Coordination Chemistry -- Practice Problems

Coordination Chemistry — Practice Problems

10 MCQ questions covering crystal field theory, octahedral/tetrahedral complexes, spectrochemical series, isomerism, and magnetic properties. Select an option to check your answer.

Worked Examples

Example 1: Crystal Field Splitting — Colour Calculation

Problem: $[\text{Ti}(\text{H}_2\text{O})_6]^{3+}$ absorbs at 493 nm. Calculate $\Delta_o$ in cm⁻¹ and kJ/mol.

Solution:

$\tilde{\nu} = \frac{1}{\lambda} = \frac{1}{493 \times 10^{-7} \text{ cm}} = 20,284 \text{ cm}^{-1}$

Converting to energy:

$\Delta_o = hc\tilde{\nu} = (6.626 \times 10^{-34})(3.00 \times 10^{10})(20,284) = 4.03 \times 10^{-19} \text{ J}$

$\Delta_o = 4.03 \times 10^{-19} \times 6.022 \times 10^{23} = 242.7 \text{ kJ/mol}$

Key insight: The colour we see is complementary to the absorbed colour. Absorbing yellow-green (493 nm) → the complex appears purple.

Example 2: Magnetic Moment Calculation

Problem: Calculate the spin-only magnetic moment for $[\text{Mn}(\text{H}_2\text{O})_6]^{2+}$ and predict whether it is high-spin or low-spin.

Solution:

$\text{Mn}^{2+}$: $[\text{Ar}] 3d^5$

$\text{H}_2\text{O}$ is a weak-field ligand → high-spin

Configuration: $t_{2g}^3 e_g^2$ → 5 unpaired electrons

$\mu_{s.o.} = \sqrt{n(n+2)} = \sqrt{5(5+2)} = \sqrt{35} = 5.92 \text{ BM}$

Comparison with experimental value: The experimental magnetic moment of $[\text{Mn}(\text{H}_2\text{O})_6]^{2+}$ is approximately 5.9 BM, confirming the high-spin $d^5$ configuration.

Key insight: For first-row transition metals, the spin-only formula works well. Deviations indicate orbital angular momentum contribution (significant for $d^1$, $d^2$, $d^6$ (high-spin), $d^7$ (high-spin)).

Example 3: Isomer Counting

Problem: How many geometric and optical isomers does $[\text{Co}(\text{en})_2\text{Cl}_2]^+$ have?

Solution:

Step 1: Identify the geometry

Octahedral complex with two bidentate ethylenediamine (en) ligands and two chloride ligands.

Step 2: Geometric isomers

• cis: Cl ligands at 90° (adjacent positions)
• trans: Cl ligands at 180° (opposite positions)

Step 3: Optical isomers

• cis: No internal mirror plane → optically active (two enantiomers: Δ and Λ)
• trans: Internal mirror plane → optically inactive (meso form)

Total isomers: 3 (cis-Δ, cis-Λ, trans)

Key insight: The cis isomer of $[\text{Co}(\text{en})_2\text{Cl}_2]^+$ was one of the first coordination compounds resolved into enantiomers by Alfred Werner, proving the octahedral geometry of coordination compounds.

Crystal Field Theory and Splitting

Isomerism, Magnetism, and Advanced Topics

Intuition

Coordination compounds are metal atoms surrounded by ligands: Transition metals form complexes where ligands (molecules or ions) donate electron pairs to the metal centre. The geometry (octahedral, tetrahedral, square planar) determines the compound’s colour, magnetism, and reactivity.

Why it matters: Coordination chemistry underpins catalysis (Wilkinson’s catalyst), medicine (cisplatin anticancer drug), biology (hemoglobin carries oxygen via an iron complex), and materials science (ruby colour comes from Cr³⁺ in Al₂O₃).

The key insight: Crystal field theory explains why transition metal complexes are coloured — the d-orbital splitting caused by ligands absorbs specific wavelengths of visible light.

Common Mistakes

Confusing crystal field theory with ligand field theory: Crystal field theory treats ligands as point charges and explains d-orbital splitting purely electrostatically. Ligand field theory adds molecular orbital concepts (sigma donation, pi back-bonding) and explains phenomena like the spectrochemical series. Using crystal field theory for pi-bonding effects gives incorrect predictions.

Misidentifying the oxidation state of a metal in a complex: The oxidation state is calculated by assuming all ligands donate their full charge to the metal. For [Fe(CN)₆]³⁻, each CN⁻ is −1, so Fe is +3. A common error is forgetting to account for the overall charge of the complex when calculating the metal’s oxidation state.

Confusing high-spin and low-spin complexes: Strong-field ligands (CN⁻, CO) cause large Δ and favour low-spin (paired electrons). Weak-field ligands (F⁻, H₂O) cause small Δ and favour high-spin (unpaired electrons). Tetrahedral complexes are almost always high-spin because Δ_tet ≈ 4/9 Δ_oct. Do not assume all octahedral complexes are high-spin.

See Also

• Inorganic Chemistry
• Coordination Chemistry
• Inorganic Chemistry — Practice Problems

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

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Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.