Chemistry 1B Notes (5)

Chemistry 1B Winter Quarter 2026 - Lecture Notes

Course Overview

• Course Code: 40120

• Instructor: Dr. A. J. Shaka

• Institution: University of California, Irvine

• Focus: General Chemistry 1B

Lecture 5 Topics

• More on Solids

• Types of Solids

• Lattice Enthalpy

• Melting Points

• Bragg’s Law

Inferring Stoichiometry

• Unit Cell: A repeating unit of a crystal lattice.

• Molecular Formula: Can be inferred from the unit cell.

  • Importance of counting spheres on faces and corners properly.

  • Example: A unit cell for niobium oxide is presented.

  • Niobium atoms are represented in blue.

  • Oxygen atoms are represented in red.

  • Query: Determine the molecular formula for niobium oxide based on the presented unit cell.

Practice Problem 12 (Niobium Oxide)

• Image representation of unit cell (source: King's College, London).

• Analysis:

  • Six niobium atoms counted on faces contribute as 3 Nb (1/2 per face).

  • Twelve oxygen atoms contributing as 3 O (1/4 per atom).

• Conclusion: The molecular formula appears to be Nb3O3, which simplifies to NbO. Niobium exhibits multiple oxidation states including Nb(II) oxide, NbO2, and Nb2O5.

X-ray Diffraction

• Periodic Crystal Structure: Creates a periodic electron density.

• X-rays: Appropriate wavelength for inducing diffraction patterns.

  • Results in spots of high intensity due to constructive interference.

• Bragg's Contributions: Father-son duo known for correlating scattering angle with spacing between crystal planes.

Bragg’s Law

• Constructive Interference Condition: Defined by the equation $n\lambda = 2d \sin\theta$

  • Where:

  • $n$ = order of the maximum (an integer)

  • $\lambda$ = wavelength of incident X-rays

  • $d$ = distance between crystal planes

  • $\theta$ = angle of diffraction

Types of Solids

• Solids can be categorized into:

  • Atomic solids (network solids)

  • Ionic solids

  • Molecular solids

Metals

• Characteristics: Atoms on lattice points with minimal barriers for outer electron mobility.

Lattice Enthalpy

• Definition: Energy comparison (per mole) of an ionic solid relative to ions at infinite separation.

• Formula for electric potential energy between two point charges: $E = \frac{1}{4\pi\epsilon<em>0}\frac{q</em>1q_2}{r}$

  • Where:

    • $\epsilon_0$ = permittivity of free space

    • $q<em>1, q</em>2$ = magnitudes of the charges

    • $r$ = separation distance between charges

One-Dimensional Infinite Lattice

• Developing the Coulomb potential energy while treating ions as point charges.

• Energy contributions calculated as:
  $E<em>{lattice} = E</em>{attraction} - E_{repulsion}$

• Requires mathematical calculations for series summations of interactions between cations and anions.

Energy Calculations Using Harmonic Series

• Through mathematical summations, deriving relationships to define lattice enthalpy for ionically bonded solids, corresponding to properties of their respective structures.

Data Analysis of Lattice Enthalpy

• Comparison of calculated lattice enthalpy with experimentally measured values.

• Electrical Potential Energy Estimation: Higher charges (MgO compared to LiF) typically yield increased lattice enthalpy.

  • Example: LiF (1017 kJ/mol) and MgO (3890 kJ/mol) suggests a lattice energy ratio close to 4 due to charge interactions.

Correlation Between Lattice Enthalpy and Melting Point

• Conceptual relationship: Lattice enthalpy and melting point correlate as both involve energy transitions involving ionic solids.

  • Suggested graphical representation of data to visualize relationships.

Models Versus Reality

• Theoretical models of ionic radius may have limitations and are subject to variations due to lattice structure complexities such as hybridization and coordination.

Rule-Based Predictions in Ionic Solids

• Goldschmidt’s Model: Ion behavior modeled as incompressible hard spheres which informs stability predictions.

  • Pauling’s Rules help to determine structural arrangements:

  1. Each ion's coordination must maximize interactions with neighboring ions.

  2. Local charge neutrality is critical.

  3. Polyhedra may share vertices, edges, and faces to minimize energy.

Trends in Ionic Radii

• General trends observed:

  • Decrease across the periodic table for ions with equal charge.

  • Increase down groups with exceptions like the Lanthanide Contraction.

  • Cation size tends to be smaller than corresponding anions due to effective nuclear charge.

Phase and Allotropes

• Definitions: A phase is a state of matter with uniformity in composition and state.

• Examples: Liquid water vs. solid water (ice).

• Allotropes distinguished by structural forms, e.g., graphite vs. diamond.

• Stability conditions and energy barriers for converting between allotropes are discussed, emphasizing diamond's metastable nature.