The d-and f-Block Elements — NCERT Solutions

The actinoids and lanthanoids are similar in some respects, but actinoid chemistry is more complex.

(i) Electronic configuration

• Lanthanoids: the electrons are added mainly to the 4f subshell; their stable ions are generally of type $4f^n$.
• Actinoids: electrons are added to 5f orbitals, but 6d and 7s levels are also close in energy, so configurations are more irregular.

(ii) Atomic and ionic sizes

• In both series, there is a gradual decrease in atomic and ionic radii across the series.
• This is called lanthanoid contraction in lanthanoids and actinoid contraction in actinoids.
• The contraction is greater in actinoids because 5f electrons shield the nuclear charge poorly, so size decreases more rapidly.

(iii) Oxidation state

• Lanthanoids mostly show only the +3 oxidation state; +2 and +4 occur only occasionally.
• Actinoids show a wider range of oxidation states from about +3 to +7, especially in the earlier part of the series, because 5f, 6d and 7s orbitals are close in energy.

(iv) Chemical reactivity

• Lanthanoids are reactive metals, but their chemistry is fairly regular.
• Actinoids are generally more reactive and chemically more complex.
• Many actinoids are also radioactive, and their outer electrons participate in bonding more readily than in lanthanoids.

So, actinoids are more variable in oxidation state and more complex in chemical behaviour than lanthanoids.

(i) Cr$^{2+}$ is strongly reducing while Mn(III) is strongly oxidising

• Cr$^{2+}$ has configuration $d^4$ and is easily oxidised to Cr$^{3+}$, which is $d^3$ and relatively more stable.
• Mn$^{3+}$ also has $d^4$ configuration, but it is readily reduced to Mn$^{2+}$, which is $d^5$ and especially stable because of the half-filled $d$ subshell.
• Therefore, Cr$^{2+}$ acts as a reducing agent, while Mn$^{3+}$ acts as an oxidising agent.

(ii) Cobalt(II) is stable in aqueous solution but in presence of complexing reagents it is easily oxidised

• In water, Co$^{2+}$ is reasonably stable.
• In presence of complexing ligands, Co$^{3+}$ is stabilised much more strongly due to formation of complexes.
• So oxidation of Co$^{2+}$ to Co$^{3+}$ becomes easier.

(iii) The $d^1$ configuration is very unstable in ions

• A $d^1$ ion tends to lose its single $d$ electron to reach a more stable configuration such as $d^0$.
• It is therefore easily oxidised or reduced depending on the system.
• Because $d^0$ and sometimes $d^3$ or $d^5$ configurations are more stable, the $d^1$ state is generally unstable in ions.

Disproportionation means that the same species in a particular oxidation state undergoes both oxidation and reduction at the same time, producing one product in a higher oxidation state and another in a lower oxidation state.

Examples in aqueous solution:

1. $$2\mathrm{Cu^+}(aq)\rightarrow \mathrm{Cu^{2+}}(aq)+\mathrm{Cu}(s)$$
2. $$3\mathrm{MnO_4^{2-}}+4\mathrm{H^+}\rightarrow 2\mathrm{MnO_4^-}+\mathrm{MnO_2}+2\mathrm{H_2O}$$

In both cases, one species is simultaneously oxidised and reduced.

Copper shows the $+1$ oxidation state most frequently.

Reason:

• Cu$^{+}$ has the stable $3d^{10}$ configuration.
• This filled $d$ subshell gives extra stability to the +1 state.

However, in aqueous solution Cu$^{+}$ is not very stable and tends to disproportionate:
$$2\mathrm{Cu^+}\rightarrow \mathrm{Cu^{2+}}+\mathrm{Cu}$$

So copper most often shows the +1 state because of its stable filled $d$ configuration.

Using the electronic configurations of the gaseous ions:

• Mn$^{3+}$ = $3d^4$ → 4 unpaired electrons
• Cr$^{3+}$ = $3d^3$ → 3 unpaired electrons
• V$^{3+}$ = $3d^2$ → 2 unpaired electrons
• Ti$^{3+}$ = $3d^1$ → 1 unpaired electron

Among these, Cr$^{3+}$ is the most stable in aqueous solution because the $d^3$ state is especially stable compared with the alternatives.

(i) Lowest oxide is basic, highest is amphoteric/acidic

• In lower oxidation states, the metal has more ionic character, so the oxide is generally basic.
• In higher oxidation states, the metal has greater covalent character and a stronger tendency to form oxo-species, so the oxide becomes amphoteric or acidic.
• Example: CrO is basic, Cr$_2$O$_3$ is amphoteric, while CrO$_3$ is acidic.

(ii) Highest oxidation state in oxides and fluorides

• Oxygen and fluorine are small and highly electronegative, so they can stabilise very high oxidation states of metals.
• Fluorine stabilises them by strong M–F bonding and lattice energy.
• Oxygen can stabilise high oxidation states even better because it can form multiple bonds with metals.
• Examples: CrF$_6$, Mn$_2$O$_7$, CoF$_3$.

(iii) Highest oxidation state in oxoanions

• Oxoanions stabilise high oxidation states because the negative charge is spread over oxygen atoms and because of strong M–O bonding.
• The metal is thus stabilised in a high oxidation state in ions such as chromate, dichromate and permanganate.
• Examples:
• Cr(VI) in $CrO_4^{2-}$ and $Cr_2O_7^{2-}$
• Mn(VII) in $MnO_4^-$
• V(V) in $VO_4^{3-}$

These oxoanions are especially stable forms for high oxidation states.

(i) Preparation of $K_2Cr_2O_7$ from chromite ore

1. Fusion of chromite ore $FeCr_2O_4$ with sodium carbonate in the presence of air to form sodium chromate:

$$4FeCr_2O_4 + 8Na_2CO_3 + 7O_2 \rightarrow 8Na_2CrO_4 + 2Fe_2O_3 + 8CO_2$$

2. The yellow sodium chromate solution is acidified to form sodium dichromate:

$$2Na_2CrO_4 + 2H^+ \rightarrow Na_2Cr_2O_7 + 2Na^+ + H_2O$$

3. Treat sodium dichromate with potassium chloride; less soluble potassium dichromate crystallises out:

$$Na_2Cr_2O_7 + 2KCl \rightarrow K_2Cr_2O_7 + 2NaCl$$

Effect of increasing pH

Chromate and dichromate are interconvertible:

• In acidic medium, chromate changes to dichromate:

$$2CrO_4^{2-} + 2H^+ \rightarrow Cr_2O_7^{2-} + H_2O$$

• In alkaline medium, dichromate changes to chromate:

$$Cr_2O_7^{2-} + 2OH^- \rightarrow 2CrO_4^{2-} + H_2O$$
So, increasing pH shifts the equilibrium towards chromate ion.

(ii) Preparation of $KMnO_4$ from pyrolusite ore

1. Fuse MnO$_2$ with alkali metal hydroxide and an oxidising agent to form potassium manganate:

$$2MnO_2 + 4KOH + O_2 \rightarrow 2K_2MnO_4 + 2H_2O$$

2. Convert manganate to permanganate by disproportionation in neutral or acidic medium:

$$3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^- + MnO_2 + 2H_2O$$

3. Commercially, manganate is also converted to permanganate by electrolytic oxidation.

Thus, $KMnO_4$ is obtained through the intermediate formation of $K_2MnO_4$.

Alloys are blends of metals prepared by mixing the components. They may be homogeneous solid solutions in which atoms of one metal are distributed randomly among the atoms of the other.

An important alloy containing lanthanoid metals is mischmetall.

• It consists of about 95% lanthanoid metals and about 5% iron, with traces of S, C, Ca and Al.

Uses:

• It is used in Mg-based alloys to produce bullets, shell and lighter flint.
• Lanthanoid mixed oxides are also used as catalysts in petroleum cracking, but the alloy itself is especially noted for the uses mentioned above.

Inner transition elements are the elements of the f-block, i.e. the lanthanoids and actinoids, in which the 4f and 5f orbitals are progressively filled.

From the given atomic numbers:

• 59 = Praseodymium, a lanthanoid
• 95 = Americium, an actinoid
• 102 = Nobelium, an actinoid

So the inner transition elements are 59, 95 and 102.

The chemistry of actinoids is not smooth because they show a wide range of oxidation states, unlike lanthanoids which mostly show the +3 state.

Examples from the chapter:

• Th shows mainly +4
• Pa shows +5
• U shows +6
• Np shows +7
• Later actinoids mainly show +3, but some also show +4 or other states

This irregularity occurs because the 5f, 6d and 7s orbitals are of comparable energies, so different numbers of electrons can take part in bonding. Also, the 5f electrons are not as deeply buried as 4f electrons, so they can participate in bonding much more readily.

The last element in the actinoid series is lawrencium (Lr, Z = 103).

Its electronic configuration is given in the chapter as:
$$[\mathrm{Rn}]\,5f^{14}6d^{1}7s^{2}$$

The possible oxidation state is mainly +3. The actinoids generally show +3 oxidation state, and for the later members this is the most common state.

Cerium ion, Ce$^{3+}$ has the configuration:
$$\mathrm{Ce}: [Xe]4f^15d^16s^2$$

To form Ce$^{3+}$, three electrons are removed, giving:
$$\mathrm{Ce^{3+}} : [Xe]4f^1$$

So there is one unpaired electron in the $4f$ subshell.

Using the spin-only formula:
$$\mu = \sqrt{n(n+2)}$$
where $n = 1$.

Thus,
$$\mu = \sqrt{1(1+2)} = \sqrt{3} = 1.73\ \text{BM}$$

So, the magnetic moment of Ce$^{3+}$ is 1.73 BM.

The lanthanoids that exhibit +4 oxidation state are:

• Ce, Pr, Nd, Tb and Dy

The lanthanoids that exhibit +2 oxidation state are:

• Eu, Sm, Tm and Yb

Correlation with electronic configuration:

• Ce$^{4+}$ is favoured by a noble gas configuration.
• Eu$^{2+}$ is formed by losing two $s$ electrons and has $f^7$, a half-filled configuration.
• Yb$^{2+}$ has $f^{14}$, a completely filled configuration.
• Tb$^{4+}$ has half-filled $f$ orbitals and is therefore stabilized.
• Sm also shows both +2 and +3 states because of similar stability considerations.

The actinoids and lanthanoids differ in the following ways:

(i) Electronic configuration

• Lanthanoids: atoms have common 6s² configuration with variable occupancy of 4f orbitals.
• Actinoids: atoms have common 7s² configuration with variable occupancy of 5f and 6d orbitals.
• In actinoids, the 5f electrons can participate in bonding to a much greater extent than 4f electrons in lanthanoids.

(ii) Oxidation states

• Lanthanoids: mostly show only the +3 oxidation state; +2 and +4 are seen only occasionally.
• Actinoids: show a much wider range of oxidation states, especially in the first half of the series.
• Th: +4
• Pa: +5
• U: +6
• Np: +7
• Later actinoids mostly return to +3.

(iii) Chemical reactivity

• Lanthanoids: relatively reactive, resemble calcium in early members and aluminium in later members; they form Ln$^{3+}$ compounds readily.
• Actinoids: more complex and reactive; they are highly reactive metals, especially when finely divided, react with water, acids and many non-metals, and are more variable because of the multiple oxidation states and the greater participation of 5f electrons.

Thus, actinoid chemistry is much less smooth and much more complicated than lanthanoid chemistry.

From the table in the chapter, the electronic configurations are:

• 61 (Pm): $$[Xe]\,4f^5 6s^2$$
• 91 (Pa): $$[Rn]\,5f^2 6d^1 7s^2$$
• 101 (Md): $$[Rn]\,5f^{13} 7s^2$$
• 109 (Mt): $$[Rn]\,5f^7 6d^7 7s^2$$

The first transition series differs from the second and third series in the following respects:

(i) Electronic configurations

• First series: electrons fill the 3d orbitals.
• Second series: electrons fill the 4d orbitals.
• Third series: electrons fill the 5d orbitals.
• In general, transition elements have configuration $(n-1)d^{1-10}ns^{1-2}$.
• There are exceptions such as Cr, Cu and Pd.

(ii) Oxidation states

• The first series shows a wide range of oxidation states, but the higher oxidation states become less stable as we go toward the end of the series.
• In the second and third series, higher oxidation states are often more stable than in the first series.
• The chapter notes that Mo(VI) and W(VI) are more stable than Cr(VI).
• This is why Cr(VI) is a strong oxidising agent, while MoO$_3$ and WO$_3$ are not.

(iii) Ionisation enthalpies

• The second and third series generally have greater enthalpies of atomisation than the first series.
• Their ionisation enthalpies are influenced by the greater nuclear charge and the lanthanoid contraction.
• The variation in ionisation enthalpy along a transition series is much smaller than in main-group elements.

(iv) Atomic sizes

• Atomic radii increase from the 3d series to the 4d series.
• But the 5d series has radii very similar to the 4d series because of lanthanoid contraction.
• Example given: Zr 160 pm and Hf 159 pm.

So, second- and third-series transition metals are generally more similar in size and often more similar in chemistry than the first-series members are to them.

For these ions, electrons are removed first from the 4s orbital and then from the 3d orbitals.

• Ti$^{2+}$: Ti = $3d^2 4s^2$ → Ti$^{2+}$ = $3d^2$
• V$^{2+}$: V = $3d^3 4s^2$ → V$^{2+}$ = $3d^3$
• Cr$^{3+}$: Cr = $3d^5 4s^1$ → Cr$^{3+}$ = $3d^3$
• Mn$^{2+}$: Mn = $3d^5 4s^2$ → Mn$^{2+}$ = $3d^5$
• Fe$^{2+}$: Fe = $3d^6 4s^2$ → Fe$^{2+}$ = $3d^6$
• Fe$^{3+}$: Fe$^{3+}$ = $3d^5$
• Co$^{2+}$: Co = $3d^7 4s^2$ → Co$^{2+}$ = $3d^7$
• Ni$^{2+}$: Ni = $3d^8 4s^2$ → Ni$^{2+}$ = $3d^8$
• Cu$^{2+}$: Cu = $3d^{10} 4s^1$ → Cu$^{2+}$ = $3d^9$

For hydrated ions in octahedral fields, the five $3d$ orbitals are split into:

• lower energy $t_{2g}$: 3 orbitals
• higher energy $e_g$: 2 orbitals

Occupancy:

• Ti$^{2+}$ ($d^2$): $t_{2g}^2 e_g^0$
• V$^{2+}$ ($d^3$): $t_{2g}^3 e_g^0$
• Cr$^{3+}$ ($d^3$): $t_{2g}^3 e_g^0$
• Mn$^{2+}$ ($d^5$): high spin $t_{2g}^3 e_g^2$
• Fe$^{2+}$ ($d^6$): high spin $t_{2g}^4 e_g^2$
• Fe$^{3+}$ ($d^5$): high spin $t_{2g}^3 e_g^2$
• Co$^{2+}$ ($d^7$): high spin $t_{2g}^5 e_g^2$
• Ni$^{2+}$ ($d^8$): $t_{2g}^6 e_g^2$
• Cu$^{2+}$ ($d^9$): $t_{2g}^6 e_g^3$

The first transition series shows many properties that differ from the heavier transition elements because of differences in size, electron configuration and contraction effects.

Main points:

• The 3d elements have smaller atomic radii and generally more pronounced irregularities in properties.
• The 4d and 5d elements are more similar to each other because of lanthanoid contraction; for example, Zr and Hf have almost identical radii.
• The heavier transition elements often show greater enthalpies of atomisation and hence more frequent metal–metal bonding.
• Their oxidation states and chemical behaviour can be more regular in some groups, and higher oxidation states may be more stable than in the first series.
• The first series generally shows stronger variations in properties across the period, while the heavier series resemble each other more closely within a group.

So, the first transition series is chemically less like the second and third series than the second and third series are like each other.

The magnetic moments show the number of unpaired electrons and hence the likely geometry / spin state.

• K$_4$[Mn(CN)$_6$] has magnetic moment 2.2 BM, which is low. This indicates few unpaired electrons and a low-spin complex because CN$^-$ is a strong-field ligand.
• [Fe(H$_2$O)$_6$]$^{2+}$ has magnetic moment 5.3 BM, close to the value for 4 unpaired electrons. This shows it is a high-spin complex.
• K$_2$[MnCl$_4$] has magnetic moment 5.9 BM, corresponding to 5 unpaired electrons. This indicates a high-spin tetrahedral complex.

So the observed magnetic moments infer that strong-field ligands produce low-spin complexes, while weak-field ligands produce high-spin complexes.