d) Cl-
›Reveal solutionSolution
An ambidentate ligand has two different donor atoms but binds through only one of them at a time, depending on conditions.

H2O, NH3 and Cl- each have only one type of donor atom, so they are simple monodentate ligands, not ambidentate. …
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CBSE 2026Set ANNUAL1 markMCQ
$Q. Coordination number of Pt in [Pt(NH3)2 Cl (NO2)] complex is$
(a) 3
(b) 4
(c) 5
(d) 6
›Reveal solutionSolution

Coordination number = the total number of ligand donor atoms directly bonded to the central metal atom/ion.

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q. Identify the homoleptic complex among the following compounds:$
(a) [Co(NH3)4Cl2]+
(b) [Ni(CN)4]2-
(c) [Cr(NH3)2Cl2(en)]+
(d) Both (A) and (C)
›Reveal solutionSolution
A homoleptic complex is one in which the metal is bonded to only a single kind of donor ligand; a heteroleptic complex has more than one kind.

Checking each option:

[Co(NH3)4Cl2]+: contains two different ligands, NH3 and Cl- (heteroleptic).

[Ni(CN)4]2-: contains only CN- ligands, all of the same type (homoleptic). …
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CBSE 2026Set ANNUAL1 markMCQ
$Q. Which of the following is a bidentate ligand?$
(a) CN-
(b) NH3
(c) C2O4^2-
(d) CO3^2-
›Reveal solutionSolution
A bidentate ligand has two donor atoms that simultaneously coordinate to the same central metal atom, forming a ring (chelate).

CN- has one donor atom (C), so it is monodentate.

NH3 has one donor atom (N), so it is monodentate.

C2O4^2- (oxalate ion) has two oxygen atoms, one from each carboxylate group, that can each donate a lone pair to the metal simultaneously - this makes it bidentate, forming a five-membered chelate ring. …
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CBSE 2026Set ANNUAL1 markMCQ
$Q. The co-ordination number of Cr in K3[Cr(C2O4)3] is: (as printed; the paper's option values are +3/+4/+2/+6)$
(a) +3
(b) +4
(c) +2
(d) +6
›Reveal solutionSolution

As printed, the options ( $+3,+4,+2,+6$ ) are oxidation-state values, so this question is really testing the oxidation number of Cr, which is $+3$ . (For completeness: the true coordination number — the count of donor atoms bonded to Cr — is 6, not among the given options, since oxalate is bidentate and there are three oxalate ligands.)

Oxidation number of Cr: In $K_3[Cr(C_2O_4)_3]$ , potassium contributes $+1$ each (three K $^+$ ions), and each oxalate ion $C_2O_4^{2-}$ carries a charge of $-2$ . Let the oxidation number of Cr be $x$ :

$3(+1) + x + 3(-2) = 0$

$3 + x - 6 = 0 \implies x = +3$

…

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CBSE 2026Set ANNUAL1 mark
$[Fe(CN)_6]^{4-}$
›Reveal solutionSolution

Balancing the ligand charges against the overall complex-ion charge gives the oxidation state of iron.

Working it out

Let the oxidation number of Fe be $x$ . Cyanide is an anionic ligand, $CN^-$ , contributing $-1$ each; there are 6 of them:

$x + 6(-1) = -4\ (\text{overall charge of the complex ion})$ …

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CBSE 2026Set ANNUAL1 mark
$Q. What is the coordination number of Fe in [Fe(EDTA)]⁻?$
›Reveal solutionSolution

EDTA is a hexadentate chelating ligand (2 N + 4 O donor atoms), so a single EDTA fills all six coordination sites — coordination number of Fe = 6.

Concept. The coordination number of a metal ion is the number of ligand donor atoms directly bonded to it (the number of coordinate bonds), not the number of ligand molecules.

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q. Assertion (A): Glycinate ion H₂NCH₂COO⁻ is a chelating ligand. Reason (R): It can link through either nitrogen or anionic oxygen.$
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is correct.
›Reveal solutionSolution

A (glycinate is chelating) is true, but the reason given describes ambidentate behaviour (binding through one OR the other), not chelation (binding through both at once), so R is false — option (C).

Assertion (A): The glycinate ion $H_2N-CH_2-COO^-$ is a chelating ligand. This is true: it is a bidentate ligand that binds a metal through the nitrogen of the $-NH_2$ group and the anionic oxygen of the $-COO^-$ group at the same time, forming a stable five-membered chelate ring.

…

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Why Werner Coordination Theory is the key

Step-by-step reasoning

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