Chemistry Lecture Notes: Density, Energy, and Atomic Concepts (Chapter E and Chapter One)

Monday is a holiday; next class is Wednesday. SI sessions are being scheduled and the instructor will share the schedule over the weekend once confirmed.
Chapter E homework is due on Sunday (about 580–600 students are enrolled). Do not wait until the last minute; build a regular study habit.
A worksheet will be given next Thursday; topics will cover concepts up to Wednesday’s material; details will be announced as soon as they're ready.
After finishing a module in class, lecture notes will be posted in the same Canvas module under a new file (e.g., post-class notes).
Weekend announcements will outline the plan for the coming week; reading in advance is encouraged; adjust Canvas notifications to receive announcements by email if desired.
If you need a periodic table, you can pick one up from the instructor.

Problem: Determine the density of a copper cube with side length $s = 3.00\,\text{in}$ and mass $m = 3.96\,\text{kg}$ ; answer in $\text{g cm}^{-3}$ .
Key formula: $\rho = \frac{m}{V}$
Volume for a cube: $V = s^{3}$ ; here in inches, then convert to cm³.
Conversions (exact):
- $1\,\text{in} = 2.54\,\text{cm}$
- $1\,\text{kg} = 1000\,\text{g}$
Compute volume in cm³:
- $V = (3.00\text{ in})^{3} = 27\text{ in}^3$
- $V = 27\times (2.54)^{3} = 27\times 16.387064 \approx 442.53\text{ cm}^{3}$
Convert mass to grams: $m = 3.96\,\text{kg} = 3960\,\text{g}$
Density:
- $\rho = \frac{3960\,\text{g}}{442.53\text{ cm}^{3}} \approx 8.95\,\text{g cm}^{-3}$
- Report to 3 significant figures: $\rho \approx 8.95\,\text{g cm}^{-3}$
Important reminder on sig figs: multiply/divide results use the fewest significant figures from the inputs.

Internal energy: $E = U = K + U_p$ where
- Kinetic energy contributes from translation, rotation, and vibration (in gases, liquids, and even solids to some extent).
- Potential energy is associated with relative positions (e.g., electrostatic interactions in bonds).
Heat vs temperature
- Heat $Q$ : energy transfer due to a temperature difference; flows from hot to cold.
- Temperature: measure of the average kinetic energy (motion) of particles in a substance.
Work
- Work is energy transfer due to a force moving a mass against resistance.
First law of thermodynamics (conceptual form)
- Change in internal energy: $\Delta U = q + w$ (sign convention depends on whether q/w are heat/work added to the system).
Energy units
- SI unit: $\text{J}$ (joule). $1\ \text{J} = 1\ \text{kg}\,\text{m}^{2}\,\text{s}^{-2}$
- Calorie conversions:
- $1\ \text{cal} \approx 4.184\ \text{J}$ (lowercase c)
- $1\ \text{Cal} = 1\ \text{kcal} = 1000\ \text{cal} \approx 4.184\ \text{kJ}$ (uppercase C)
- Other energy units:
- $1\ \text{kWh} = 3.6\times 10^{6}\ \text{J}$
Power
- Watt: $1\ \text{W} = 1\ \text{J s}^{-1}$
- Energy can be expressed as $\text{Energy} = \text{Power} \times \text{Time}$

The distinction between heat and temperature will be revisited when introducing calorimetry and energy transfer.
The unit table and exact conversions used in class are given for exact values (e.g., in the instructor’s slides). See the accompanying table for reference.

Setup: density problem with mass and density: $m = 10.0\,\text{g}, \quad \rho = 10.49\,\text{g cm}^{-3}$
Solve for volume: $V = \frac{m}{\rho} = \frac{10.0}{10.49} \approx 0.954\ \text{cm}^{3}$
Report with appropriate sig figs (inputs: 3 sig figs for 10.0 g and 4 sig figs for density; the result should have the fewest sig figs → 3 sig figs): $V \approx 0.955\ \text{cm}^{3}$
Takeaway: always check units and sig figs; write out the setup first rather than relying solely on a calculator.

Learning objectives (three categories in the slides):
- Worth being familiar with
- Important to know
- Enduring understanding
Core topics to expect:
- Atoms and their parts; the concept of the mole; the role of models in representing atomic-scale world.
- How matter is classified: solids, liquids, gases; elements, compounds, mixtures (homogeneous vs heterogeneous).
Representations
- Visual models for atoms and molecules (ball-and-stick, color conventions: O red, H white, C black, N blue, halogens green, others gray).
- Balancing simple chemical relationships (e.g., H2O, electrolysis outcomes) to illustrate conservation and stoichiometry groundwork.
States and properties
- Physical properties vs chemical properties; extensive vs intensive properties; examples include density (intensive) and mass/volume (extensive).
- Phase changes (melting/boiling) as physical properties; chemical changes involve making or breaking bonds.
Practical guidance for studying
- Focus on making quick, conceptual connections between macroscopic observations and atomic models.
- Be prepared to discuss how models help explain why graphite and diamond, though both pure carbon, have different properties.

Matter types:
- Pure substances: elements vs compounds
- Mixtures: homogeneous vs heterogeneous
States of matter:
- Solids: fixed shape and volume; high density; low compressibility
- Liquids: definite volume, takes shape of container; moderate compressibility
- Gases: no fixed volume or shape; highly compressible; fills space
Physical vs chemical changes/properties
- Physical: no chemical identity change (e.g., melting, boiling, density)
- Chemical: substance identity changes (e.g., combustion, synthesis)
Intensive vs extensive properties
- Intensive: independent of amount (e.g., density, boiling point)
- Extensive: depends on amount (e.g., mass, volume)

For density problems: always check units; convert to consistent units; apply the smallest significant figures from inputs.
For energy and thermodynamics: understand that internal energy changes relate to heat and work, with units in joules; memorize or be comfortable with common conversions (calories, kilocalories, kilowatt-hours).
In Chapter 1: focus on the big ideas—atoms, the mole, how to model unseen particles, and how to classify matter; use models to connect micro with macro observations.