Q.Explain the violet colour of the complex [Ti(H2O)6]3+ on the basis of crystal field theory.
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🔒 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
Crystal Field Splitting is the splitting of degenerate d orbitals of a transition metal ion into two or more sets of different energies, caused by the electrostatic repulsion between the metal's d electrons and the negative charge (or dipole) of surrounding ligands.
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 dx2−y2 and dz2 orbitals point their lobes directly along these axes. These are the eg set. They feel maximum repulsion → higher energy.
- The dxy, dxz, and dyz orbitals point their lobes between the axes (into the octahedral faces). These are the t2g set. They feel less repulsion → lower energy.
The energy gap between these two sets is denoted by Δo (or 10Dq). The t2g set drops by 0.4Δo and the eg set rises by 0.6Δo, keeping the average energy unchanged (the "barycentre" rule).
The labels eg and t2g 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 t2g to eg by absorbing visible light. The gap Δo determines the colour you see.
- Magnetism — if Δo is large, electrons pair up in the lower t2g set (low spin). If Δo 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:
- dxy, dxz, dyz — lobes lie between the x, y, z axes (called t2g set in octahedral symmetry)
- dx2−y2, dz2 — lobes point directly along the x, y, z axes (called eg set)
Key idea: The spatial orientation of each orbital determines how it interacts with approaching ligands.
2. The Octahedral Case: Why eg Orbitals Are Higher in Energy
Imagine six ligands approaching along the +x, –x, +y, –y, +z, –z axes (octahedral geometry).
What happens to dx2−y2 and dz2?
- 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 dxy, dxz, dyz?
- Their lobes point between the axes (e.g., dxy 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 eg set.
The Splitting Pattern
Δoct=E(eg)−E(t2g)
Where:
- E(eg) = energy of dx2−y2 and dz2 (higher)
- E(t2g) = energy of dxy, dxz, dyz (lower)
- Δoct is called the crystal field splitting energy (CFSE)
Why the name? The eg orbitals are "doubly degenerate" (2 orbitals), t2g 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 eg orbitals go up by +0.6Δoct each
- 3 t2g orbitals go down by −0.4Δoct each
Check:
2×(+0.6Δ)+3×(−0.4Δ)=1.2Δ−1.2Δ=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 dxy, dxz, dyz orbitals now point closer to the ligands (more repulsion).
- The dx2−y2 and dz2 orbitals point away from ligands (less repulsion).
Result:
- e set ( dx2−y2, dz2 ) — lower energy
- t2 set ( dxy, dxz, dyz ) — higher energy
The splitting is inverted compared to octahedral.
Magnitude:
Δtet≈94Δoct
Why smaller?
- Only 4 ligands (vs. 6) → less total repulsion.
- Ligands are not directly along axes → weaker interaction. …
The violet colour arises from a d-d electronic transition within the split d-orbitals of the Ti3+ ion.
- Electronic configuration: Ti3+ has a 3d1 configuration. In the octahedral field of six water ligands, the single d-electron occupies the lower-energy t2g set.
- Crystal field splitting: The energy gap between the t2g and eg sets is Δo (or 10Dq). …
The violet colour of [Ti(H2O)6]3+ arises from a single d-d electronic transition in the t2g1 configuration, where the lone electron absorbs blue-green light (≈ 20,300 cm⁻¹, ~498 nm) and the complementary transmitted colour is violet.
Why Crystal Field Theory Explains Colour
Transition metal complexes appear coloured because electrons in partially filled d-orbitals can absorb visible light and jump to a higher energy level. The key is that in an octahedral field, the five degenerate d-orbitals split into two sets: the lower-energy t2g (three orbitals) and the higher-energy eg (two orbitals). The energy gap between them, denoted Δo or 10Dq, determines which wavelength of light gets absorbed.
For [Ti(H2O)6]3+, titanium is in the +3 oxidation state. Ti has atomic number 22, so Ti³⁺ has the electronic configuration [Ar]3d1. This single d-electron is the entire story — there are no other d-electrons to complicate things with electron-electron repulsion or multiple transitions.
Octahedral crystal field splitting: Δo=E(eg)−E(t2g)
Step-by-Step Reasoning
-
Identify the metal ion and its d-electron count.
Ti in [Ti(H2O)6]3+ is Ti³⁺. The ground state configuration is 3d1. In an octahedral field, this single electron occupies the lower-energy t2g set. The eg orbitals are empty.
-
Determine the possible electronic transition.
The only allowed d-d transition is from t2g to eg: the electron absorbs a photon of energy exactly equal to Δo and jumps up. No other transitions are possible because there is only one electron.
-
Find the magnitude of Δo for this complex.
Experimentally, the absorption spectrum of [Ti(H2O)6]3+ shows a single broad peak centred at about 20,300 cm⁻¹ (which corresponds to a wavelength of roughly 490–500 nm). This is the energy of the t2g→eg transition.
TipThe wavenumber ν~=20,300 cm−1 corresponds to λ=ν~1≈4.93×10−5 cm=493 nm, which lies in the blue-green region of the visible spectrum.
-
Relate absorbed colour to observed colour. …
Method: Crystal Field Theory (CFT) – d-orbital splitting and d–d transition
Why this method?
Crystal Field Theory explains colour in transition metal complexes as arising from electronic transitions between split d-orbitals. The colour observed is complementary to the wavelength of light absorbed during this transition.
Steps
1. Identify the metal ion and its electron configuration
- In [Ti(H2O)6]3+, titanium is in the +3 oxidation state.
- Ti atomic number = 22 → Ti3+ has one d-electron (configuration: 3d1).
2. Determine the geometry and crystal field splitting
- The complex is octahedral (six water ligands).
- In an octahedral field, the five d-orbitals split into:
- Higher energy: eg orbitals (dx2−y2, dz2)
- Lower energy: t2g orbitals (dxy, dxz, dyz)
- The energy gap between these sets is denoted as Δo (or 10Dq).
3. Place the electron in the lower energy orbital
- The single d-electron occupies one of the t2g orbitals (lowest energy state).
4. Identify the electronic transition responsible for colour
- When visible light falls on the complex, the electron can absorb energy and jump from t2g to eg level.
- This is called a d–d transition.
- The energy of the absorbed photon equals Δo. …
Here are the most common mistakes students make when explaining the violet colour of [Ti(H2O)6]3+ using crystal field theory, along with how to avoid each.
Mistake 1: Forgetting the d1 Configuration
- The Mistake: Students often try to apply logic for high-spin vs. low-spin configurations or start calculating pairing energies. They might incorrectly state that the d orbital is completely filled or empty.
- Why it’s wrong: Ti3+ has an electronic configuration of [Ar]3d1. There is only one electron in the d orbitals. There is no possibility of pairing, so high-spin/low-spin is irrelevant.
- How to Avoid: Always start by finding the oxidation state of the metal and then its dn configuration. For Ti3+, it is simply d1. Write this down before discussing splitting.
Mistake 2: Describing the Wrong Geometry or Splitting Pattern
- The Mistake: Assuming the complex is tetrahedral or square planar, or drawing the wrong splitting diagram (e.g., eg above t2g in an octahedral field).
- Why it’s wrong: [Ti(H2O)6]3+ is an octahedral complex. In an octahedral field, the d orbitals split into the lower energy t2g set (dxy,dxz,dyz) and the higher energy eg set (dx2−y2,dz2).
- How to Avoid: Memorize the standard geometries and their splitting patterns. For a complex with six ligands, always draw the octahedral splitting diagram first. The single electron will occupy the lower energy t2g set.
Mistake 3: Confusing the Colour with the Absorbed Colour
- The Mistake: Stating that the complex is violet because it absorbs violet light.
- Why it’s wrong: The colour we see is the complement of the colour absorbed. [Ti(H2O)6]3+ appears violet because it absorbs light in the blue-green region of the spectrum (around 490–500 nm, experimentally ~498 nm).
- How to Avoid: Use a colour wheel. If the complex appears violet, the absorbed colour is blue-green. Always state: "The complex appears violet because it absorbs blue-green light, and we see the transmitted complementary colour."
Mistake 4: Ignoring the d−d Transition Mechanism
- The Mistake: Saying the electron jumps from the ligand to the metal (charge transfer) or that the colour is due to the ligand itself.
- Why it’s wrong: The colour arises from a d−d transition. The single electron in the t2g orbital absorbs a photon of visible light and gets excited to the eg orbital.
- How to Avoid: Explicitly state the transition: "The electron undergoes a t2g→eg transition." This is the core of the crystal field explanation.
Mistake 5: Not Mentioning the Crystal Field Splitting Energy (Δo)
- The Mistake: Describing the transition without linking it to the energy gap. …
Showing the 12 most recent of 17 on this concept.
- KEAM 2026Set eng-2026-04184 marksMCQQ.Which of the following complex ion absorbs yellow colour in the visible region? (A) [Co(NH3)6]+3 (B) [Co(CN)6]3− (C) [Cu(H2O)4]+2 (D) [Co(NH3)5(H2O)]+3 (E) [CoCl(NH3)5]+2
›Reveal solutionSolution
A complex absorbs the colour complementary to the one it appears; the violet/purple [CoCl(NH3)5]2+ absorbs yellow.
Observed colour is complementary to the absorbed colour. A species that absorbs yellow light appears violet/purple. …
- KEAM 2026Set eng-2026-04204 marksMCQQ.The order of field strength of the following ligands in the spectrochemical series is (A) NCS−<CN−<SCN−<S2−<OH− (B) NCS−<OH−<S2−<NCS−<CN− (C) CN−<S2−<OH−<NCS−<SCN− (D) SCN−<S2−<OH−<NCS−<CN− (E) SCN−<S2−<CN−<NCS−<OH−
›Reveal solutionSolution
Field strength increases: SCN−<S2−<OH−<NCS−<CN−. …
- KEAM 2026Set eng-2026-04214 marksMCQQ.The correct increasing order of wavelength of absorption of the following complexes is(i) [CoCl(NH3)5]2+(ii) [Co(NH3)5(H2O)]3+(iii) [Co(NH3)6]3+(iv) [Co(CN)6]3− (A)(i) <(ii) <(iii) <(iv) (B)(i) <(ii) <(iv) <(iii) (C)(ii) <(i) <(iv) <(iii) (D)(iv) <(iii) <(ii) <(i) (E)(iv) <(i) <(ii) < (iii)
›Reveal solutionSolution
Wavelength is inverse to Δo; increasing λ: (iv)<(iii)<(ii)<(i). …
- KEAM 2026Set pha-2026-0420F4 marksMCQQ.Which one of the statements is not the limitation of valence bond theory of complexes? (A) It does not give a quantitative interpretation of the thermodynamic stabilities. (B) It does not give quantitative interpretation of magnetic properties.. (C) It explains the colour exhibited by coordination compounds. (D) It does not distinguish between weak and strong ligands. (E) It does not make exact predictions regarding the tetrahedral structures of 4-coordinated complexes.
›Reveal solutionSolution
A recognised limitation of VBT is that it fails to explain colour; the statement that it explains colour (C) is therefore not a limitation.
Valence bond theory has several well-known limitations: it gives no quantitative account of thermodynamic stabilities (A), no quantitative account of magnetic properties (B), does not distinguish strong from weak ligands (D), and makes no exact prediction of tetrahedral geometries (E) — all genuine shortcomings. …
- KEAM 2025Set eng-2025-04294 marksMCQQ.The complex ions [NiCl4]2− and [Ni(CN)4]2− differ by(i) Magnetic moment(ii) Geometry(iii) Hybridisation of central metal ion(iv) Oxidation state of nickel (A) (i),(ii) and(iv) (B) (i),(ii) and(iii) (C) (ii),(iii) and(iv) (D)(ii) and(iii) (E) (i), (ii),(iii) and (iv)
›Reveal solutionSolution
Both have Ni in the +2 state, so (iv) does not differ. They differ in magnetic moment (i), geometry (ii) and hybridisation (iii) — option (B).
Both complexes have Ni2+ (d8), so the oxidation state (iv) is the same in both — it cannot be a point of difference.
- [NiCl4]2−: Cl− is a weak-field ligand, so no pairing occurs. Configuration d8 with 2 unpaired electrons → sp3 hybridisation → tetrahedral, paramagnetic. …
- KEAM 2025Set eng-2025-04294 marksMCQQ.Four complex ions are given in Column I and the colours of light absorbed are given in Column II. Match the correct answer from the codes given below. Complex:(a) [Ti(H2O)6]3+;(b) [Cu(H2O)4]2+;(c) [CoCl(NH3)5]2+;(d) [Co(NH3)6]3+ Colour of light absorbed:(i) Blue;(ii) Yellow;(iii) Blue green;(iv) Red (A) (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i) (B) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i) (C) (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i) (D) (a)-(i), (b)-(iv), (c)-(ii), (d)-(iii) (E) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
›Reveal solutionSolution
[!TLDR]
Using crystal-field strength to rank the d-d absorption energies, [Ti(H2O)6]3+ absorbs blue-green, [Cu(H2O)4]2+ red, [CoCl(NH3)5]2+ yellow and [Co(NH3)6]3+ blue — option (A).
Concept
In a transition-metal complex, d-electrons are excited across the crystal-field gap Δ. The complex absorbs the wavelength matching Δ; a stronger ligand field means a larger Δ and absorption of higher-energy (shorter-wavelength, toward blue/violet) light. This CFT reasoning is standard in the NCERT/CBSE coordination-chemistry chapter that the KEAM syllabus draws from.
Solution
- (b) [Cu(H2O)4]2+: aqua ligands give a small Δ; the deep-blue solution absorbs low-energy red light ⇒ (iv).
- (a) [Ti(H2O)6]3+: a single d-d band near 500nm absorbs blue-green light (complex looks purple) ⇒ (iii). …
- KEAM 2025Set pha-2025-0424F4 marksMCQQ.Which of the following is a spin free complex? (A) [Ni(CO)4] (B) [Co(NH3)6]3+ (C) [Ni(CN)4]2− (D) [CoF6]3− (E) [Mn(CN)6]3−
›Reveal solutionSolution
"Spin free" = high spin. Only [CoF6]3−, with the weak-field F− ligand, keeps its d-electrons unpaired (high spin).
A spin-free (high-spin) complex forms with weak-field ligands, where the crystal-field splitting is too small to force pairing.
- [Ni(CO)4]: CO strong field, Ni(0) d10 — diamagnetic, not relevant as "spin-free."
- [Co(NH3)6]3+: NH3 strong-ish field, Co3+ d6 — low spin.
- [Ni(CN)4]2−: CN− strong field — low-spin, square planar, diamagnetic. …
- KEAM 2025Set pha-2025-0424A4 marksMCQQ.Which of the following complex ion is diamagnetic? (A) [MnCl6]3− (B) [Fe(CN)6]3− (C) [Co(C2O4)3]3− (D) [FeF6]3− (E) [CoF6]3−
›Reveal solutionSolution
[Co(C2O4)3]3− is diamagnetic.
Check the unpaired electrons in each ion:
- [MnCl6]3−: Mn3+ d4, weak-field Cl− ⇒ 4 unpaired — paramagnetic.
- [Fe(CN)6]3−: Fe3+ d5 low spin t2g5 ⇒ 1 unpaired — paramagnetic.
- [Co(C2O4)3]3−: Co3+ d6; oxalate is a fairly strong field ligand giving low spin t2g6eg0 ⇒ 0 unpaired — diamagnetic. …
- KEAM 2025Set pha-2025-0429F4 marksMCQQ.Which of the following is an outer orbital complex? (A) [Co(NH3)6]3+ (B) [Mn(CN)6]3− (C) [Co(C2O4)3]3− (D) [MnCl6]3− (E) [Fe(CN)6]3−
›Reveal solutionSolution
Outer-orbital (high-spin) complexes form with weak-field ligands that use the outer d orbitals (sp3d2). Among the options only [MnCl6]3− has a weak-field ligand (Cl−); the rest have strong-field ligands (CN−, NH3, C2O42−) giving inner-orbital (d2sp3) complexes.
Reasoning
Whether a complex is inner- or outer-orbital depends on the ligand field strength:
- [Co(NH3)6]3+ — NH3 strong field, d2sp3, inner orbital.
- [Mn(CN)6]3− — CN− strong field, inner orbital.
- [Co(C2O4)3]3− — Co(III) with oxalate, low-spin inner orbital. …
- KEAM 2024Set eng-2024-06094 marksMCQQ.The type of d-d transition of the electron occurs in [Ti(H2O)6]3+ is (A) t2g2eg1→t2g1eg2 (B) t2g1eg0→t2g1eg0 (C) t2g1eg0→t2g0eg1 (D) t2g0eg1→t2g1eg0 (E) t2g2eg0→t2g1eg1
›Reveal solutionSolution
Ti3+ is a d1 ion; the single electron jumps t2g→eg.
In [Ti(H2O)6]3+, titanium is in the +3 state: Ti is [Ar]3d24s2, so Ti3+ is [Ar]3d1 — a single d electron. In an octahedral field it occupies the lower t2g set: t2g1eg0. Absorption of light (giving the violet col …
- KEAM 2024Set eng-2024-06094 marksMCQQ.The increasing order of field strength of ligands in the spectrochemical series is (A) CO<H2O<Cl−<I− (B) Cl−<H2O<CO<I− (C) H2O<CO<I−<Cl− (D) H2O<I−<Cl−<CO (E) I−<Cl−<H2O<CO
›Reveal solutionSolution
Increasing field strength: I−<Cl−<H2O<CO.
In the spectrochemical series the ligands are arranged by increasing crystal-field splitting power. The relevant fragment is
I−<Br−<Cl−<F−<H2O<NH3<en<CN−≈CO.
Hence for the given ligands the increasing field strength is …
- KEAM 2024Set eng-2024-06094 marksMCQQ.The number of unpaired electrons in [CoF6]3− is (A) one (B) four (C) zero (D) two (E) three
›Reveal solutionSolution
[CoF6]3− is a high-spin d6 complex (weak-field F−) with 4 unpaired electrons.
Cobalt in [CoF6]3− is Co3+: [Ar]3d6. Fluoride is a weak-field ligand, so the splitting Δo is small and the complex is high spin. The six d electrons fill as
t2g4eg2, …
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