Assigning cobalt(III) ammine chloride formulas from conductivity and chloride titration
Three violet solids, A, B and C, are submitted for identification; the bottle labels have been lost and these are the only cobalt complexes in the store. Each contains cobalt(III), ammonia and chloride only. A stock solution of each is prepared to be 1.00×10−3 M in the complex. Molar conductivities in water are A 402, B 261 and C 98 S cm2 mol−1. On adding excess AgNO3, 1.00 mmol of A gives 3.00 mmol AgCl, 1.00 mmol of B gives 2.00 mmol, and 1.00 mmol of C gives 1.00 mmol. All three are diamagnetic at room temperature. The supervisor suspects A = [Co(NH3)6]Cl3, B = [Co(NH3)5Cl]Cl2 and C = [Co(NH3)4Cl2]Cl, but asks for evidence rather than formula matching. C is also reported to exist as two isomers of the same conductivity, and the laboratory has conductance and magnetic susceptibility data only, with no single-crystal X-ray diffractometer.
1. Use the conductivity and AgCl precipitation data to justify the formula assignments. Explain why conductance alone would not be enough.
Read the worked answer
AgNO3 counts only chloride ions outside the coordination sphere. A gives 3 mol AgCl per mol complex, so it has three ionisable Cl−:
[Co(NH3)6]Cl3 → [Co(NH3)6]3+ + 3Cl−
B gives 2 mol AgCl, so it has two ionisable Cl−:
[Co(NH3)5Cl]Cl2 → [Co(NH3)5Cl]2+ + 2Cl−
C gives 1 mol AgCl, so it has one ionisable Cl−:
[Co(NH3)4Cl2]Cl → [Co(NH3)4Cl2]+ + Cl−
The conductance order 402 > 261 > 98 S cm2 mol−1 follows the number of ions per formula unit, 4 > 3 > 2, so the two measurements agree. Conductance alone would not prove the structures because it gives only the number of ions, not which ligands are inside the coordination sphere. The AgCl titre supplies that internal/external distinction.
2. Explain why all three complexes are diamagnetic using crystal-field reasoning. Does the result distinguish the three formulas?
Read the worked answer
Co(III) is d6. In an octahedral field Co3+ has a large Δo because of its high charge, so the sixth electron pairs in the t2g set: t2g6 eg0. All electrons are paired, μ = 0, hence diamagnetic. This remains true for [Co(NH3)4Cl2]+ even though Cl− is a weaker-field ligand than NH3, because Co3+ is sufficiently high-charged to remain low-spin.
The result does not distinguish A, B and C. All three are Co(III) low-spin complexes with the same d6 count, so all are diamagnetic. The magnetic measurement supports the oxidation/spin state, not the coordination-sphere composition.
3. C exists as two isomers of the same conductivity. Identify the isomerism and explain whether conductivity can distinguish the isomers. What measurement would?
Read the worked answer
C exists as cis- and trans-[Co(NH3)4Cl2]+. Both are 1:1 electrolytes and both give exactly one free Cl− per formula unit, so their molar conductivities and AgCl titres are essentially identical. Conductivity cannot distinguish them.
The cis isomer has a net dipole moment; the trans isomer is centrosymmetric and has zero dipole moment. Dipole moment measurement, or IR/Raman or electronic spectra, can distinguish them. If the question asks which isomer has higher conductivity, the answer is that the difference is too small and unreliable; the number of ions is the same.