6.3.3 Coloured Complexes

One of the most striking features of transition metal chemistry is the brilliant array of colors displayed by their complexes. From the deep blue of copper(II) sulfate to the green of nickel(II) salts, these colors are not just aesthetically pleasing; they provide valuable information about the electronic structure of the metal ion. This section explains why transition metal complexes are colored and how the color relates to the splitting of d orbitals.

Main Idea

The main idea is that transition metal complexes are colored because they absorb a portion of the visible light and transmit the remaining light. This absorption occurs when electrons in the d orbitals of the metal ion are excited from a lower energy level to a higher energy level. The energy difference between these levels corresponds to the energy of a specific wavelength of visible light. The color we see is the complementary color of the light that is absorbed.

Core Concept

The core concept is d-d electronic transitions. In an isolated transition metal ion, all five d orbitals have the same energy (they are degenerate). However, when ligands approach the metal ion to form a complex, the electric field of the ligands causes the d orbitals to split into two sets of different energies. When white light passes through the complex, an electron can absorb a photon of the right energy and jump from the lower energy d orbital to the higher energy d orbital. The wavelength of light absorbed depends on the energy gap (Δ E) between the split d orbitals. The color observed is the complementary color of the absorbed light.

Detailed Explanation

Why Are Some Complexes Colored and Others Not?

• Colored Complexes: Transition metal ions in solution or solid form are colored because they absorb a part of visible light and the remaining part is transmitted. Light is absorbed by those transition metal complexes which have incomplete 3d sub-shells.
• Example: Copper(II), [Ar]3d⁹, has an incomplete d sub-shell, so it has colored compounds.
• Colorless Complexes: On the other hand, zinc(II), [Ar]3d¹⁰, is a colorless compound because it has a complete d sub-shell. Without an incomplete d sub-shell, there can be no d-d transitions, so no visible light is absorbed.

The Nature of d Orbitals

Before digging into the topic in detail, we must know about d orbitals. All d orbitals in a d sub-shell have the same energy, so they are called degenerate orbitals. However, they are oriented in different directions along the x, y, and z axes.

• d_xy, d_yz, d_xz: These orbitals lie between the axes.
• d_x²-y², d_z²: These orbitals lie along the axes.

Splitting of d Orbitals in an Octahedral Complex

Consider an octahedral complex where six ligands approach the central metal ion along the x, y, and z axes. Almost all transition metals have octahedral complexes. The interaction between the ligands and the central metal ion causes the splitting of the d sub-shell into two sets of orbitals.

• Higher Energy Set (e_g): The ligands interact with the two d orbitals lying along the x, y, and z axes (d_x²-y² and d_z²). These orbitals experience greater repulsion from the ligands' lone pairs, so they are raised to a higher energy level. This set is called the e_g set.
• Lower Energy Set (t_2g): The ligands interact less with the d orbitals oriented between the axes (d_xy, d_yz, and d_xz). These orbitals experience lesser repulsion, so they remain at a lower energy level. This set is called the t_2g set.

The overall energy of both the e_g and t_2g orbitals of the complex is higher than the degenerate 3d orbitals of the metal ion without ligands.

How Color is Produced

When white light strikes a transition metal complex, the complex absorbs light of a specific energy that matches the energy gap (Δ E) between the t_2g and e_g orbitals. This energy is used to promote an electron from the lower energy t_2g orbital to the higher energy e_g orbital.

• Example: [Ti(H_2O)_6]³⁺
• This complex has an octahedral shape with six water molecules acting as ligands around the titanium ion.
• The t_2g set of orbitals has lower energy while the e_g set has higher energy.
• When white light strikes [Ti(H_2O)_6]³⁺, the complex absorbs yellow-green light for the excitation of an electron.
• The color observed (transmitted) is the complementary color, which is red-violet.

• Example: [Ni(H_2O)_6]²⁺
• The nickel complex absorbs red light from white light and appears green, which is the complementary color to red.

• Example: [Cu(H_2O)_6]²⁺
• The copper complex absorbs orange light and appears blue (a complementary color to orange).

The textbook summarizes this with a diagram showing that when white light passes through a solution of Cu^{2+} ions, the orange light is absorbed, and the transmitted light is blue.

Factors Affecting the Color

• The nature of the metal ion: Different metal ions have different numbers of d electrons and different nuclear charges, which affects the splitting.
• The oxidation state of the metal ion: A higher oxidation state generally leads to a larger splitting.
• The nature of the ligands: Different ligands cause different degrees of splitting. This is known as the spectrochemical series.

Intermediate Level

The color of transition metal complexes arises from d-d transitions. In an octahedral complex, the five d orbitals split into two sets: a lower energy set of three orbitals (t_2g) and a higher energy set of two orbitals (e_g). The energy difference between these sets is Δ E. When white light passes through the complex, an electron can be excited from the t_2g to the e_g set by absorbing a photon with energy equal to Δ E. The wavelength of light absorbed depends on the magnitude of Δ E, which in turn depends on the metal ion, its oxidation state, and the ligands. The color observed is the complementary color of the absorbed light. For example, if a complex absorbs orange light, it appears blue. If a complex has a full d subshell (like Zn^{2+}), no d-d transitions are possible, so the complex is colorless.

Important Points

• - Color: Caused by absorption of visible light due to d-d electronic transitions.
• - d-d Transitions: Electrons jump from lower energy t_2g to higher energy e_g orbitals.
• - Requirement: The metal ion must have an incomplete d sub-shell (e.g., Cu^{2+}, Ni^{2+}, Ti^{3+}).
• - Colorless Complexes: Ions with a complete d sub-shell (e.g., Zn^{2+}) are colorless because no d-d transitions are possible.
• - Complementary Color: The color observed is the complement of the color absorbed.
• - Energy Gap (Δ E): Determines the color; depends on the metal, its oxidation state, and the ligands.
• - Octahedral Splitting: t_2g (lower energy) and e_g (higher energy).
• - Example: [Ti(H_2O)_6]³⁺ absorbs yellow-green, appears red-violet.

Remember

• - Color in transition metal complexes = d-d transitions.
• - Absorbed color + Observed color = complementary.
• - Incomplete d subshell is required for color.
• - t_2g = lower energy (3 orbitals); e_g = higher energy (2 orbitals).
• - Zn²⁺ (3d¹⁰) is colorless.
• - Cu²⁺ (3d⁹) is colored.
• - Example: [Cu(H_2O)_6]²⁺ absorbs orange, appears blue.
• - Ligands affect the size of Δ E and thus the color.

Common Mistakes

• - Thinking that the color observed is the color absorbed. It is the complementary color.
• - Forgetting that a complete d subshell means no color. Zn^{2+} is colorless because it has no d-d transitions.
• - Assuming that all transition metal complexes are colored. Some are colorless (e.g., those with d⁰ or d¹⁰ configurations).
• - Confusing the e_g and t_2g sets. e_g is higher in energy, t_2g is lower in energy.
• - Thinking that the metal ion alone determines the color. The ligands also play a crucial role in determining the magnitude of Δ E and hence the color.

Quick Revision

Transition metal complexes are colored due to d-d electronic transitions. When ligands approach the metal ion, the five d orbitals split into two sets: a lower energy t_2g set and a higher energy e_g set. The energy difference (Δ E) between these sets corresponds to the energy of a specific wavelength of visible light. When white light passes through the complex, an electron absorbs a photon of that energy and jumps from the t_2g to the e_g} set. The color observed is the complementary color of the light absorbed. Complexes with an incomplete d subshell (like Cu^{2+}) are colored, while those with a complete d subshell (like Zn^{2+}) are colorless. The exact color depends on the metal, its oxidation state, and the nature of the ligands.

60-Second Revision

Transition metal complexes are colored because of d-d transitions. Ligands split the d orbitals into lower t_2g and higher e_g sets. The energy gap (Δ E) determines the color of light absorbed. The observed color is the complementary color. Complexes with an incomplete d subshell are colored; those with a complete d subshell (like Zn^{2+}) are colorless. The color depends on the metal, its oxidation state, and the ligands.

Frequently Asked Questions (FAQs)

Q1. Why are transition metal complexes colored? Answer: Transition metal complexes are colored because of d-d electronic transitions. When ligands approach the metal ion, the d orbitals split into two sets of different energies. When white light passes through the complex, an electron can absorb a specific wavelength of light and jump from the lower energy set to the higher energy set. The color observed is the complementary color of the light absorbed.

Q2. Why is the [Ti(H_2O)_6]³⁺ complex colored? Answer: The [Ti(H_2O)_6]³⁺ complex has an incomplete d subshell (Ti^{3+} is 3d¹). The d orbitals split into lower t_2g and higher e_g sets. When white light strikes the complex, the electron absorbs yellow-green light and is excited from the t_2g to the e_g} orbital. The complementary color, red-violet, is observed.

Q3. Why is the [Zn(H_2O)_6]²⁺ complex colorless? Answer: The [Zn(H_2O)_6]²⁺ complex is colorless because the zinc ion (Zn^{2+}) has a completely filled 3d subshell (3d¹⁰). There are no vacant d orbitals for an electron to transition to, so no d-d transitions can occur. Therefore, the complex does not absorb visible light and appears colorless.

Q4. Explain the splitting of d orbitals in an octahedral complex. Answer: In an octahedral complex, six ligands approach the metal ion along the x, y, and z axes. The two d orbitals that lie along the axes (d_x²-y² and d_z²) experience greater repulsion from the ligands and are raised to a higher energy level (the e_g set). The three d orbitals that lie between the axes (d_xy, d_yz, and d_xz) experience less repulsion and remain at a lower energy level (the t_2g set).

Q5. What is the relationship between the color absorbed and the color observed? Answer: The color observed is the complementary color of the color absorbed. For example, if a complex absorbs orange light, it will appear blue. If it absorbs red light, it will appear green.

Q6. What is the e_g set of orbitals? Answer: The e_g set consists of the two d orbitals (d_x²-y² and d_z²) that point directly along the axes where the ligands approach in an octahedral complex. These orbitals experience greater repulsion from the ligands and are therefore higher in energy.

Q7. What is the t_2g set of orbitals? Answer: The t_2g set consists of the three d orbitals (d_xy, d_yz, and d_xz) that lie between the axes in an octahedral complex. These orbitals experience less repulsion from the ligands and are therefore lower in energy.

Q8. How do ligands affect the color of a complex? Answer: Different ligands cause different degrees of splitting of the d orbitals. Strong-field ligands (like CN^-) cause a larger splitting (Δ E), while weak-field ligands (like H_2O or Cl^-) cause a smaller splitting. The size of Δ E determines the energy of the light absorbed, and thus the color observed.

• Q9. What is the color of the [Cu(H_2O)_6]²⁺ complex and why?
• Answer: The [Cu(H_2O)_6]²⁺ complex is blue. It absorbs orange light, and the complementary color of orange is blue.

Multiple Choice Questions (MCQs)

Q1. Why is the hexaaquacopper(II) ion blue in color? A. The d-d electronic transition absorbs blue wavelength of visible spectrum. B. The d-d electronic transition absorbs all wavelengths except blue. C. The d-d electronic transition transmits all wavelengths of white light except blue. D. The d-d electronic transition absorbs red wavelength and transmits the remaining light. Correct Answer: B Explanation: The [Cu(H_2O)_6]²⁺ ion absorbs orange light and transmits the remaining light, which appears blue. The absorption is due to a d-d transition.

Q2. What is the name of the splitting of d orbitals in an octahedral complex? A. Crystal field splitting B. Ligand field splitting C. d-d splitting D. All of the above Correct Answer: D Explanation: The splitting of d orbitals in a complex is known as crystal field splitting or ligand field splitting. It is also referred to as d-d splitting because it involves the d orbitals.

Q3. Which of the following complexes is colorless? A. [Cu(H_2O)_6]²⁺ B. [Ni(H_2O)_6]²⁺ C. [Zn(H_2O)_6]²⁺ D. [Ti(H_2O)_6]³⁺ Correct Answer: C Explanation: [Zn(H_2O)_6]²⁺ is colorless because Zn^{2+} has a completely filled 3d subshell (3d¹⁰), so no d-d transitions are possible.

• Q4. What is the color of the [Ni(H_2O)_6]²⁺ complex?
• A. Blue
• B. Green
• C. Red
• D. Yellow
• Correct Answer: B
• Explanation: The [Ni(H_2O)_6]²⁺ complex absorbs red light and appears green, which is the complementary color.

Q5. In an octahedral complex, which set of d orbitals is higher in energy? A. t_2g B. e_g C. Both are equal D. It depends on the metal Correct Answer: B Explanation: The e_g set (d_x²-y² and d_z²) points directly at the ligands and experiences greater repulsion, so it is higher in energy than the t_2g set.

• Q6. What is the complementary color of the light absorbed by [Ti(H_2O)_6]³⁺?
• A. Yellow-green
• B. Red-violet
• C. Blue
• D. Orange
• Correct Answer: B
• Explanation: [Ti(H_2O)_6]³⁺ absorbs yellow-green light. The complementary color is red-violet.

Q7. Why does a transition metal complex with a d¹⁰ configuration appear colorless? A. Because it has no unpaired electrons. B. Because it has no d-d transitions. C. Because it absorbs all light. D. Because it reflects all light. Correct Answer: B Explanation: A d¹⁰ configuration has a full d subshell, so there are no vacant d orbitals for electrons to transition to. Therefore, no d-d transitions can occur, and the complex is colorless.

• Q8. What is the name of the lower energy set of d orbitals in an octahedral complex?
• A. e_g
• B. t_2g
• C. d_xy
• D. d_x²-y²
• Correct Answer: B
• Explanation: The lower energy set is the t_2g set, which consists of the d_xy, d_yz, and d_xz orbitals.

Q9. Which of the following factors does NOT affect the color of a transition metal complex? A. The nature of the metal ion. B. The oxidation state of the metal ion. C. The nature of the ligands. D. The concentration of the complex. Correct Answer: D Explanation: The concentration of the complex affects the intensity of the color but not the color itself. The color is determined by the energy gap (Δ E), which depends on the metal, its oxidation state, and the ligands.

• Q10. In the complex [Cu(H_2O)_6]²⁺, what color of light is absorbed?
• A. Blue
• B. Green
• C. Orange
• D. Red
• Correct Answer: C
• Explanation: The [Cu(H_2O)_6]²⁺ complex absorbs orange light and appears blue.

Multiple Choice Questions (MCQs)

• Q1. Why is the hexaaquacopper(II) ion blue in color?
• A. The d-d electronic transition absorbs blue wavelength of visible spectrum.
• B. The d-d electronic transition absorbs all wavelengths except blue.
• C. The d-d electronic transition transmits all wavelengths of white light except blue.
• D. The d-d electronic transition absorbs red wavelength and transmits the remaining light.
• Correct Answer: B
• Explanation: The [Cu(H_2O)_6]²⁺ ion absorbs orange light and transmits the remaining light, which appears blue.

• Q2. What is the name of the splitting of d orbitals in an octahedral complex?
• A. Crystal field splitting
• B. Ligand field splitting
• C. d-d splitting
• D. All of the above
• Correct Answer: D
• Explanation: The splitting is known as crystal field splitting, ligand field splitting, or d-d splitting.

• Q3. Which of the following complexes is colorless?
• A. [Cu(H_2O)_6]²⁺
• B. [Ni(H_2O)_6]²⁺
• C. [Zn(H_2O)_6]²⁺
• D. [Ti(H_2O)_6]³⁺
• Correct Answer: C
• Explanation: [Zn(H_2O)_6]²⁺ is colorless because Zn^{2+} has a full 3d subshell.

• Q4. What is the color of the [Ni(H_2O)_6]²⁺ complex?
• A. Blue
• B. Green
• C. Red
• D. Yellow
• Correct Answer: B
• Explanation: The [Ni(H_2O)_6]²⁺ complex absorbs red light and appears green.

• Q5. In an octahedral complex, which set of d orbitals is higher in energy?
• A. t_2g
• B. e_g
• C. Both are equal
• D. It depends on the metal
• Correct Answer: B
• Explanation: The e_g set is higher in energy.

• Q6. What is the complementary color of the light absorbed by [Ti(H_2O)_6]³⁺?
• A. Yellow-green
• B. Red-violet
• C. Blue
• D. Orange
• Correct Answer: B
• Explanation: [Ti(H_2O)_6]³⁺ absorbs yellow-green light and appears red-violet.

• Q7. Why does a transition metal complex with a d¹⁰ configuration appear colorless?
• A. Because it has no unpaired electrons.
• B. Because it has no d-d transitions.
• C. Because it absorbs all light.
• D. Because it reflects all light.
• Correct Answer: B
• Explanation: A d¹⁰ configuration has no vacant d orbitals for transitions.

• Q8. What is the name of the lower energy set of d orbitals in an octahedral complex?
• A. e_g
• B. t_2g
• C. d_xy
• D. d_x²-y²
• Correct Answer: B
• Explanation: The lower energy set is the t_2g set.

• Q9. Which of the following factors does NOT affect the color of a transition metal complex?
• A. The nature of the metal ion.
• B. The oxidation state of the metal ion.
• C. The nature of the ligands.
• D. The concentration of the complex.
• Correct Answer: D
• Explanation: Concentration affects intensity, not color.

• Q10. In the complex [Cu(H_2O)_6]²⁺, what color of light is absorbed?
• A. Blue
• B. Green
• C. Orange
• D. Red
• Correct Answer: C
• Explanation: The [Cu(H_2O)_6]²⁺ complex absorbs orange light.

Multiple Choice Questions (MCQs)

• Q1. The [Ti(H_2O)_6]³⁺ ion is violet because it absorbs:
• A. Red light
• B. Yellow-green light
• C. Blue light
• D. Orange light
• Correct Answer: B
• Explanation: The [Ti(H_2O)_6]³⁺ ion absorbs yellow-green light and appears violet (red-violet).

• Q2. Which of the following complexes is expected to be colorless?
• A. [Cu(H_2O)_6]²⁺
• B. [Ti(H_2O)_6]³⁺
• C. [Zn(H_2O)_6]²⁺
• D. [Ni(H_2O)_6]²⁺
• Correct Answer: C
• Explanation: [Zn(H_2O)_6]²⁺ is colorless because Zn^{2+} has a 3d¹⁰ configuration.

• Q3. What is the complementary color of blue?
• A. Red
• B. Green
• C. Orange
• D. Yellow
• Correct Answer: C
• Explanation: The complementary color of blue is orange.

• Q4. What is the name of the energy gap between the t_2g and e_g orbitals?
• A. Crystal field splitting energy (Δ)
• B. Ionization energy
• C. Lattice energy
• D. Hydration energy
• Correct Answer: A
• Explanation: The energy gap between the t_2g and e_g orbitals is called the crystal field splitting energy (Δ).

• Q5. In an octahedral complex, the d_xy, d_yz, and d_xz orbitals belong to the:
• A. e_g set
• B. t_2g set
• C. d_x²-y² set
• D. d_z² set
• Correct Answer: B
• Explanation: The d_xy, d_yz, and d_xz orbitals belong to the t_2g set, which is lower in energy.

• Q6. Which of the following statements is true about the color of transition metal complexes?
• A. The color observed is the same as the color absorbed.
• B. The color observed is the complementary color of the color absorbed.
• C. The color observed is always blue.
• D. The color observed is independent of the ligands.
• Correct Answer: B
• Explanation: The color observed is the complementary color of the light absorbed.

• Q7. The [Cu(H_2O)_6]²⁺ ion appears blue because it absorbs:
• A. Blue light
• B. Green light
• C. Orange light
• D. Red light
• Correct Answer: C
• Explanation: The [Cu(H_2O)_6]²⁺ ion absorbs orange light and appears blue.

• Q8. Which of the following is NOT a factor that affects the color of a transition metal complex?
• A. The nature of the metal ion
• B. The oxidation state of the metal ion
• C. The nature of the ligands
• D. The size of the container
• Correct Answer: D
• Explanation: The size of the container has no effect on the color of a complex.

• Q9. The [Ni(H_2O)_6]²⁺ ion appears green because it absorbs:
• A. Green light
• B. Red light
• C. Blue light
• D. Yellow light
• Correct Answer: B
• Explanation: The [Ni(H_2O)_6]²⁺ ion absorbs red light and appears green.

• Q10. What is the color of the [Ti(H_2O)_6]³⁺ complex?
• A. Blue
• B. Green
• C. Red-violet
• D. Orange
• Correct Answer: C
• Explanation: The [Ti(H_2O)_6]³⁺ complex appears red-violet.