Three Unlabelled Cobalt(III) Ammine Bottles
A college stockroom has three unlabelled bottles known to contain cobalt(III) ammine complexes with the formulae [Co(NH3)6]Cl3, [Co(NH3)5Cl]Cl2 and [Co(NH3)4Cl2]Cl, but the labels have peeled off. The available equipment is limited to distilled water, a conductivity meter, 0.1 M AgNO3 solution and a Gouy balance; no spectrometer is working. Three 0.01 M aqueous solutions, P, Q and R, are prepared. Their measured molar conductances fall in the order P > Q > R. On adding excess AgNO3 to one mole of each complex, P gives 3 mol, Q gives 2 mol and R gives 1 mol of AgCl. A student proposes to identify the cis and trans forms of one of these complexes by magnetic measurement, and is told that only one of the three complexes can exist as cis–trans isomers at all.
1. Assign each solution to a formula, justifying the assignment from both measurements.
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The decisive idea is that only chloride ions outside the coordination sphere ionise in water, so only they are precipitated immediately by AgNO3 at room temperature; coordinated chloride is held by the metal and is not free.
- P gives 3 mol AgCl per mole → all three chlorides are ionic → 4 ions per formula unit → [Co(NH3)6]Cl3.
- Q gives 2 mol AgCl → two ionic chlorides, one coordinated → 3 ions per formula unit → [Co(NH3)5Cl]Cl2.
- R gives 1 mol AgCl → one ionic chloride, two coordinated → 2 ions per formula unit → [Co(NH3)4Cl2]Cl.
The conductance order P > Q > R is exactly what the ion counts predict: molar conductance of an electrolyte rises with both the number of ions and their charge, so the 1:3 electrolyte with four ions conducts best and the 1:1 electrolyte with two ions least. The two measurements are therefore independent and mutually consistent, which is what makes the assignment safe. A strong answer states the caveat that conductance also depends on ion size and mobility, so it is used as corroboration and the AgCl count is treated as the primary evidence.
2. Which complex can show cis–trans isomerism, and how would you establish which isomer is optically active without a polarimeter-grade instrument?
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Only [Co(NH3)4Cl2]Cl, i.e. R, can show geometrical isomerism. Octahedral [Co(NH3)4Cl2]⁺ has two possible arrangements of the two Cl ligands: adjacent (cis) and opposite (trans).
In the trans isomer the two Cl and the four NH3 lie in mutually perpendicular planes; the complex possesses a plane of symmetry (and an inversion centre), so it is superimposable on its mirror image - achiral and optically inactive. In the cis isomer the two Cl are adjacent; the complex has no plane or centre of symmetry, so it is chiral and exists as a pair of enantiomers (Δ and Λ) that are non-superimposable mirror images. Only the cis form rotates plane-polarised light.
For [Co(NH3)5Cl]Cl2 (Q) there is no geometrical isomerism: five identical NH3 ligands occupy five sites and the sixth must be Cl, so only one arrangement exists - a common error is to expect cis/trans here. [Co(NH3)6]Cl3 likewise has only one form.
Practical check without a polarimeter: separate the two forms (they differ in colour and in dipole moment) and compare their reactions with a chiral or optically active reagent, or simply note that the cis form has a significant dipole moment whereas the trans form does not, so the cis isomer is much more soluble in polar solvents. Optical activity is then inferred from the existence of the enantiomeric pair rather than measured directly.
3. The student proposes to use the Gouy balance to tell the three apart. Evaluate this proposal.
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The proposal will not work, and the reason is worth spelling out. In all three complexes the metal is cobalt(III), a d⁶ ion. NH3 and Cl⁻ both lie towards the strong-field end of the spectrochemical series, so Δo exceeds the pairing energy P and the configuration is low-spin t2g⁶ eg⁰. Every electron is paired, the complexes are diamagnetic, and the measured magnetic moment is essentially zero for all three. A Gouy balance would therefore give identical readings and could not distinguish P, Q and R.
The measurement would only become useful if the oxidation state changed. A cobalt(II) complex is d⁷; in an octahedral field that gives t2g⁶ eg¹ with one unpaired electron and a spin-only moment of about 1.7–1.9 BM (higher if orbital contribution or tetrahedral geometry is involved). So magnetic measurement is a good probe of oxidation state and spin state, not of the number of ionisable chlorides.
The correct division of labour is: AgNO3 precipitation and conductance count the ions and hence locate the chlorides; magnetic measurement establishes spin state and, indirectly, the field strength of the ligands. The student has confused two different structural questions, and the answer should say which technique answers which.