The d- and f- Block Elements Set-5

$1.73\ \mathrm{BM}$

$2.83\ \mathrm{BM}$

$3.87\ \mathrm{BM}$

$5.92\ \mathrm{BM}$

$[Cu(H_2O)_6]^{2+}$

$[Mn(H_2O)_6]^{2+}$

$[V(H_2O)_6]^{2+}$

$[Fe(H_2O)_6]^{2+}$

0 and 5

3 and 3

2 and 4

5 and 1

$Fe^{3+}$ has greater electron–electron repulsion in the $3d^5$ configuration, so it has a larger ionic radius than $Mn^{2+}$.

$Fe^{3+}$ has higher effective nuclear charge (one extra proton) for the same number of electrons, so electrons are held more tightly and the radius is smaller.

$Mn^{2+}$ has more shielding electrons than $Fe^{3+}$, so it is larger.

$Fe^{3+}$ is larger because increased electron–electron repulsion in $3d^5$ overcomes the higher nuclear attraction.

$Ce^{3+}\ (4f^1)$

$Pr^{3+}\ (4f^2)$

$Gd^{3+}\ (4f^7)$

$Yb^{3+}\ (4f^{13})$

4 unpaired electrons; $\mu_{\text{spin}}=4.90\ \mathrm{BM}$

3 unpaired electrons; $\mu_{\text{spin}}=3.87\ \mathrm{BM}$

5 unpaired electrons; $\mu_{\text{spin}}=5.92\ \mathrm{BM}$

2 unpaired electrons; $\mu_{\text{spin}}=2.83\ \mathrm{BM}$

$Lu^{3+}$ — due to lanthanide contraction $Lu^{3+}$ has a smaller ionic radius and higher charge density, so its hydration enthalpy is more negative.

$La^{3+}$ — larger ionic radius allows coordination of more water molecules, making its hydration enthalpy more negative.

Both have nearly equal hydration enthalpies because both carry the same $+3$ charge.

$La^{3+}$ — lanthanide contraction reduces interaction of heavier lanthanides with water, so lighter ones like La have more negative hydration enthalpy.

$[Ni(CN)_4]^{2-}$ — square planar d$^8$ with CN$^-$ (strong field), expected to be diamagnetic

$[Fe(CN)_6]^{4-}$ — Fe$^{2+}$ (d$^6$) with strong-field CN$^-$, expected to be low-spin diamagnetic

$[Co(NH_3)_6]^{3+}$ — Co$^{3+}$ (d$^6$) with NH$_3$, expected to be low-spin diamagnetic

$[Mn(H_2O)_6]^{2+}$ — Mn$^{2+}$ (d$^5$) with weak-field H$_2$O, expected to be high-spin and paramagnetic

$Mn^{3+}$ has a fully filled $d$-subshell making it electronically unstable and prone to disproportionation.

$Mn^{3+}$ in octahedral complexes is often high-spin $d^4$, which is Jahn–Teller active; the resulting electronic/vibrational instability lowers its stability and favours disproportionation to $Mn^{2+}$ ($d^5$) and $Mn^{4+}$ ($d^3$).

The hydration enthalpy of $Mn^{3+}$ is excessively exothermic, so it disproportionates to reduce hydration energy.

The ionization energy of $Mn^{3+}$ is unusually low, so it readily loses an electron to form $Mn^{4+}$ and thus disproportionates.

$Ti^{3+}$ — lower oxidation state leads to reduced shielding and therefore larger $\Delta_0$

Both will have identical $\Delta_0$ because they are isoelectronic ($d^1$)

$V^{4+}$ — higher effective nuclear charge and smaller ionic radius give stronger metal–ligand overlap and thus a larger $\Delta_0$

$Ti^{3+}$ — although $V^{4+}$ has higher charge, the stronger attraction in $V^{4+}$ weakens effective metal–ligand overlap due to ligand distortion, giving a smaller $\Delta_0$

$0.00\ \mathrm{BM}$

$3.87\ \mathrm{BM}$

$5.92\ \mathrm{BM}$

$4.90\ \mathrm{BM}$

High-spin favored; high-spin more stable by $40\ \mathrm{kJ\,mol^{-1}}$

Low-spin favored; low-spin more stable by $40\ \mathrm{kJ\,mol^{-1}}$

High-spin favored; high-spin more stable by $160\ \mathrm{kJ\,mol^{-1}}$

Low-spin favored; low-spin more stable by $200\ \mathrm{kJ\,mol^{-1}}$

$[\mathrm{Ni(CN)_4}]^{2-}$

$[\mathrm{NiCl_4}]^{2-}$

$[\mathrm{Fe(CN)_6}]^{4-}$

$[\mathrm{Co(NH_3)_6}]^{3+}$

Both A and R are false.

A is true but R is false.

Both A and R are true but R is NOT the correct explanation of A.

Both A and R are true and R is the correct explanation of A.

Extra stability gained from exchange energy and reduced electron–electron repulsion for half-filled ($3d^5$) and fully-filled ($3d^{10}$) $3d$ subshells offsets the promotion energy, resulting in $4s^1\,3d^5$ and $4s^1\,3d^{10}$.

$4s$ orbitals are always lower in energy than $3d$ in neutral atoms, so electrons preferentially occupy $4s^2$ giving $4s^2\,3d^4$ and $4s^2\,3d^9$.

Hund's rule forces one electron into $4s$ to maximize multiplicity of the entire atom, directly producing the observed configurations.

Relativistic stabilization of $4s$ orbitals relative to $3d$ is the primary cause of the anomalous configurations.