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A formula such as CrCl₃·6H₂O hides the question that matters: how many of the three chlorides are bonded to the metal, and how many float free in water? Alfred Werner answered this kind of question for cobalt-ammonia compounds with silver nitrate and conductivity. Exam questions now ask you to do the same thing with numbers. This post shows three tests that count free ions, works them on chromium and cobalt compounds and lists the traps.
Where is this in the syllabus?
Werner's theory opens the NCERT Class 12 unit Coordination Compounds (reprint 2026-27), with the AgCl data, Table 5.1 and Example 5.1. The JEE (Main) 2026 syllabus and the NEET (UG) 2026 syllabus both list "Werner's theory" and isomerism, and the van 't Hoff factor in their solutions units. The JEE (Advanced) 2026 brochure names Werner's theory and ionisation isomerism. Check the current year's documents.
What does "ionisable" mean here?
NCERT's statement of Werner's postulates is the key. Primary valences "are normally ionisable"; secondary valences "are non ionisable" and equal the coordination number. In modern notation, everything inside the square brackets stays together in solution, and only the counter ions outside are free.
So for any complex, three numbers should agree:
moles of AgCl precipitated per mole of complex, with excess AgNO₃ in the cold
the electrolyte type from conductivity (1:1, 1:2, 1:3)
the van 't Hoff factor i, the number of particles per formula unit
NCERT's Table 5.1 shows the pattern for cobalt: [Co(NH₃)₆]Cl₃ is a 1:3 electrolyte, [CoCl(NH₃)₅]Cl₂ is 1:2 and [CoCl₂(NH₃)₄]Cl is 1:1. More ions per formula unit means higher molar conductivity at the same concentration.
Worked example 1: which chromium hydrate?
NCERT's section on solvate isomerism gives violet [Cr(H₂O)₆]Cl₃ and its grey-green isomer [Cr(H₂O)₅Cl]Cl₂·H₂O, both CrCl₃·6H₂O.
Sample numbers: 1.332 g of one isomer is dissolved and treated with excess AgNO₃, giving 1.433 g of AgCl.
Molar mass of CrCl₃·6H₂O = 52.00 + 3(35.453) + 6(18.015) ≈ 266.4 g/mol, so moles = 1.332 ÷ 266.4 = 0.00500 mol.
Molar mass of AgCl = 107.87 + 35.45 = 143.32 g/mol, so moles of AgCl = 1.433 ÷ 143.32 = 0.0100 mol.
Ratio = 0.0100 ÷ 0.00500 = 2. Two chlorides are free.
Formula: [CrCl(H₂O)₅]Cl₂·H₂O, the grey-green isomer.
The violet isomer would give three chlorides, 0.0150 mol or 2.15 g of AgCl. A third arrangement with only one free chloride, [CrCl₂(H₂O)₄]Cl·2H₂O, would give 0.00500 mol, or 0.717 g.
Worked example 2: freezing point as a cross-check
The NCERT Class 12 unit Solutions gives ΔTf = i Kf m, with Kf = 1.86 K kg/mol for water.
Sample numbers: a 0.010 mol/kg solution of CoCl₃·5NH₃ freezes 0.050 K below pure water.
i = ΔTf ÷ (Kf m) = 0.050 ÷ (1.86 × 0.010) ≈ 2.7.
That is closest to 3 particles: one complex ion and two chlorides, so [CoCl(NH₃)₅]Cl₂, matching NCERT's 1:2 electrolyte.
Why 2.7 and not 3? Real solutions fall short of complete dissociation values. NCERT's Table 1.4 shows K₂SO₄, which also gives three ions, with i = 2.70 at 0.01 m. A result near 2.7 rules out two particles, which could give at most 0.037 K. Our post on colligative properties covers i in more detail.
Worked example 3: telling ionisation isomers apart
NCERT gives [Co(NH₃)₅(SO₄)]Br and [Co(NH₃)₅Br]SO₄. Both are 1:1 electrolytes, so conductivity alone cannot separate them. A precipitation test can:
With AgNO₃, only the first gives a precipitate, because its bromide is outside the bracket.
With BaCl₂, only the second gives BaSO₄. Sample numbers: 0.0100 mol of it gives 0.0100 mol of BaSO₄ (233.4 g/mol), or 2.33 g.
Which mistakes cost marks?
Assuming every chloride precipitates. Only those outside the bracket do.
Forgetting the cold, excess AgNO₃ condition in Werner's data.
Counting lattice water as a ligand.
Treating a non-electrolyte, such as NCERT's PtCl₂·2NH₃ in Example 5.1, which gives no AgCl, as a mistake in the question. Zero free chlorides is a valid answer.
Confusing the coordination number with the oxidation state.
The history behind these tests is in our post on Alfred Werner, who published his paper on the constitution of inorganic compounds in 1893.
When the octahedral picture of what sits inside the bracket feels hazy, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, each with its own lesson and its place in the map.
A practice routine
For each compound in NCERT Example 5.1, write the formula with brackets from the AgCl count.
For five complexes, predict moles of AgCl, electrolyte type and ideal i, and check that all three agree.
Work one freezing point problem and one BaCl₂ or AgNO₃ test with your own sample numbers.
Name ten complexes after bracketing them, using our guide to naming coordination compounds.
Today, take CoCl₃·4NH₃ and write down the AgCl moles, electrolyte type and ideal i you would expect.
