Assertion: Linkage isomerism arises in coordination compounds containing ambidentate ligand. Reason: Ambidenta

NCERT Exemplar · Q48

Q. Assertion: Linkage isomerism arises in coordination compounds containing ambidentate ligand. Reason: Ambidentate ligand has two different donor atoms.

(i) Assertion and reason both are true, reason is correct explanation of assertion.

(ii) Assertion and reason both are true but reason is not the correct explanation of assertion.

(iii) Assertion is true, reason is false.

(iv) Assertion is false, reason is true.

Yanam BieapMCQ· 1mImportance★★★★★

95% · 96/101 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Concept understanding — Crystal Field Splitting

Crystal Field Splitting: From Intuition to Precision

Imagine you are a negatively charged electron sitting on a metal ion. All around you, the space is perfectly spherical — every direction feels the same. Your energy depends only on how far you are from the nucleus, not on which way you face.

Now imagine that six negative ions (or the negative ends of polar molecules) march in from the $x$ , $y$ , and $z$ axes and stop close to you. Suddenly, the space around you is no longer uniform. If you try to move straight toward one of these approaching ions, you feel a strong repulsion — that path costs extra energy. If you move between the axes (say, along a diagonal), you feel less repulsion because you are farther from the incoming charges.

This is the core intuition: when ligands approach a metal ion, they break the spherical symmetry of the space around the metal. Different directions in space are no longer equivalent. Electrons in orbitals that point directly at the ligands get pushed up in energy; electrons in orbitals that point between the ligands stay lower.

The Precise Statement

d

For the most common geometry — octahedral — here is what happens:

Six ligands sit at the corners of an octahedron, along the $+x$ , $-x$ , $+y$ , $-y$ , $+z$ , $-z$ axes.
The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals point their lobes directly along these axes. These are the $e_g$ set. They feel maximum repulsion → higher energy.
The $d_{xy}$ , $d_{xz}$ , and $d_{yz}$ orbitals point their lobes between the axes (into the octahedral faces). These are the $t_{2g}$ set. They feel less repulsion → lower energy.

The energy gap between these two sets is denoted by $\Delta_o$ (or $10\,Dq$ ). The $t_{2g}$ set drops by $0.4\Delta_o$ and the $e_g$ set rises by $0.6\Delta_o$ , keeping the average energy unchanged (the "barycentre" rule).

Note

The labels $e_g$ and $t_{2g}$ come from group theory — they describe how the orbitals transform under the symmetry operations of an octahedron. You do not need to memorise the derivation, but the notation is standard in every exam.

Why This Matters

Crystal field splitting explains three things you will see repeatedly:

Colour — electrons can jump from $t_{2g}$ to $e_g$ by absorbing visible light. The gap $\Delta_o$ determines the colour you see.
Magnetism — if $\Delta_o$ is large, electrons pair up in the lower $t_{2g}$ set (low spin). If $\Delta_o$ is small, electrons spread out (high spin). This changes the number of unpaired electrons. …

Why this formula?

Crystal Field Splitting: Why the Energy Splitting Occurs

Crystal Field Theory (CFT) explains how the d-orbitals of a transition metal ion split in energy when placed in an electrostatic field created by surrounding ligands (anions or polar molecules). The key result is that five degenerate d-orbitals split into two or more sets with different energies. Let's understand why this happens.

1. The Starting Point: Degenerate d-Orbitals

In a free transition metal ion (no ligands), all five d-orbitals have the same energy (degenerate). Their shapes are:

$d_{xy}$ , $d_{xz}$ , $d_{yz}$ — lobes lie between the x, y, z axes (called $t_{2g}$ set in octahedral symmetry)
$d_{x^2-y^2}$ , $d_{z^2}$ — lobes point directly along the x, y, z axes (called $e_g$ set)

Key idea: The spatial orientation of each orbital determines how it interacts with approaching ligands.

2. The Octahedral Case: Why $e_g$ Orbitals Are Higher in Energy

Imagine six ligands approaching along the +x, –x, +y, –y, +z, –z axes (octahedral geometry).

What happens to $d_{x^2-y^2}$ and $d_{z^2}$ ?

Their lobes point directly at the ligands.
The negatively charged ligands repel the electron density in these orbitals.
This repulsion raises the energy of these orbitals — they become less stable (higher energy).

What happens to $d_{xy}$ , $d_{xz}$ , $d_{yz}$ ?

Their lobes point between the axes (e.g., $d_{xy}$ lobes lie in the xy-plane but at 45° to x and y).
They avoid the ligands — less repulsion.
Their energy is lower than the $e_g$ set.

The Splitting Pattern

\Delta_{\text{oct}} = E(e_g) - E(t_{2g})

Where:

$E(e_g)$ = energy of $d_{x^2-y^2}$ and $d_{z^2}$ (higher)
$E(t_{2g})$ = energy of $d_{xy}$ , $d_{xz}$ , $d_{yz}$ (lower)
$\Delta_{\text{oct}}$ is called the crystal field splitting energy (CFSE)

Why the name? The $e_g$ orbitals are "doubly degenerate" (2 orbitals), $t_{2g}$ are "triply degenerate" (3 orbitals). The letters come from group theory symmetry labels.

3. The Energy Conservation Rule

The total energy of all five d-orbitals must remain constant (no energy is created or destroyed). So:

The center of gravity (average energy) of the split set equals the original degenerate energy.
For octahedral splitting:
- 2 $e_g$ orbitals go up by $+0.6\Delta_{\text{oct}}$ each
- 3 $t_{2g}$ orbitals go down by $-0.4\Delta_{\text{oct}}$ each

Check:

2 \times (+0.6\Delta) + 3 \times (-0.4\Delta) = 1.2\Delta - 1.2\Delta = 0

This conservation of energy is a fundamental constraint — the splitting is not arbitrary.

4. The Tetrahedral Case: Why It's Opposite and Smaller

In a tetrahedral complex, four ligands approach from alternate corners of a cube. The axes are different:

The $d_{xy}$ , $d_{xz}$ , $d_{yz}$ orbitals now point closer to the ligands (more repulsion).
The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals point away from ligands (less repulsion).

Result:

$e$ set ( $d_{x^2-y^2}$ , $d_{z^2}$ ) — lower energy
$t_2$ set ( $d_{xy}$ , $d_{xz}$ , $d_{yz}$ ) — higher energy

The splitting is inverted compared to octahedral.

Magnitude:

\Delta_{\text{tet}} \approx \frac{4}{9} \Delta_{\text{oct}}

Why smaller?

Only 4 ligands (vs. 6) → less total repulsion.
Ligands are not directly along axes → weaker interaction. …

Start your 14-day free trial to unlock the full solution →

The assertion is true — linkage isomerism does arise from ambidentate ligands — and the reason is also true, because an ambidentate ligand has two different donor atoms. The reason correctly explains the assertion, so option (i) is correct.

The Core Idea: Why Ambidentate Ligands Cause Linkage Isomerism

Coordination compounds can show isomerism when the same set of atoms can be arranged differently around the metal. Linkage isomerism is a special type where the same ligand binds to the metal through different atoms in different isomers. This is only possible if the ligand has more than one potential donor atom — that is, if it is ambidentate.

The word "ambidentate" literally means "both-toothed" — the ligand has two different "teeth" (donor atoms) it can use to bite the metal. When the metal chooses one donor atom over the other, the connectivity changes, and you get a different isomer.

Watch out

A common mistake is to think that any ligand with two donor atoms is ambidentate. For example, ethylenediamine (en) has two N atoms, but they are identical — so it is bidentate, not ambidentate. Ambidentate requires the donor atoms to be different (e.g., N and O in NO₂⁻, or S and N in SCN⁻).

Step-by-Step Reasoning

Understand the assertion: "Linkage isomerism arises in coordination compounds containing ambidentate ligand."

This is true. Classic examples include:
- Nitrito ligand ( $\ce{NO2-}$ ): can bind through N (nitro isomer, $\ce{[Co(NH3)5NO2]^{2+}}$ ) or through O (nitrito isomer, $\ce{[Co(NH3)5ONO]^{2+}}$ ).
- Thiocyanate ligand ( $\ce{SCN-}$ ): can bind through S (thiocyanato) or through N (isothiocyanato).
- Cyanide ( $\ce{CN-}$ ): can bind through C or N (though C-binding is far more common).
In each case, the same ligand attaches to the metal via a different atom, producing distinct compounds with different properties — that is linkage isomerism.
Understand the reason: "Ambidentate ligand has two different donor atoms."

This is also true. By definition, an ambidentate ligand must have at least two different atoms that can donate a lone pair to the metal. If the atoms were the same (like the two N atoms in en), the ligand would be bidentate but not ambidentate — and linkage isomerism would not occur because switching between identical atoms gives the same structure.
Check if the reason explains the assertion: …

Start your 14-day free trial to unlock the full solution →

Common Mistakes & How to Avoid Them

Mistake 1: Confusing "Ambidentate" with "Polydentate"

The error: Students often think any ligand with multiple donor atoms is ambidentate. They then incorrectly mark the Reason as false.

Why it happens: Both terms involve "multiple donor atoms," but the meaning is different.

How to avoid:

Ambidentate ligand = has two different donor atoms, but can bind through only one at a time (e.g., $\mathrm{NO_2^-}$ can bind through N or O).
Polydentate ligand = has multiple donor atoms that can bind simultaneously (e.g., EDTA binds through 6 atoms at once).

Key rule: Ambidentate → different atoms, one at a time. Polydentate → multiple atoms, all at once.

Mistake 2: Thinking Linkage Isomerism Requires Only One Donor Atom

The error: Some students believe linkage isomerism happens when a ligand has just one donor atom but can switch bonding modes.

Why it happens: They confuse linkage isomerism with other isomerism types (like ionization or hydrate isomerism).

How to avoid:

Linkage isomerism requires a ligand with at least two different donor atoms.
Example: $\ce{[Co(NH3)5(NO2)]Cl2}$ and $\ce{[Co(NH3)5(ONO)]Cl2}$ — here $\mathrm{NO_2^-}$ uses N in one isomer and O in the other.

Remember: If the ligand has only one donor atom, linkage isomerism is impossible.

Mistake 3: Thinking a Definition Can't Also Be an Explanation

The error: Students think that because the Reason merely defines an ambidentate ligand, it cannot also be the explanation for the Assertion, and default to option (ii).

Why it happens: They assume a definition and an explanation must be different things.

How to avoid:

Check if the Reason directly causes the Assertion.
Here:
- Assertion: Linkage isomerism arises because of ambidentate ligands.
- Reason: Ambidentate ligands have two different donor atoms.
Having two different donor atoms is exactly what allows the same ligand to bind through either atom — which is exactly what produces linkage isomers. The Reason IS the mechanism, not just a coincidental fact. …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ47 — Assertion: [Cr(H₂O)₆]Cl₂ and [Fe(H₂O)₆]Cl₂ are reducing in nature. Rea…→Next questionQ49 — Assertion: Complexes of MX₆ and MX₅L type (X and L are unidentate) do …

Q.Assertion: Linkage isomerism arises in coordination compounds containing ambidentate ligand.
Reason: Ambidentate ligand has two different donor atoms.

Concept understanding — Crystal Field Splitting

Crystal Field Splitting: From Intuition to Precision

The Precise Statement

Why This Matters

Why this formula?

Crystal Field Splitting: Why the Energy Splitting Occurs

1. The Starting Point: Degenerate d-Orbitals

2. The Octahedral Case: Why $e_g$ Orbitals Are Higher in Energy

What happens to $d_{x^2-y^2}$ and $d_{z^2}$ ?

What happens to $d_{xy}$ , $d_{xz}$ , $d_{yz}$ ?

The Splitting Pattern

3. The Energy Conservation Rule

4. The Tetrahedral Case: Why It's Opposite and Smaller

Result:

Magnitude:

The Core Idea: Why Ambidentate Ligands Cause Linkage Isomerism

Step-by-Step Reasoning

Method: Assertion–Reason Analysis

Steps

Common Mistakes & How to Avoid Them

Mistake 1: Confusing "Ambidentate" with "Polydentate"

Mistake 2: Thinking Linkage Isomerism Requires Only One Donor Atom

Mistake 3: Thinking a Definition Can't Also Be an Explanation

Q.Assertion: Linkage isomerism arises in coordination compounds containing ambidentate ligand. Reason: Ambidentate ligand has two different donor atoms.

The Core Idea: Why Ambidentate Ligands Cause Linkage Isomerism

Step-by-Step Reasoning

🎓Unlock everything free for 14 days

Q.Assertion: Linkage isomerism arises in coordination compounds containing ambidentate ligand.
Reason: Ambidentate ligand has two different donor atoms.

Unlock everything free for 14 days