Q.On the basis of the following observations made with aqueous solutions, assign secondary valences to metals in the following compounds: Formula — Moles of AgCl precipitated per mole of the compounds with excess AgNO3
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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 CoClX3, and when you dissolve it in water, you expect to find CoX3+ and ClX− 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 CoClX3⋅6NHX3 (orange-yellow) and CoClX3⋅5NHX3 (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:
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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.
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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)
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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.
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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).
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The primary valency is non-directional — it is just a number, not a spatial arrangement.
How It Explains the Puzzle
Take the compound CoClX3⋅6NHX3 (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: [Co(NHX3)X6]ClX3. All three chlorides precipitate with AgNOX3.
Now take CoClX3⋅5NHX3 (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: [Co(NHX3)X5Cl]ClX2. Only two chlorides precipitate.
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 CoClX3 ⋅6NHX3 (one of Werner's classic compounds).
- The compound is electrically neutral overall.
- Adding AgNOX3 precipitates all 3 Cl⁻ as AgCl — meaning all chlorides are free ions.
- Therefore, the NHX3 molecules must be directly bonded to 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:
Coordination number=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 CoClX3 ⋅6NHX3, adding acid doesn't remove NHX3 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 [Co(NHX3)X6]ClX3, conductivity measurements show 4 ions in solution ([Co(NHX3)X6]X3+ + 3 Cl⁻).
If you had [Co(NHX3)X5Cl]ClX2, 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 [Co(NHX3)X6]X3+ is octahedral — no other arrangement gives equal bond angles and distances.
4. The Isomer Counting Formula: Why 2n or n! Appears
Werner used isomer counts to confirm geometry. For an octahedral complex [MaX2bX2cX2]:
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. …
Concept: Werner Coordination Theory — secondary valences (coordination number) are satisfied by neutral molecules or negative ions that do not precipitate with AgNO3; only free chloride ions (outside the coordination sphere) give AgCl.
Reasoning steps:
- Each mole of AgCl precipitated corresponds to one mole of free Cl− ions in solution.
- The total number of Cl atoms in the formula minus the free Cl− gives the number of Cl inside the coordination sphere (satisfying secondary valence).
- The secondary valence (coordination number) is the total number of ligands (neutral molecules + coordinated Cl) attached to the metal.
| Compound | Free Cl− (from AgCl) | Total Cl | Coordinated Cl | Neutral ligands | Secondary valence | …
Werner’s coordination theory distinguishes primary (ionic) valency from secondary (coordination) valency. The moles of AgCl precipitated equal the number of chloride ions outside the coordination sphere. Using this, we deduce the secondary valence (coordination number) for each metal complex.
Werner’s theory is the key here. He proposed that metals have two types of valency: primary valency (ionisable, satisfied by anions, shown as oxidation state) and secondary valency (non-ionisable, satisfied by ligands or water, fixed for a given metal). In solution, only chloride ions that are outside the coordination sphere (i.e., not directly bonded to the metal) will precipitate as AgCl with AgNO₃. Chloride ions inside the coordination sphere are covalently bonded and do not precipitate.
So, the number of moles of AgCl precipitated tells us exactly how many Cl⁻ ions are ionic (outside the sphere). The total chloride in the formula minus that number gives the chloride inside the sphere. The secondary valence (coordination number) is the total number of ligands (NH₃, H₂O, or Cl⁻) directly attached to the metal.
Let’s work through each compound step by step.
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Compound (i): PdCl2⋅4NH3 — 2 moles AgCl
- Total Cl atoms in formula = 2.
- AgCl precipitated = 2 → both Cl⁻ are ionic (outside sphere).
- So, inside the coordination sphere: 0 Cl⁻, but 4 NH₃ molecules.
- Secondary valence of Pd = number of ligands attached = 4 (all NH₃).
- The complex is [Pd(NH3)4]Cl2.
-
Compound (ii): NiCl2⋅6H2O — 2 moles AgCl
- Total Cl = 2.
- AgCl = 2 → both Cl⁻ are ionic.
- Inside sphere: 0 Cl⁻, but 6 H₂O molecules.
- Secondary valence of Ni = 6 (all H₂O).
- The complex is [Ni(H2O)6]Cl2.
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Compound (iii): PtCl4⋅2HCl — 0 moles AgCl
- Total Cl = 4 (from PtCl₄) + 2 (from 2HCl) = 6.
- AgCl = 0 → no chloride is ionic; all Cl⁻ are inside the coordination sphere.
- So, inside sphere: all 6 Cl⁻ are bonded to Pt.
- Secondary valence of Pt = 6.
- The complex is [PtCl6]2− (the 2H⁺ are counterions, but the question asks for the metal’s secondary valence). …
Method: Werner's Coordination Theory – Secondary Valence Assignment via Conductivity / Precipitation Data
Concept First (Why this works)
Werner proposed that metal ions have two kinds of valences:
- Primary valence (ionizable, satisfied by anions, corresponds to oxidation state)
- Secondary valence (non-ionizable, satisfied by ligands, corresponds to coordination number)
When a coordination compound dissolves in water, only the ions outside the coordination sphere (satisfying primary valence) are free to react. AgCl precipitation with excess AgNO3 tells us how many Cl− ions are free (outside the coordination sphere) — each free Cl− gives 1 mole of AgCl.
Steps to Solve
- Identify the metal's primary valence (oxidation state) from the formula.
- Count total Cl atoms in the formula.
- From moles of AgCl precipitated, find how many Cl− are free (ionizable).
- Subtract free Cl− from total Cl → these Cl atoms satisfy secondary valence (inside coordination sphere).
- Assign secondary valence = number of ligands (including coordinated Cl and NH3 or H2O) directly attached to the metal.
Application to Given Compounds
(i) PdCl2⋅4NH3 — AgCl = 2
- Total Cl = 2
- Free Cl− = 2 (all Cl are ionizable)
- Coordinated Cl = 0
- Secondary valence = number of ligands = 4NH3 = 4
(ii) NiCl2⋅6H2O — AgCl = 2
- Total Cl = 2
- Free Cl− = 2
- Coordinated Cl = 0
- Secondary valence = 6H2O = 6
(iii) PtCl4⋅2HCl — AgCl = 0
- Total Cl = 6
- Free Cl− = 0 (no AgCl)
- Coordinated Cl = 6 …
Common Mistakes & How to Avoid Them (Werner Coordination Theory)
Mistake 1: Confusing Primary Valence with Secondary Valence
The error: Students often think the number of AgCl precipitated equals the total chlorine atoms in the formula. For example, in PdCl2⋅4NH3, they see 2 Cl atoms and assume secondary valence = 2.
Why it's wrong:
- Primary valence = oxidation state (ionizable Cl⁻ ions)
- Secondary valence = coordination number (ligands directly attached to metal)
- AgNO3 only precipitates free Cl⁻ ions — those outside the coordination sphere.
How to avoid:
- Remember: Precipitated Cl⁻ = Primary valence (ionizable)
- Total Cl – Precipitated Cl = Coordinated Cl
- Secondary valence = number of all ligands (NH₃, H₂O, Cl⁻ inside sphere)
Mistake 2: Forgetting that Neutral Ligands Also Count
The error: Students count only Cl atoms when assigning secondary valence, ignoring NH₃ and H₂O.
Example: For NiCl2⋅6H2O, they see 2 Cl precipitated → secondary valence = 2. Wrong.
Correct reasoning:
- 2 Cl⁻ precipitated → 2 Cl⁻ are outside sphere (primary valence = 2)
- But the complex has 6 H₂O molecules as ligands
- Secondary valence = 6 (from 6 H₂O)
How to avoid:
- Secondary valence = total number of donor atoms (neutral + anionic) directly bonded to metal
- Count NH₃, H₂O, and any Cl⁻ that is not precipitated
Mistake 3: Misinterpreting Zero Precipitation
The error: When 0 moles of AgCl precipitate (e.g., PtCl4⋅2HCl), students think there are no Cl atoms at all.
Why it's wrong:
- Zero precipitation means all Cl atoms are inside the coordination sphere
- They are covalently bonded to the metal, not free ions
Example: PtCl4⋅2HCl
- Total Cl = 6
- Precipitated Cl = 0 → All 6 Cl are coordinated
- Secondary valence = 6 (all Cl ligands)
How to avoid:
- Zero precipitation ≠ zero chlorine
- It means 100% of Cl is in coordination sphere
Mistake 4: Forgetting to Account for All Ligands in Secondary Valence
The error: In CoCl3⋅4NH3, students see 1 Cl precipitated → they assign secondary valence = 1.
Correct approach:
- 1 Cl⁻ precipitated → 1 Cl⁻ outside sphere
- Total Cl = 3 → Coordinated Cl = 3 – 1 = 2
- Also 4 NH₃ ligands
- Secondary valence = 2 (Cl) + 4 (NH₃) = 6
How to avoid:
- Always: Secondary valence = (Coordinated Cl) + (Neutral ligands)
- Never skip counting neutral ligands
Mistake 5: Mixing Up Oxidation State and Coordination Number …
Showing the 12 most recent of 14 on this concept.
- GSEB Higher Secondary Certificate (HSC) Examination 2026Set ANNUAL1 markMCQQ.The sum of coordination number and oxidation number of the metal M in the complex [M(en)2(C2O4)]Cl is:(a) 7(b) 8(c) 9(d) 6
›Reveal solutionSolution
Find the metal's oxidation number from overall charge balance, and its coordination number by counting donor atoms from each ligand (remembering en and oxalate are bidentate).
Complex: [M(en)2(C2O4)]Cl
Oxidation number of M: The complex ion [M(en)2(C2O4)]⁺ must carry a +1 charge to balance the one Cl⁻ counter-ion. en (ethylenediamine) is a neutral ligand (charge 0); C2O4²⁻ (oxalate) carries a −2 charge.
x + 2(0) + (−2) = +1 → x = +3
…
- GSEB Higher Secondary Certificate (HSC) Examination 2025Set ANNUAL1 markMCQQ.The Primary and Secondary valency of the central metal ion in K[Co(OX)2(NH3)2] complex is _____ and _____ respectively.(a) 3, 4(b) 4, 3(c) 6, 3(d) 3, 6
›Reveal solutionSolution
Primary valency is the oxidation state of the metal ion; secondary valency is the coordination number - both are computed from the formula K[Co(OX)2(NH3)2].
Complex: K[Co(C2O4)2(NH3)2]. The complex ion is [Co(C2O4)2(NH3)2]-, since one K+ balances a single negative charge.
Finding the oxidation state (primary valency) of Co: oxalate (C2O4^2-) contributes -2 charge each (x2 ligands = -4), NH3 is neutral (x2 = 0). Let oxidation state of Co = x.
x + (-4) + 0 = -1 (overall charge of the complex ion)
x = +3
So primary valency = 3.
…
- GUJCET 2024Set 131 markMCQQ.In the complex K[Cr(H2O)2(C2O4)2]⋅3H2O, oxidation state and co-ordination number of the central metal ion is ________ and ________. (A) +4, 4 (B) +3, 4 (C) +4, 6 (D) +3, 6
›Reveal solutionSolution
Oxalate is a −2 bidentate ligand and water is neutral; use overall charge for the oxidation state and count donor atoms for coordination number.
Concept: In K[Cr(H2O)2(C2O4)2]⋅3H2O, K+ balances a −1 complex ion. Let Cr =x:
x+2(0)+2(−2)=−1⇒x−4=−1⇒x=+3 …
- GSEB Higher Secondary Certificate (HSC) Examination 2024Set ANNUAL1 markMCQQ.Primary and Secondary valancy of Co in the complex compound [Co(en)3]Cl3 is respectively ________.(a) 2, 3(b) 3, 6(c) 3, 3(d) 4, 6
›Reveal solutionSolution
In [Co(en)3]Cl3, cobalt is in the +3 oxidation state (primary valency = 3), and it is coordinated by 3 bidentate ethylenediamine (en) ligands, giving a coordination number of 6 (secondary valency = 6).
Primary valency = ionisable valency = oxidation state of the central metal ion = +3 for Co here (balanced by the 3 Cl- counter-ions outside the coordination sphere). …
- GUJCET 2023Set 091 markMCQQ.Which of the following species is not expected to be a ligand? (A) NH4+ (B) NO (C) H2N−CH2−CH2−NH2 (D) CO
›Reveal solutionSolution
[!TLDR]
NH4+ has no lone pair to donate, so it cannot function as a ligand.
Concept
A ligand is a Lewis base that donates one or more lone pairs of electrons to a central metal ion to form a coordinate (dative) bond.
Solution
- NH4+: nitrogen's lone pair is already used to bond the fourth H (giving the +1 charge); no lone pair remains → cannot be a ligand.
- NO: has a lone pair on N (and can donate) → ligand. …
- GUJCET 2022Set 171 markMCQQ.How many numbers of mole Ions produced from aqueous solution of 1 mole Iron (III) hexacyanido Ferrate (II) complex? (A) 4 (B) 7 (C) 5 (D) 6
›Reveal solutionSolution
Fe4[Fe(CN)6]3→4Fe3++3[Fe(CN)6]4− = 7 ions.
Concept. "Iron(III) hexacyanidoferrate(II)" has the cation Fe3+ and the complex anion [Fe(CN)6]4−. Charge balance requires 4 cations (+12) for 3 anions (−12):
Fe4[Fe(CN)6]3 …
- GSEB Higher Secondary Certificate (HSC) Examination 2022Set ANNUAL1 markMCQQ.In [Co(C2O4)2(H2O)2]-, what are the primary and secondary valencies of the central metal atom, respectively?(a) 2 and 4(b) 3 and 6(c) 3 and 4(d) 1 and 6
›Reveal solutionSolution
Primary valency corresponds to the oxidation state of the metal; secondary valency corresponds to the coordination number.
In [Co(C2O4)2(H2O)2]-, oxalate (C2O4^2-) is a bidentate ligand contributing 2 donor atoms each, and there are 2 water molecules (neutral, 1 donor atom each): total donor atoms = 2×2 + 2×1 = 6 → coordination number (secondary valency) = 6. …
- GUJCET 2021Set 151 markMCQQ.Which is not act as ligand? (A) NO (B) H2NCH2CH2NH2 (C) NH4+ (D) CO
›Reveal solutionSolution
NH₄⁺ cannot donate an electron pair (nitrogen's lone pair is used in the fourth N–H bond), so it is not a ligand.
Concept: A ligand must have a lone pair to donate to the metal. NO, ethylenediamine (H₂NCH₂CH₂NH₂) and CO all have donor lone pairs. I …
- GUJCET 2021Set 151 markMCQQ.Which type of Isomerism in isomers [Co(NH3)5(SO4)]Br and [Co(NH3)5Br]SO4? (A) Linkage (B) Ionisation (C) Coordination (D) Solvate
›Reveal solutionSolution
When a counter-ion and a ligand exchange places (inside vs outside the coordination sphere), giving different ions in solution, it is ionisation isomerism.
Concept: Ionisation isomers have the same composition but differ in which group is bound to the metal and which is the free counter-ion; they therefore give different ions on dissolving.
Here:
- [Co(NH3)5(SO4)]Br → sulfate is coordinated, Br− is the counter-ion (gives Br− in solution).
- [Co(NH3)5Br]SO4 → bromide is coordinated, SO42− is the counter-ion (gives SO42− in solution). …
- GUJCET 2020Set 071 markMCQQ.The complex having highest electrical conductivity in aqueous solution under similar conditions is ______. (A) Tetra aqua dichlorido cobalt (III) chloride (B) Triaqua trichlorido cobalt (III) (C) Penta aqua chlorido cobalt (III) chloride (D) Hexa aqua cobalt (III) chloride
›Reveal solutionSolution
[Co(H2O)6]Cl3 gives the most ions (4), so highest conductivity.
Concept — number of ions vs. conductivity. Molar conductivity rises with the number of free ions produced.
- (A) [CoCl2(H2O)4]Cl→ 2 ions
- (B) [CoCl3(H2O)3]→ neutral, 0 ions …
- GUJCET 2020Set 071 markMCQQ.Which soluble complex is formed in the leaching process of Gold? (A) [Au(OH)4]2− (B) [Au(CN)4]2− (C) [Au(OH)2]− (D) [Au(CN)2]−
›Reveal solutionSolution
Cyanide leaching of gold gives the soluble [Au(CN)2]−.
Concept — cyanide (MacArthur–Forrest) leaching. 4Au+8CN−+2H2O+O2→4[Au(CN)2]−+4OH−. Gold is Au(I) with coordination …
- GUJCET 2019Set 131 markMCQQ.The primary valency and secondary valency of central metal ion and the no. of total ions produced in aqueous solution for K[Co(OX)2(NH3)2] complex respectively is___ (A) 3, 6, 1 (B) 3, 6, 2 (C) 4, 4, 2 (D) 3, 4, 2
›Reveal solutionSolution
For K[Co(ox)2(NH3)2]: primary valency = 3, secondary valency = 6, ions in solution = 2.
Concept: Primary valency = oxidation state of the metal; secondary valency = coordination number; ionisation gives the counter-ion plus the complex ion.
Steps:
- Charge balance: complex ion charge is −1 (to balance K+). With oxalate =−2 each and NH3 neutral: x+2(−2)+0=−1⇒x=+3. Primary valency =3. …
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