Chemistry: Key Vocabulary from Chapter 1 (Matter, Measurements, and Dimensional Analysis)

1.1 The Study of Chemistry

Chemistry is the study of matter and the changes that matter undergoes.
- Matter: anything that has mass and occupies space.
- All activities and technologies rely on chemistry (everyday relevance).
Learning objectives for 1.1: Chemistry in context, historical development, everyday life applications, the scientific method, distinguishing hypotheses, theories, and laws, and understanding macroscopic, microscopic, and symbolic domains.
Chemistry in Context: definition of chemistry as the study of the composition, properties, and interactions of matter.
Historical development overview:
- Greeks proposed that matter consisted of four elements: earth, air, fire, and water.
- Alchemists attempted to transform base metals into noble metals; contributions to manipulating matter but not scientific by modern standards.
Chemistry and everyday life examples:
- Digesting food, synthesizing polymers for clothing, cookware, and credit cards, refining crude oil into gasoline and other products.
- Through this course you will explore changes in composition/structure of matter, classify changes, and understand associated energy changes.
The Scientific Method:
- Chemistry is based on observation and experimentation.
- Hypothesis: a tentative explanation of observations.
- Laws: summarize a vast number of experimental observations and describe or predict aspects of the natural world.
- Theory: a well-substantiated, comprehensive, testable explanation of a particular aspect of nature.
Visual aid: Figure 1.4 illustrating the scientific method as a non-linear, open-ended process needing inquiry and revision.
Connections to other disciplines: chemistry is central to understanding many other STEM fields (interrelationships shown in Figure 1.3).

1.2 Phases and Classification of Matter

Core definitions:
- Matter: anything that occupies space and has mass.
- The three common states (phases):
- Solid: rigid with a definite shape.
- Liquid: flows and takes the shape of its container.
- Gas: expands to fill both the shape and volume of its container.
Mass vs. weight:
- Mass = amount of matter in an object.
- Weight = force of gravity on an object; depends on gravity, so weight differs with location (earth vs moon).
Law of conservation of matter:
- There is no detectable change in the total quantity of matter present when matter converts from one type to another.
- Applies to both chemical and physical changes.
Elements and the periodic table:
- An element is a pure substance that cannot be broken down into simpler substances by chemical changes.
- >100 known elements; ~90 occur naturally; ~two dozen created in laboratories.
Pure substances vs mixtures:
- Pure substances have constant composition.
- Elements: one type of substance (cannot be broken down chemically).
- Compounds: two or more types of elements chemically bonded; can be broken down by chemical changes; properties differ from the uncombined elements.
- Mixtures: two or more types of matter that can be present in varying amounts and separated by physical changes.
Types of mixtures:
- Homogeneous (solutions): uniform composition throughout.
- Heterogeneous: composition varies from point to point (e.g., oil and water, trail mix).
- Visual examples: Figure 1.10 shows heterogeneous dressing and homogeneous sports drink; Figure 1.11 depicts classification possibilities.
Atoms and molecules:
- Atom: the smallest particle of an element that has the properties of that element and can enter into a chemical combination.
- Historical context: idea proposed by Leucippus and Democritus (5th century BCE); Dalton later supported with quantitative measurements.
- Molecule: two or more atoms bonded together.
Additional notes:
- Figure 1.15 demonstrates decomposition of water at macroscopic, microscopic, and symbolic levels: battery provides current (microscopic) and decomposes water into H2 and O2 (macroscopic); symbolic representation shows H2O → H2 + O2.
Everyday-life and technology link: understanding phase changes and mixtures underpins real-world materials and processes.

1.3 Physical and Chemical Properties

Core idea: distinguishing whether a property or change is physical or chemical.
Physical properties:
- Characteristics that do not involve a change in chemical composition.
- Examples: density, color, hardness, melting/boiling points, electrical conductivity.
Physical changes:
- Changes in state or properties of matter without changing chemical composition.
- Examples: melting butter (solid → liquid), steam condensing to liquid water.
Chemical properties:
- Characteristics that involve a chemical change or the potential for such change.
- Examples: flammability, toxicity, acidity, reactivity, heat of combustion.
Chemical changes:
- Involve transformation into a different substance with different properties (chemical bonds broken/formed).
- Examples: copper reacting with nitric acid to form copper nitrate and nitrogen dioxide; combustion of a match; oxidation of myoglobin in red meat; browning of a banana (new substances form).
Adhesion to rule set for classification:
- Some processes show both physical and chemical aspects (e.g., crystallization or dissolution can involve changes at different levels).
1.3 exercises (in the transcript):
- Multiple-choice questions on identifying pure substances and types of changes (e.g., among orange juice, steam, wine, oxygen, vegetable soup; identifying physical vs chemical changes).
The “Extensive vs Intensive” distinction appears later (1.6), but it is a key practical tool for characterizing matter:
- Extensive properties depend on the amount of matter (e.g., mass, volume).
- Intensive properties do not depend on amount (e.g., density, temperature).

1.4 Measurements

Core concept: measurements provide information used to form hypotheses, theories, and laws.
Each measurement yields three pieces of information:
- Size or magnitude (a number).
- Standard of comparison (a unit).
- Uncertainty (the degree of precision).
Units and SI system:
- SI units provide a standardized system for measurements.
- The base SI units include length (m), mass (kg), time (s), temperature (K), electric current (A), amount of substance (mol), luminous intensity (cd).
- The table of base units (Table 1.2) defines each with its symbol.
Prefixes and derived units:
- Common prefixes allow creating fractional or large units (Table 1.3).
- Derived units: volume (m^3), density (kg/m^3), etc. For volume, 1 dm^3 = 1 L and 1 cm^3 = 1 mL.
Practical examples and conversions:
- The meter is defined by the distance light travels in vacuum in 1/299,792,458 of a second.
- The centimeter and liter relationships (1 dm^3 = 1 L; 1 cm^3 = 1 mL).
- Temperature scales: Kelvin (K); Celsius (°C) allowed; conversions between °C and K; 0 °C = 273.15 K; 100 °C = 373.15 K.
Temperature and time examples:
- 54 °C can be converted to Fahrenheit and Kelvin (practice problems).
- Temperature limits on containers (e.g., 130 °F) require conversions to Celsius and Kelvin for safety guidelines.
Extra context and examples:
- The distance to Proxima Centauri example introduces parsecs and light-year conversions, illustrating large-scale unit handling in dimensional analysis.
- Volume and density as derived SI units emphasize how base units combine to form practical measurements.
Practical measurement issues:
- Accuracy, precision, and potential systematic errors highlighted (e.g., NASA Mars Climate Orbiter loss due to English-to-metric conversion error).

1.5 Measurement Uncertainty, Accuracy, and Precision

Definitions:
- Accuracy: how close a measurement is to the true or accepted value.
- Precision: how repeatable or consistent measurements are when repeated under the same conditions.
- Exact numbers: counting measurements and defined quantities are considered exact (infinite significant figures).
Significant figures (sig figs):
- Any measured value has uncertainty; the last digit is typically estimated.
- Rules for determining sig figs:
- Nonzero digits are always significant.
- Captive zeros (zeros between nonzeros) are significant.
- Trailing zeros are significant if there is a decimal point.
- Leading zeros are not significant.
- Examples of sig figs formatting and interpretation are given (e.g., 0.028675 → 0.0287; 18.3384 → 18.3; 6.8752 → 6.88; 92.85 → 92.8).
Reading measurements and uncertainty:
- The uncertain digit is estimated; measurements are reported with appropriate digits to reflect uncertainty.
- Graduated cylinder example: read to the bottom of the meniscus and estimate the last digit; typical uncertainty is ±1 in the last digit.
Propagation of uncertainty and rounding rules:
- Addition/Subtraction: result should have the same number of decimal places as the quantity with the fewest decimal places (least precise).
- Multiplication/Division: result should have the same number of significant figures as the quantity with the fewest significant figures.
- Rounding convention: when the dropped digit is >5, round up; if <5, round down; if exactly 5, round to make the retained digit even (banker's rounding).
Exact numbers and their role in calculations:
- Exact numbers have infinite significant figures and do not limit the result’s sig figs (e.g., defined quantities, counting quantities).
Worked examples and practice:
- Example: reading a 21.6 mL measurement with 2 significant digits certain and 6 as the uncertain digit; discussion of acceptable variations (4.56–4.57 mL acceptable; 4.63 mL would be misreported).
- Practice problems illustrate how to report temperature and other measurements with correct significant figures.

1.6 Mathematical Treatment of Measurement Results (Dimensional Analysis)

Dimensional analysis overview:
- A powerful method for converting units and performing calculations with quantities by treating units as mathematical factors that must cancel appropriately.
- Conversion factors are ratios of equivalent quantities expressed in different units (e.g., 1 in = 2.54 cm).
Common conversion factors (Table 1.6 and related content):
- Length: 1 m = 1.0936 yd; 1 in = 2.54 cm (exact); 1 km = 0.62137 mi.
- Volume: 1 L = 1 dm^3; 1 gal = 3.7854 L; 1 cm^3 = 1 mL.
- Mass: 1 kg = 2.2046 lb; 1 lb = 453.59 g; 1 am = 0.39370 in; 1 (avoirdupois) oz = 28.349 g.
- Temperature: 0 K corresponds to −273.15 °C; conversion relations between Kelvin, Celsius, and Fahrenheit: °F = (°C × 9/5) + 32; °C = (°F − 32) × 5/9.
- Energy, pressure, and other derived units with relationships such as 1 J = 1 kg·m^2/s^2 and 1 Pa = 1 N/m^2.
Worked examples illustrating dimensional analysis:
- Example: FDA sodium intake recommendation of no more than 2400 mg per day, converted to pounds using the relationships 1 g = 1000 mg and 1 lb = 453.6 g. The method emphasizes proper unit cancellation and magnitude sanity checks.
- Dimensional analysis for converting 34 inches to centimeters: use 1 in = 2.54 cm and 1 m = 1.0936 yd along with the appropriate conversion chain to obtain the final value in cm.
- Blood volume example: 5.2 L → m^3 by recognizing 1 L = 1×10^−3 m^3; thus 5.2 L = 5.2 × 10^−3 m^3.
- Area and paint coverage problem: convert 955 ft^2 to yd^2 and relate to gallon coverage (15 yd^2 per gallon) to determine required gallons; result around 7.0 gallons.
- Lead density example: 11.4 g/cm^3; convert to lb/ft^3 to compare densities across units.
- Density problem framework: density = mass/volume; use given units to yield consistent SI units (kg/m^3) or common units (g/cm^3, g/L).
Practical and real-world relevance:
- Dimensional analysis helps prevent unit errors in engineering, medicine, and science (e.g., Mars Orbiter unit mismatch anecdote).
- The method underpins safe and reliable design, testing, and data interpretation by ensuring unit consistency.

Key formulas and concepts (summary with LaTeX)

Fundamental definitions:
- Mass vs. weight: W = m g, where g is the local acceleration due to gravity.
- Density: d = rac{m}{V} with SI unit kg/m^3 (or g/cm^3 for solids and liquids; g/L for gases).
- Volume: The SI-derived unit is ext{m}^3; common practical units include ext{L} = 1 ext{ dm}^3, ext{mL} = 10^{-3} ext{ L}, ext{cm}^3 = ext{mL}.
SI base units (examples):
- Length: ext{m}; Mass: ext{kg}; Time: ext{s}; Temperature: ext{K}; Electric current: ext{A}; Amount of substance: ext{mol}; Luminous intensity: ext{cd}.
Temperature relationships:
- T( ext{K}) = T(^{
  m o}C) + 273.15
- ^{
  m o}C = rac{5}{9}(^{
  m o}F - 32)
Dimensional analysis core principle:
- Use conversion factors to cancel units and obtain the desired unit.
- Example conversions: 1~ ext{in} = 2.54~ ext{cm} ext{ (exact)}, 1~ ext{L} = 1~ ext{dm}^3 = 1000~ ext{cm}^3, 1~ ext{gal} = 3.7854~ ext{L}.
Sig figs rounding rules (brief):
- Addition/subtraction: round to the least number of decimal places.
- Multiplication/division: round to the least number of significant figures.
- Rounding convention for ties: round to the nearest even digit.

Real-world applications and connections

Open-ended, non-linear nature of scientific progress reflected in the scientific method figure; progress often requires reworking questions and ideas.
Connections to other disciplines demonstrated by the interdisciplinarity of chemistry (biochemistry, physics, geology, environmental science, etc.).
Practical implications of measurement: ensuring safety, quality control, and scientific integrity when recording data (e.g., medical measurements, laboratory results, industrial tolerances).
Ethical and practical implications:
- Unit conversion errors can have catastrophic consequences (e.g., Mars Climate Orbiter loss) highlighting the importance of precision, standardization, and attention to detail in measurements and reporting.

Quick-reference table (condensed)

SI base units: length (m), mass (kg), time (s), temperature (K), electric current (A), amount of substance (mol), luminous intensity (cd).
Derived units and common conversions: 1~ ext{L} = 1~ ext{dm}^3 = 1000~ ext{cm}^3, 1~ ext{g} = 0.001~ ext{kg}, 1~ ext{cm}^3 = 1~ ext{mL}, 1~ ext{in} = 2.54~ ext{cm}, 1~ ext{gal} = 3.7854~ ext{L}, 1~ ext{ft}^3 = 28.317~ ext{L}.
Common properties: physical (density, color, melting/boiling points) vs chemical (flammability, reactivity, heat of combustion).
Key ideas for study: macroscopic (observables), microscopic (particle-level), and symbolic (equations/representations) domains.
Practice emphasis: solving qualitative classification problems, performing unit conversions with dimensional analysis, and applying significant-figure rules in calculations.

1.1 The Study of Chemistry

Chemistry is the study of matter and the changes it undergoes.
The Scientific Method is based on observation and experimentation:
- Hypothesis: tentative explanation.
- Law: summarizes observations, describes/predicts natural aspects.
- Theory: well-substantiated, comprehensive explanation.
Chemistry involves macroscopic, microscopic, and symbolic domains.

1.2 Phases and Classification of Matter

Matter: anything with mass and volume.
States (phases): Solid (definite shape/volume), Liquid (definite volume, takes container shape), Gas (no definite shape/volume).
Mass vs. Weight: Mass is amount of matter; Weight is gravitational force.
Law of Conservation of Matter: Matter is conserved during chemical and physical changes.
Elements: Pure substances, cannot be broken down chemically.
Compounds: Two or more elements chemically bonded, properties differ from elements.
Mixtures: Two or more types of matter, varying amounts, separable by physical changes.
- Homogeneous (solutions): Uniform composition.
- Heterogeneous: Non-uniform composition.
Atom: Smallest particle of an element.
Molecule: Two or more atoms bonded.

1.3 Physical and Chemical Properties

Physical properties: Do not change chemical composition (e.g., density, color, melting point).
Physical changes: Alter state or properties without changing chemical composition (e.g., melting).
Chemical properties: Involve potential for chemical change (e.g., flammability, reactivity).
Chemical changes: Transform into different substances with new properties (e.g., combustion, oxidation).
Extensive properties: Depend on amount of matter (e.g., mass, volume).
Intensive properties: Do not depend on amount (e.g., density, temperature).

1.4 Measurements

Measurements provide: size, unit, and uncertainty.
SI Units: Standardized system (e.g., length (m), mass (kg), time (s), temperature (K)).
Prefixes: Used for fractional or large units (e.g., kilo-, milli-).
Derived Units: Combinations of base units (e.g., volume ( ext{m}^3), density ( ext{kg/m}^3)).
Temperature Conversions: T( ext{K}) = T(^{
m o}C) + 273.15; ^{
m o}C =􏰄rac{5}{9}(^{
m o}F - 32).

1.5 Measurement Uncertainty, Accuracy, and Precision

Accuracy: How close a measurement is to the true value.
Precision: How repeatable measurements are.
Exact numbers: Counted values or definitions, have infinite significant figures.
Significant Figures (Sig Figs):
- Nonzero digits are significant.
- Captive zeros are significant.
- Trailing zeros are significant only if a decimal point is present.
- Leading zeros are not significant.
Rounding Rules:
- Addition/Subtraction: Round to fewest decimal places.
- Multiplication/Division: Round to fewest significant figures.

1.6 Mathematical Treatment of Measurement Results (Dimensional Analysis)

Dimensional analysis: Method using conversion factors to change units properly.
Conversion factors: Ratios of equivalent quantities (e.g., 1 hinspace ext{in} = 2.54 hinspace ext{cm}). Unit cancellation is key.
Prevents errors, crucial in science and engineering (e.g., Mars Climate Orbiter).

Key Formulas and Concepts

Density: d = rac{m}{V}
Volume: ext{L} = 1 ext{ dm}^3, ext{mL} = 10^{-3} ext{ L}, ext{cm}^3 = ext{mL}
Temperature: T( ext{K}) = T(^{
m o}C) + 273.15, ^{
m o}C = rac{5}{9}(^{
m o}F - 32), ^{
m o}F = rac{9}{5}(^{
m o}C) + 32

Real-world Applications

Chemistry is interdisciplinary, central to many STEM fields.
Precision and standardization in measurements prevent catastrophic errors.