Inorganic Chemistry -- Practice Problems

Inorganic Chemistry — Practice Problems

Intuition

Inorganic chemistry covers the rest of the periodic table: While organic chemistry focuses on carbon, inorganic chemistry encompasses metals, minerals, and coordination compounds. It explains why transition metals form coloured compounds, why catalysts work, and how solid-state materials conduct electricity.

Why it matters: Inorganic chemistry underpins catalysis, materials science, medicine (metal-based drugs), and biological systems (metalloenzymes).

The key insight: The d-block elements are special because their partially filled d-orbitals enable variable oxidation states, coloured compounds, and catalytic activity that main-group elements cannot match.

Worked Examples

Example 1: Crystal Field Theory — Colour Prediction

Problem: $[\text{Ti}(\text{H}_2\text{O})_6]^{3+}$ absorbs light at 493 nm. Calculate the crystal field splitting energy $\Delta_o$ and predict the colour of the complex.

Solution:

Step 1: Calculate the energy of absorbed light

$E = \frac{hc}{\lambda} = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{493 \times 10^{-9}} = 4.03 \times 10^{-19} \text{ J}$

Step 2: Convert to kJ/mol

$\Delta_o = (4.03 \times 10^{-19} \text{ J}) \times (6.022 \times 10^{23} \text{ mol}^{-1}) = 242.7 \text{ kJ/mol}$

Step 3: Determine the colour

The complex absorbs yellow-green light (493 nm). The complementary colour (what we see) is purple/violet.

Key insight: The colour of transition metal complexes arises from d-d transitions. The wavelength of absorbed light equals the crystal field splitting energy. Strong-field ligands (like CN⁻) produce large $\Delta_o$ → absorb high-energy (blue) light → appear yellow/orange. Weak-field ligands (like H₂O) produce small $\Delta_o$ → absorb low-energy (red) light → appear blue/green.

Example 2: Unit Cell Calculations

Problem: Iron crystallizes in a BCC structure with a lattice parameter $a = 286.6$ pm. Calculate the atomic radius and packing fraction.

Solution:

Step 1: Relate lattice parameter to atomic radius

In BCC, atoms touch along the body diagonal: $4r = a\sqrt{3}$

$r = \frac{a\sqrt{3}}{4} = \frac{286.6 \times \sqrt{3}}{4} = \frac{286.6 \times 1.732}{4} = 124.1 \text{ pm}$

Step 2: Calculate packing fraction

BCC has 2 atoms per unit cell. Volume of atoms:

$V_{\text{atoms}} = 2 \times \frac{4}{3}\pi r^3 = 2 \times \frac{4}{3}\pi (124.1)^3 = 1.602 \times 10^7 \text{ pm}^3$

Volume of unit cell:

$V_{\text{cell}} = a^3 = (286.6)^3 = 2.355 \times 10^7 \text{ pm}^3$

Packing fraction:

$\text{PF} = \frac{V_{\text{atoms}}}{V_{\text{cell}}} = \frac{1.602 \times 10^7}{2.355 \times 10^7} = 0.680$

Comparison: BCC packing fraction (0.68) is less than FCC/HCP (0.74). This explains why BCC metals (Fe, Cr, W) are generally less dense than FCC metals (Cu, Ag, Au) of similar atomic mass.

Example 3: Coordination Number and Geometry

Problem: Determine the coordination number, geometry, and magnetic properties of $[\text{Fe}(\text{CN})_6]^{4-}$.

Solution:

Step 1: Determine the oxidation state of Fe

$\text{CN}^-$ has charge $-1$. Total charge: $-4$

$\text{Fe} + 6(-1) = -4 \implies \text{Fe} = +2$

Step 2: Electron configuration

$\text{Fe}^{2+}$: $[\text{Ar}] 3d^6$

Step 3: Determine high-spin vs low-spin

$\text{CN}^-$ is a strong-field ligand (high in spectrochemical series). Large $\Delta_o$ → low-spin

$t_{2g}^6 \, e_g^0$

All 6 electrons paired in $t_{2g}$ orbitals.

Step 4: Properties

Key insight: The strong-field CN⁻ ligand forces all electrons into the lower $t_{2g}$ set, creating a diamagnetic complex. With a weak-field ligand like H₂O, the same Fe²⁺ would be high-spin ($t_{2g}^4 e_g^2$, 4 unpaired electrons, paramagnetic).

Chemical Bonding and Periodicity

Coordination Chemistry

Solid State Chemistry

See Also

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

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.