Q.On the basis of Lanthanoid contraction, explain the following:

Concept: Lanthanoid Contraction — the steady decrease in ionic radii from La³⁺ to Lu³⁺ due to poor shielding by 4f electrons.

1. Nature of bonding in La₂O₃ and Lu₂O₃ As ionic radius decreases, polarising power (charge/size) increases. La³⁺ is larger, so La₂O₃ is more ionic. Lu³⁺ is smaller, so Lu₂O₃ has greater covalent character.
2. Trends in stability of oxo salts of lanthanoids Smaller Ln³⁺ ions polarise the oxoanion more, making salts like carbonates and sulphates less thermally stable. Stability decreases from La to Lu.
3. Stability of complexes of lanthanoids Lanthanoid complexes are primarily ionic. Smaller Ln³⁺ ions form stronger electrostatic bonds with ligands, so complex stability increases from La to Lu.
4. Radii of 4d and 5d block elements …

The Core Idea: Why Lanthanoid Contraction Matters

Lanthanoid contraction is the gradual decrease in atomic and ionic radii as we move from lanthanum ($Z=57$) to lutetium ($Z=71$). This happens because the 4f electrons are poor at shielding the nuclear charge — each added proton pulls the electron cloud inward more than the added 4f electron pushes it outward. The result is a cumulative contraction of about 15 pm across the series.

This seemingly small change has enormous consequences for bonding, stability, and trends in properties. Let's see how it plays out in each part of the question.

(i) Nature of bonding in $La_2O_3$ and $Lu_2O_3$

1. The principle: Ionic character depends on the charge density of the cation — smaller, more highly charged cations polarise the anion more, shifting bonding toward covalent character.

2. Apply the contraction: $La^{3+}$ is the largest lanthanoid ion (radius ~106 pm), while $Lu^{3+}$ is the smallest (radius ~85 pm). Both have the same +3 charge.

3. The consequence: $La^{3+}$ has low charge density — it holds its electrons loosely and interacts with $O^{2-}$ primarily through electrostatic attraction. So $La_2O_3$ is predominantly ionic.

$Lu^{3+}$, being much smaller, has high charge density. It strongly polarises the oxide ion, pulling electron density toward itself. This introduces significant covalent character into the Lu–O bond. So $Lu_2O_3$ is more covalent (or less ionic) than $La_2O_3$.

(ii) Trends in the stability of oxo salts of lanthanoids from La to Lu

1. What are oxo salts? These are salts like carbonates, sulfates, nitrates, and phosphates — compounds where the lanthanoid ion is bonded to an oxoanion ($CO_3^{2-}$, $SO_4^{2-}$, $NO_3^-$, $PO_4^{3-}$).

2. The stability factor: Thermal stability of these salts depends on how strongly the lanthanoid cation holds the oxoanion. A smaller cation with higher charge density binds the anion more tightly, making the salt harder to decompose.

3. The trend: As we go from La to Lu, ionic radius decreases. So the lattice energy of the oxo salt increases (smaller cation → stronger electrostatic attraction). This makes the salt more stable toward thermal decomposition.

For example, lanthanum carbonate decomposes at a lower temperature than lutetium carbonate. The same trend holds for sulfates, nitrates, etc.

(iii) Stability of the complexes of lanthanoids

1. The challenge: Lanthanoid ions are large and have 4f orbitals that are deeply buried inside the atom. These orbitals don't extend outward enough to form strong covalent bonds with ligands. So lanthanoid complexes are primarily ionic in nature.

2. The contraction effect: As ionic radius decreases from La to Lu, the charge density of the $Ln^{3+}$ ion increases. This strengthens the electrostatic attraction between the metal ion and the ligand.

3. The result: Complex stability increases slightly from La to Lu. The increase is modest because the bonding is still largely ionic — but the trend is clear: smaller lanthanoids form more stable complexes.

(iv) Radii of 4d and 5d block elements

1. The puzzle: Elements in the 5d series (like Hf, Ta, W) have nearly the same atomic radii as their 4d counterparts (Zr, Nb, Mo). Normally, we'd expect 5d elements to be larger because they're in a higher principal quantum shell. …

Method: Lanthanoid Contraction Analysis

This method uses the steady decrease in ionic radii across the lanthanoid series (La to Lu) — caused by poor shielding of the 4f electrons — to explain periodic trends in bonding, stability, and properties.

Steps

Step 1: State the core concept

• Across the lanthanoid series (atomic number 57–71), the 4f orbitals are filled.
• 4f electrons shield the nuclear charge poorly → effective nuclear charge ($Z_{\text{eff}}$) increases.
• Result: ionic radii decrease steadily from La³⁺ to Lu³⁺ — this is lanthanoid contraction.

Step 2: Apply to each sub-question

(i) Nature of bonding in $\mathbf{La_2O_3}$ and $\mathbf{Lu_2O_3}$

• La³⁺ is larger → lower charge density → more ionic bonding with O²⁻.
• Lu³⁺ is smaller → higher charge density → greater polarising power → bond has more covalent character.
• Result: $\mathbf{La_2O_3}$ is predominantly ionic; $\mathbf{Lu_2O_3}$ shows significant covalent character.

(ii) Trends in stability of oxo salts (e.g., carbonates, sulphates) from La to Lu

• Larger La³⁺ stabilises large oxoanions (e.g., $\text{CO}_3^{2-}$, $\text{SO}_4^{2-}$) via better lattice energy.
• As radius decreases → lattice energy of oxo salts decreases → thermal stability decreases from La to Lu.
• Result: La oxo salts are most stable; Lu oxo salts decompose more easily on heating.

(iii) Stability of complexes of lanthanoids

• Lanthanoids form complexes mainly via electrostatic interactions.
• Smaller Lu³⁺ has higher charge density → stronger electrostatic attraction with ligands.
• Result: Complex stability increases from La to Lu (Lu forms the most stable complexes).

(iv) Radii of 4d and 5d block elements

• After lanthanoids, 5d elements (e.g., Hf, Ta, W) have nearly same radii as their 4d counterparts (e.g., Zr, Nb, Mo).
• Reason: Lanthanoid contraction cancels the expected increase in size from adding a shell.
• Result: Zr and Hf have almost identical atomic/ionic radii → similar chemical properties.

(v) Trends in acidic character of lanthanoid oxides …

Here are the common mistakes students make when answering questions on Actinoid Contraction (often confused with Lanthanoid Contraction) and how to avoid them.

Mistake 1: Confusing Lanthanoid Contraction with Actinoid Contraction

• The Error: Students often write "Actinoid contraction is greater than Lanthanoid contraction" but then explain it using the Lanthanoid series (4f electrons). They fail to mention the 5f electrons and the poor shielding of the 5f orbital.
• Why it happens: The concept is similar, but the series (4f vs 5f) and the magnitude are different.
• How to Avoid: Always specify the series.
  • Lanthanoid Contraction: Due to poor shielding of 4f electrons.
  • Actinoid Contraction: Due to poor shielding of 5f electrons.
  • Key Fact: Actinoid contraction is greater because 5f orbitals are more diffuse and penetrate less than 4f orbitals, leading to even poorer shielding.

Mistake 2: Forgetting the "Greater" Magnitude

• The Error: Stating "Actinoid contraction is similar to Lanthanoid contraction" or giving the same numerical reasoning.
• Why it happens: Students memorize the "poor shielding" reason but ignore the comparative magnitude.
• How to Avoid: Memorize the trend: Actinoid contraction > Lanthanoid contraction. The cumulative contraction over the series is more pronounced for actinoids.

Mistake 3: Incorrectly Linking Contraction to Bonding (Part i)

• The Error: Saying $La_2O_3$ is more covalent than $Lu_2O_3$ because of contraction.
• Why it happens: Students forget that smaller size leads to higher polarising power and thus more covalent character.
• How to Avoid: Use the Fajan's rules logic:
  • $Lu^{3+}$ is smaller than $La^{3+}$ (due to contraction).
  • Smaller cation = higher charge density = greater polarising power.
  • Therefore, $Lu_2O_3$ is more covalent (less ionic) than $La_2O_3$.

Mistake 4: Confusing Stability Trends of Oxo Salts (Part ii)

• The Error: Stating stability increases from La to Lu.
• Why it happens: Students assume smaller size always means higher stability.
• How to Avoid: Remember the thermal stability trend for oxo salts (like carbonates, sulphates):
  • As we move from La to Lu, the ionic radius decreases.
  • Smaller cation = higher polarising power = greater distortion of the oxo anion.
  • This distortion makes the salt less thermally stable.
  • Correct Trend: Stability decreases from La to Lu.

Mistake 5: Misinterpreting Complex Stability (Part iii)

• The Error: Saying complex stability decreases due to contraction.
• Why it happens: Students confuse this with the oxo salt trend.
• How to Avoid: Use the Hard-Soft Acid-Base (HSAB) principle:
  • $Ln^{3+}$ ions are hard acids.
  • As size decreases (La to Lu), the charge density increases.
  • Higher charge density = stronger interaction with ligands (hard bases).
  • Correct Trend: Complex stability increases from La to Lu.

Mistake 6: Ignoring the "Radii of 4d and 5d" (Part iv)

• The Error: Only explaining lanthanoid contraction without linking it to the 5d series.
• Why it happens: Students forget that the 5d series (Hf to Hg) comes after the lanthanoids.
• How to Avoid: Draw the connection: …