Solved Examples (Dedicated Problem Set)

How to Use This Problem Set

This is your full workout for the d- and f-block, grouped by theme: electronic configurations, oxidation states and stability, spin-only magnetic moments, the dichromate and permanganate oxidising reactions, and lanthanoid-contraction reasoning.

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).
• Acidified dichromate gains 6 e$^-$; acidified permanganate gains 5 e$^-$.
• Ions lose ns before (n-1)d electrons. Cr = $3d^5 4s^1$, Cu = $3d^{10} 4s^1$.

Solved Examples — Configurations

Example 1. Configuration of Cr (Z=24)?

Solution: $[\text{Ar}]\,3d^5 4s^1$ (half-filled stability).

Example 2. Configuration of Cu$^{2+}$ (Z=29)?

Solution: Cu is $[\text{Ar}]\,3d^{10}4s^1$; Cu$^{2+}$ = $[\text{Ar}]\,3d^9$.

Example 3. Configuration of Fe$^{3+}$ (Z=26)?

Solution: $[\text{Ar}]\,3d^5$ (stable half-filled).

Solved Examples — Configurations & States

Example 4. Why is Zn not a typical transition metal?

Solution: Zn$^{2+}$ is $3d^{10}$ — a completely filled d subshell, so no partially filled d in atom or common ion.

Example 5. Maximum oxidation state of Mn and where it appears?

Solution: +7, in $\text{MnO}_4^-$ and $\text{Mn}_2\text{O}_7$.

Example 6. Which is more stable to oxidation, Mn$^{2+}$ or Fe$^{2+}$?

Solution: Mn$^{2+}$ ($3d^5$, half-filled) is more stable; Fe$^{2+}$ ($3d^6$) is readily oxidised to Fe$^{3+}$ ($d^5$).

Solved Examples — Magnetic Moments

Example 7. Spin-only moment of Mn$^{2+}$ ($d^5$)?

Solution: $n=5$; $\mu = \sqrt{35} = 5.92$ BM.

Example 8. Spin-only moment of Ti$^{3+}$ ($d^1$)?

Solution: $n=1$; $\mu = \sqrt{3} = 1.73$ BM.

Example 9. An ion shows $\mu = 4.90$ BM. Number of unpaired electrons?

Solution: $n(n+2)=24 \Rightarrow n=4$ (a $d^4$ or $d^6$ high-spin ion).

Solved Examples — Magnetic Moments (continued)

Example 10. Spin-only moment of Ni$^{2+}$ ($d^8$)?

Solution: $n=2$; $\mu = \sqrt{8} = 2.83$ BM.

Example 11. Spin-only moment of Co$^{2+}$ (Z=27)?

Solution: Co$^{2+}$ = $3d^7$, $n=3$; $\mu = \sqrt{15} = 3.87$ BM.

Example 12. Which is diamagnetic: Sc$^{3+}$, Cu$^{2+}$ or Fe$^{3+}$?

Solution: Sc$^{3+}$ ($3d^0$) — no unpaired electrons, $\mu = 0$.

Solved Examples — Colour & Stability

Example 13. Why is Sc$^{3+}$ colourless?

Solution: $3d^0$ — no d-d transition possible.

Example 14. Why is Cu$^+$ unstable in water?

Solution: It disproportionates: $2\text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu}$ (high hydration energy of Cu$^{2+}$).

Example 15. Both Cr$^{2+}$ and Mn$^{3+}$ are $d^4$; which is reducing?

Solution: Cr$^{2+}$ is reducing (oxidises to stable Cr$^{3+}$, $d^3$); Mn$^{3+}$ is oxidising (reduces to stable Mn$^{2+}$, $d^5$).

Solved Examples — Dichromate

Example 16. Oxidation state of Cr in $\text{Cr}_2\text{O}_7^{2-}$?

Solution: $2x - 14 = -2 \Rightarrow x = +6$.

Example 17. Electrons gained by acidified dichromate per ion?

Solution: 6 ($\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}$).

Example 18. Equivalent mass of $\text{K}_2\text{Cr}_2\text{O}_7$ (M=294) in acid?

Solution: $294/6 = 49$ g equiv$^{-1}$.

Solved Examples — Permanganate

Example 19. Oxidation state of Mn in $\text{MnO}_4^-$?

Solution: $x - 8 = -1 \Rightarrow x = +7$.

Example 20. Electrons gained by $\text{MnO}_4^-$ in acidic, neutral and alkaline media?

Solution: 5 (Mn$^{2+}$), 3 (MnO$_2$), 1 (MnO$_4^{2-}$) respectively.

Example 21. Equivalent mass of $\text{KMnO}_4$ (M=158) in acid?

Solution: $158/5 = 31.6$ g equiv$^{-1}$.

Solved Examples — Permanganate & f-Block

Example 22. Why is $\text{MnO}_4^-$ coloured though Mn is $d^0$?

Solution: Charge-transfer (O → Mn) transition, not d-d.

Example 23. Most stable oxidation state of lanthanoids?

Solution: +3.

Example 24. What is the lanthanoid contraction caused by?

Solution: Poor shielding by the 4f electrons, raising effective nuclear charge across the series.

Solved Examples — f-Block (continued)

Example 25. One consequence of the lanthanoid contraction?

Solution: Nearly equal radii of the 4d and 5d series (e.g. Zr and Hf).

Example 26. Why do actinoids show more oxidation states than lanthanoids?

Solution: Close energies of 5f, 6d and 7s orbitals allow more electrons to bond.

Example 27. Why is Ce$^{4+}$ a good oxidising agent?

Solution: Ce$^{4+}$ is readily reduced to Ce$^{3+}$; the +4 state is strongly oxidising because Ce$^{3+}$ is more stable in aqueous solution.

Solved Examples — Mixed

Example 28. Configuration of Mn$^{2+}$ and its number of unpaired electrons?

Solution: $[\text{Ar}]\,3d^5$; 5 unpaired electrons.

Example 29. Why are transition metals good catalysts (two reasons)?

Solution: Variable oxidation states (electron transfer) and surface adsorption of reactants.

Example 30. Colour change when acidified dichromate is reduced?

Solution: Orange → green (Cr$^{6+}$ → Cr$^{3+}$).

Example 31. Which 3d metal has a positive $E^\circ(\text{M}^{2+}/\text{M})$?

Solution: Copper (+0.34 V).