The d- and f- Block Elements Set-8

Q1. Calculate the spin-only magnetic moment (in Bohr magneton, BM) of the octahedral complex $[Fe(H_2O)_6]^{2+}$. Assume $H_2O$ is a weak-field ligand and use the spin-only formula $\mu=\sqrt{n(n+2)}$, where $n$ is the number of unpaired electrons.

Q2. For the octahedral complexes $[CoF_6]^{3-}$ and $[Co(CN)_6]^{3-}$ (metal ion $Co^{3+}$, $d^6$), predict which complex is paramagnetic and state the spin-only magnetic moment (in BM) of the paramagnetic one. Assume $F^-$ is a weak-field ligand and $CN^-$ is a strong-field ligand.

Q3. For high-spin octahedral complexes of the 3d metal ions $Mn^{2+}\;(d^5)$, $Fe^{2+}\;(d^6)$, $Co^{2+}\;(d^7)$ and $Ni^{2+}\;(d^8)$, using the CFSE expression $\mathrm{CFSE}=(-0.4\,n_{t_{2g}}+0.6\,n_{e_g})\Delta_o$ (neglect pairing-energy differences), which ion's complex has the largest stabilization (most negative CFSE)?

Q4. Which of the following statements about Jahn–Teller distortion in the octahedral complexes $[Cu(H_2O)_6]^{2+}$ and $[Cr(H_2O)_6]^{3+}$ is correct? ($Cu^{2+}$ is $d^9$, $Cr^{3+}$ is $d^3$.)

Q5. Predict the geometry and magnetic behaviour (number of unpaired electrons) of $[Ni(CN)_4]^{2-}$ and $[NiCl_4]^{2-}$ (Ni$^{2+}$, $d^8$).

Q6. The spin-only magnetic moment (in Bohr magneton, BM) of the complex $[Cr(H_2O)_6]^{2+}$ is:

Q7. Both $[CoF_6]^{3-}$ and $[Co(CN)_6]^{3-}$ contain Co in the +3 oxidation state (d$^6$). Which complex will have the lower spin-only magnetic moment?

Q8. Two octahedral complexes of Cr(II) (d$^4$) are formed: L1 gives a low-spin d$^4$ configuration (strong-field, $\Delta_0>P$) and L2 gives a high-spin d$^4$ configuration (weak-field, $\Delta_0<P$). Using $E_{CFSE}=(-0.4\,n_{t_{2g}}+0.6\,n_{e_g})\Delta_0$ and pairing energy $P$ per electron pair, if $\Delta_0=1.5P$, which complex is more easily oxidised to Cr(III) (d$^3$)?

Q9. Which of the following lanthanoid oxides is expected to be the most basic (i.e., react most readily with water to give the hydroxide)? Consider lanthanide contraction and ionic character of the oxide.

Q10. Among the trivalent ions Ce$^{3+}$, Eu$^{3+}$, Gd$^{3+}$ and Yb$^{3+}$, which ion has the largest paramagnetic moment based on Hund’s rule and the spin-only formula $\mu_{spin}=\sqrt{n(n+2)}$ (where $n$ is the number of unpaired electrons)?

Q11. Using the spin-only formula $\mu=\sqrt{n(n+2)}$ (where $n$ is the number of unpaired electrons), calculate the spin-only magnetic moment (in Bohr magneton, BM) for the high-spin octahedral ion $Mn^{2+}$ with electronic configuration $[Ar]\,3d^5$.

Q12. Assume $CN^-$ is a strong-field ligand (low-spin) and $H_2O$ is a weak-field ligand (high-spin). For $[Fe(CN)_6]^{3-}$ and $[Fe(H_2O)_6]^{3+}$ (both contain $Fe^{3+}$, $d^5$), use $\mu=\sqrt{n(n+2)}$ to estimate the ratio $\dfrac{\mu([Fe(CN)_6]^{3-})}{\mu([Fe(H_2O)_6]^{3+})}$. Which is closest to the correct value?

Q13. Calculate the crystal field stabilization energy (CFSE) in terms of $\Delta_o$ (ignore pairing energy) for $[Cr(H_2O)_6]^{3+}$ (Cr$^{3+}$, $d^3$) and $[Co(H_2O)_6]^{2+}$ (Co$^{2+}$, $d^7$, high-spin). Which complex has the greater CFSE and by how much?

Q14. For the redox couple $M^{3+}/M^{2+}$, the standard potential is $E^\circ=0.50\ \mathrm{V}$. Ligand $L$ forms 1:1 complexes with formation constants $\beta_2=10^{4}$ for $M^{2+}+L\rightleftharpoons ML^{2+}$ and $\beta_3=10^{8}$ for $M^{3+}+L\rightleftharpoons ML^{3+}$. At $298\ \mathrm{K}$ the standard potential $E'^\circ$ for the couple $ML^{3+}/ML^{2+}$ is approximately (use $0.059\ \mathrm{V}$ for $RT/F\cdot\ln10$ per electron):

Q15. Assertion (A): The ionic radii and most chemical properties of $\mathrm{Zr}$ and $\mathrm{Hf}$ are nearly identical.
Reason (R): The lanthanide contraction, arising because $4f$ electrons poorly shield the increasing nuclear charge, reduces the expected increase in size across the lanthanide series and makes $5d$ elements like $\mathrm{Hf}$ comparable in size to corresponding $4d$ elements like $\mathrm{Zr}$.
Choose the correct option.