Three chromium(III) chloride hydrates: AgCl titres, conductance and a magnetic proposal that cannot work
Three samples labelled A, B and C all analyse to the same formula, CrCl3·6H2O, but differ in colour (violet, blue-green and dark green) and in behaviour towards silver nitrate. For each, a 0.0100 mol sample is dissolved in cold water and treated with excess AgNO3: A gives 0.0300 mol AgCl, B gives 0.0200 mol and C gives 0.0100 mol. Molar conductances at the same dilution are approximately 430, 260 and 130 S cm2 mol−1 respectively. A student proposes to settle the structures by measuring magnetic moments, expecting the three solids to differ because 'the number of chloride ligands changes the crystal-field splitting'. The laboratory also has to resolve a batch of the cation present in C into its stereoisomers. Decide the structures from the precipitation and conductance data, test the student's magnetic proposal, and say what isomerism the cation in C can show.
1. Assign a structure to A, B and C, and justify each assignment from the AgCl and conductance data.
Read the worked answer
Count the ionic chlorides. Only chloride outside the coordination sphere is precipitated rapidly and completely by Ag+. A gives 3 Cl− per formula unit, B gives 2 and C gives 1, so the coordination spheres must be [Cr(H2O)6]3+, [Cr(H2O)5Cl]2+ and [Cr(H2O)4Cl2]+ respectively:
- A: [Cr(H2O)6]Cl3 - 1:3 electrolyte, highest conductance (~430 S cm2 mol−1).
- B: [Cr(H2O)5Cl]Cl2·H2O - 1:2 electrolyte, intermediate conductance (~260).
- C: [Cr(H2O)4Cl2]Cl·2H2O - 1:1 electrolyte, lowest conductance (~130).
Reasoning check. The conductance ratio 430 : 260 : 130 ≈ 3 : 2 : 1 is exactly what is expected for 1:3, 1:2 and 1:1 electrolytes at the same dilution, so the two independent measurements agree. These are hydrate (solvate) isomers: same overall formula CrCl3·6H2O, different distribution of water and chloride between the inner sphere and the lattice. Gentle heating of B and C drives off lattice water without changing the coordination sphere; A loses HCl on strong heating, not water.
2. Evaluate the student's plan to distinguish the three solids by magnetic moment. Support your answer with the spin-only formula.
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The plan fails. In every one of the three compounds the metal is Cr(III), d3, octahedral. The d3 configuration places three electrons in the t2g set: t2g^3. There is no low-spin/high-spin choice, because the eg set is empty and pairing the t2g electrons would require Δo to be overcome with no compensating stabilisation - that never happens for d3. Chloride versus water in the inner sphere changes Δo and hence colour, but not the number of unpaired electrons.
Spin-only moment: μ = √(n(n + 2)) = √(3 × 5) = √15 ≈ 3.87 BM, the same for A, B and C (small orbital contributions may shift observed values slightly, but not enough to distinguish them).
What magnetism would detect. It would separate Cr(III) from Cr(II) (d4, high-spin, ~4.9 BM) or from a Cr(VI) contaminant (d0, diamagnetic), so it is still a useful purity check - just not a structural probe here. Structure must come from the AgCl titration and conductance, which the student already has. The lesson: a technique is only diagnostic if the property it measures actually changes between the candidates.
3. What stereoisomerism can the cation in C show? Explain which isomer is optically active and how you would prove it experimentally.
Read the worked answer
C contains the octahedral ion [Cr(H2O)4Cl2]+, i.e. [CrCl2(H2O)4]+ (or written as its isomer). With two identical ligands and four identical ligands it gives two geometrical isomers:
- trans-[CrCl2(H2O)4]+: the two Cl are opposite; the ion has a plane of symmetry and is achiral.
- cis-[CrCl2(H2O)4]+: the two Cl are adjacent; the ion lacks a plane and a centre of symmetry, so it exists as a pair of non-superimposable mirror images (Δ and Λ), i.e. it is optically active.
Thus there are three stereoisomers in total: one trans (achiral) and a cis enantiomeric pair.
Experimental proof. Prepare a solution of pure cis isomer, measure optical rotation in a polarimeter; the two enantiomers rotate plane-polarised light equally but in opposite directions. If the sample is racemic, rotation is zero; resolution (e.g. by forming a diastereomeric salt with an optically pure counter-ion, or by chiral chromatography) is needed to observe rotation. Note that cis and trans also differ in dipole moment and in colour, but only rotation distinguishes the enantiomers.