Solved Examples (Dedicated Problem Set)

How to Use This Problem Set

This is your full workout for Coordination Compounds, grouped by theme: oxidation number and coordination number, IUPAC nomenclature, isomerism, VBT (hybridisation and magnetic moment), and CFT (splitting, high/low spin, CFSE).

Keep these handy:

• Spin-only moment: $\mu = \sqrt{n(n+2)}$ BM (1.73, 2.83, 3.87, 4.90, 5.92 for $n=1$ to 5).
• VBT: $sp^3$ tetrahedral, $dsp^2$ square planar, $sp^3d^2$ outer octahedral, $d^2sp^3$ inner octahedral.
• Spectrochemical (weak to strong): I$^-$ < Cl$^-$ < F$^-$ < H$_2$O < NH$_3$ < en < CN$^-$ < CO.
• Octahedral CFSE $= (-0.4\,n_{t_{2g}} + 0.6\,n_{e_g})\Delta_o$.

Solved Examples - Oxidation & Coordination Number

Example 1. Oxidation number of Fe in K$_4$[Fe(CN)$_6$]?

Solution: In $[\text{Fe(CN)}_6]^{4-}$, let oxidation state of Fe be $x$. Since each CN$^-$ is $-1$, $x-6=-4\Rightarrow x=+2$.

Example 2. Coordination number of Co in [Co(en)$_3$]$^{3+}$?

Solution: en is bidentate, so $3\times 2=6$.

Example 3. Oxidation number of Pt in [Pt(NH$_3$)$_2$Cl$_2$]?

Solution: NH$_3$ is neutral and 2 Cl$^-$ contribute $-2$. For a neutral complex, $x-2=0\Rightarrow x=+2$.

Solved Examples - Nomenclature

Example 4. IUPAC name of [Co(NH$_3$)$_6$]Cl$_3$?

Solution: hexaamminecobalt(III) chloride.

Example 5. IUPAC name of K$_3$[Fe(CN)$_6$]?

Solution: potassium hexacyanidoferrate(III).

Example 6. Formula for tetraamminecopper(II) sulphate?

Solution: [Cu(NH$_3$)$_4$]SO$_4$.

Solved Examples - Isomerism

Example 7. What isomerism does [Co(NH$_3$)$_5$(NO$_2$)]$^{2+}$ show?

Solution: Linkage isomerism, because NO$_2^-$ is ambidentate and can coordinate through N (nitro) or O (nitrito).

Example 8. How many geometric isomers does [Co(NH$_3$)$_4$Cl$_2$]$^+$ have?

Solution: Two: cis and trans.

Example 9. Total stereoisomers of [Co(en)$_2$Cl$_2$]$^+$?

Solution: 3: trans is one form, and cis exists as an enantiomeric pair.

Solved Examples - VBT

Example 10. Hybridisation and magnetism of [Co(NH$_3$)$_6$]$^{3+}$?

Solution: Co$^{3+}$ is $d^6$. With NH$_3$ and the +3 oxidation state, the complex is low spin and uses $d^2sp^3$ hybridisation, octahedral geometry, 0 unpaired electrons, and is diamagnetic.

Example 11. Hybridisation of [NiCl$_4$]$^{2-}$?

Solution: Ni$^{2+}$ is $d^8$. With weak-field Cl$^-$ ligands, it is $sp^3$, tetrahedral, with 2 unpaired electrons, so it is paramagnetic.

Example 12. Hybridisation of [Ni(CN)$_4$]$^{2-}$?

Solution: Ni$^{2+}$ is $d^8$. With strong-field CN$^-$, it is $dsp^2$, square planar, with 0 unpaired electrons, so it is diamagnetic.

Solved Examples - VBT Magnetic Moments

Example 13. Spin-only moment of [NiCl$_4$]$^{2-}$?

Solution: It has 2 unpaired electrons, so $\mu = \sqrt{2(2+2)} = \sqrt{8} = 2.83$ BM.

Example 14. Spin-only moment of [Fe(CN)$_6$]$^{3-}$?

Solution: Fe$^{3+}$ is $d^5$. CN$^-$ is strong-field, so the complex is low spin with 1 unpaired electron. Hence $\mu = \sqrt{1(1+2)} = \sqrt{3} = 1.73$ BM.

Example 15. Spin-only moment of [Fe(H$_2$O)$_6$]$^{3+}$?

Solution: Fe$^{3+}$ is $d^5$. H$_2$O is weak-field, so the complex is high spin with 5 unpaired electrons. Hence $\mu = \sqrt{5(5+2)} = \sqrt{35} = 5.92$ BM.

Solved Examples - CFT

Example 16. t$_{2g}$/e$_g$ configuration of low-spin $d^6$?

Solution: $t_{2g}^6 e_g^0$, with 0 unpaired electrons.

Example 17. Unpaired electrons in [Mn(H$_2$O)$_6$]$^{2+}$?

Solution: Mn$^{2+}$ is $d^5$. H$_2$O is weak-field, so the complex is high spin with 5 unpaired electrons.

Example 18. CFSE of an octahedral $d^3$ ion (in $\Delta_o$)?

Solution: $t_{2g}^3$: $3(-0.4\Delta_o) = -1.2\Delta_o$.

Solved Examples - CFT & Colour

Example 19. Is [Fe(CN)$_6$]$^{4-}$ high or low spin?

Solution: Fe$^{2+}$ is $d^6$. CN$^-$ is strong-field, so it is low spin with configuration $t_{2g}^6$ and 0 unpaired electrons.

Example 20. Why is [Zn(H$_2$O)$_6$]$^{2+}$ colourless?

Solution: Zn$^{2+}$ is $d^{10}$, so no $d$–$d$ transition is possible.

Example 21. Which absorbs shorter-wavelength light: aqua or cyanido complex of the same metal?

Solution: The cyanido complex, because stronger-field ligands produce a larger $\Delta_o$, so they absorb higher-energy, shorter-wavelength light.

Solved Examples - Stability & Applications

Example 22. Why is [Ni(en)$_3$]$^{2+}$ more stable than [Ni(NH$_3$)$_6$]$^{2+}$?

Solution: Because of the chelate effect, which gives a favourable entropy increase.

Example 23. Oxidation state of Ni in Ni(CO)$_4$?

Solution: 0, because CO is neutral and the molecule is neutral.

Example 24. Central metal in chlorophyll?

Solution: Magnesium (Mg).

Solved Examples - Mixed

Example 25. Coordination number of Pt in [PtCl$_6$]$^{2-}$?

Solution: 6, because there are six unidentate Cl$^-$ ligands.

Example 26. Number of ions from [Co(NH$_3$)$_6$]Cl$_3$ in solution?

Solution: 4 ions: one complex cation and three Cl$^-$ ions.

Example 27. Hybridisation of octahedral [CoF$_6$]$^{3-}$?

Solution: Co$^{3+}$ is $d^6$. F$^-$ is weak-field, so the complex is outer orbital, $sp^3d^2$, with 4 unpaired electrons.

Example 28. Geometry of [Ni(CO)$_4$]?

Solution: Tetrahedral, with $sp^3$ hybridisation; Ni is in oxidation state 0 and the complex is diamagnetic.

Solved Examples - Mixed (continued)

Example 29. IUPAC name of [Ni(CO)$_4$]?

Solution: tetracarbonylnickel(0).

Example 30. Which is optically active: cis or trans [Co(en)$_2$Cl$_2$]$^+$?

Solution: cis, because the trans form has a plane of symmetry.

Example 31. Spin-only moment of [Ti(H$_2$O)$_6$]$^{3+}$ (Ti$^{3+}$, $d^1$)?

Solution: It has 1 unpaired electron, so $\mu = \sqrt{1(1+2)} = \sqrt{3} = 1.73$ BM.

Example 32. Denticity of EDTA$^{4-}$?

Solution: Hexadentate, because it can bind through 6 donor atoms.