Foundations of Chemistry: Matter, Measurement, and Significance

Exam logistics and study tips

• 15 questions; should take about 20–25 minutes.

• Not all questions are chemistry-focused; some are math, data interpretation, or graph-reading.

• Bring a calculator and paper; use your own brain; avoid Googling answers.

• If you haven’t signed in to the online textbook, do so over the weekend to prepare for class.

Three states of matter (recap and setup for today)

• Solid, liquid, gas are the three primary states of matter.

• Differences among states:

  • How closely particles are spaced

  • How they move

  • How they occupy space

• Today we’ll discuss terminology about particles and how to talk about mass, matter, and measurements.

Mass vs. weight

• Mass vs. weight are often used interchangeably, but they are different.

• Weight depends on gravity; mass does not.

• Example: on Earth vs. Moon, weight changes due to gravity, mass stays the same.

Law of conservation of matter

• Core idea: there is no detectable change in the total quantity of matter during a transformation.

• Formal expression: mass is conserved across a process: $m<em>{ ext{initial}} = m</em>{ ext{final}}$

• Meaning: matter cannot be created or destroyed in ordinary chemical processes.

Matter definition and broad classification

• Matter: anything that has mass and occupies space.

• Classification into two broad buckets:

  • Mixtures

  • Pure substances

• Determinants: if a sample has constant properties and composition, and whether it can be physically separated.

Pure substances vs mixtures

• Pure substances have a fixed composition; they can be broken down only by chemical means.

• Mixtures can be separated physically into components.

• Sub-branches:

  • Mixtures: heterogeneous vs homogeneous

  • Pure substances: elements vs compounds

Pure substances

• Elements:

  • Substances that cannot be chemically broken down into simpler substances.

  • Examples: any on the periodic table (e.g., H, Na, O, Au).

• Compounds:

  • Composed of two or more elements in a fixed ratio.

  • Can be decomposed into simpler substances by chemical changes.

  • Examples:

  • Water: $ext{H}_2 ext{O}$

  • Sodium chloride (table salt): $ext{NaCl}$

• Key difference: elements cannot be decomposed chemically; compounds can be decomposed.

• Note: water can be decomposed into hydrogen and oxygen gases via chemical reactions: $ext{H}<em>2 ext{O} ightarrow ext{H}</em>2 + frac{1}{2} ext{O}_2$

Mixtures

• Mixtures can be separated into pure substances by physical means.

• Heterogeneous mixtures:

  • Components are distinguishable (e.g., copper penny + water; pizza slices with distinct parts like crust, sauce, cheese).

  • Example: oil and water form a heterogeneous mixture that separates into two layers.

• Homogeneous mixtures (solutions):

  • Uniform composition; components are not visually distinguishable.

  • Example: sugar or salt dissolved in water; Gatorade (water + electrolytes + sugar + other ingredients).

• Note: homogeneous mixtures are sometimes referred to as solutions.

Diatomic gases and molecular composition

• Many gases are diatomic: two atoms bonded covalently.

  • Hydrogen gas: $ext{H}_2$

  • Nitrogen gas: $ext{N}_2$

  • Oxygen gas: $ext{O}_2$

• Notation: when a chemical equation mentions nitrogen gas, it refers to $ext{N}_2$ (not monatomic N).

• Molecules can be as small as diatomic (two atoms) or can be larger with many atoms.

• Atoms and molecules:

  • Atom: the smallest unit of an element that retains its properties.

  • Molecule: two or more atoms bonded together by a strong force (chemical bond).

• Visual: ball-and-stick models show atoms (colors denote elements), connected by chemical bonds.

• Chemical bonds and forces include covalent bonds, ionic bonds, and dispersion/Van der Waals forces.

Physical vs chemical properties and changes

• Physical properties: characteristics not changing the chemical composition (e.g., color, density, phase).

• Physical changes: changes in state or form without changing chemical identity (e.g., phase transitions, tearing paper, glass shattering).

• Chemical properties: how a substance interacts with other substances or changes into new substances (e.g., flammability, reactivity).

• Chemical changes (chemical reactions): changes that alter chemical identity, producing new substances (e.g., sodium + chlorine → sodium chloride).

• Examples of chemical changes:

  • Burning/combustion, rusting, digestion, varnishing, baking.

• Important nuance: hot flames often indicate chemical changes, but there are exceptions (e.g., melting ice is a physical change even with heat).

Interpreting a change: physical vs chemical in a sequence

• If in a sequence A → B involves breaking and reforming bonds, that is typically a chemical change.

• If A → C involves a change in arrangement or phase without breaking bonds, it can be a physical change (e.g., state change).

Periodic table familiarity

• While you don’t need to memorize atomic numbers or masses, become familiar with element symbols and names.

• This helps with recognizing what makes up compounds and how reactions proceed.

Measurements and the components of a measurement

• Any measurement consists of three parts:

  • A numerical value (the number)

  • A unit

  • An uncertainty (the last digit of the measurement)

• Example structure: $ext{value} <br>ightarrow ext{unit} <br>ightarrow ext{uncertainty}$

• Five common base quantities and SI base units (for this course):

  • Length: $ext{m}$ (meter)

  • Mass: $ext{kg}$ (kilogram)

  • Time: $ext{s}$ (second)

  • Temperature: $ext{K}$ (kelvin)

  • Amount of substance: $ext{mol}$

• In practice we will use a mix of SI units and a metric system; conversion factors bridge the two systems.

Prefixes and the metric system

• Prefixes change the base unit by powers of ten; memorize them as they apply to any base unit.

• Examples of magnitude changes (positive exponents increase size; negative exponents decrease size):

  • $ext{kilo} = 10^3$ (e.g., 1 \, ext{kg} = 1000 \, ext{g})

  • $ext{milli} = 10^{-3}$ (e.g., 1 \, ext{mL} = 10^{-3} \, ext{L})

  • $ext{centi} = 10^{-2}$

  • $ext{micro} = 10^{-6}$

• Base units to attach prefixes to include length (m), mass (g or kg), volume (L), etc.

• Derived SI units arise when you multiply/base quantities (e.g., area, volume).

Derived SI units and useful equalities

• Area: $A = ext{length} imes ext{width}$ with the unit $ext{m}^2$

• Volume: $V = ext{length} imes ext{width} imes ext{height}$, or equivalently $V = A imes ext{height}$

• Common equality to remember: $1 \, ext{mL} = 1 \, ext{cm}^3$

• Volume units can be given in liters as well: 1 L = 1000 mL and 1 L = 1 dm^3.

• Density concept: $<br>ho = rac{m}{V}$

• SI unit for density is typically $ext{kg} \, ext{m}^{-3}$, but practical units include $ext{g cm}^{-3}$ or $ext{g L}^{-1}$ depending on the sample.

Density and practical notes

• Density expresses mass per unit volume; it is a convenient property for identifying substances and for calculations.

• Remember common density-based conversions when solving problems involving liquids and solids.

Measuring uncertainty and reading a graduated cylinder

• Uncertainty is the last digit that you cannot reliably determine from the instrument scale.

• Example with a graduated cylinder:

  • If the scale marks are every 1 mL and the liquid’s meniscus lies between 20 and 25 mL, you might estimate to the nearest 0.1 mL or 0.01 mL depending on the instrument precision.

  • A reading like between 21.7 and 21.8 mL indicates an uncertainty of ±0.1 mL (the last digit).

• Exact numbers vs uncertain numbers:

  • Counts (e.g., number of hats) are exact with no uncertainty.

  • Measured quantities have uncertainty in the last digit.

Significant figures (significant figures rules)

• Significance basics:

  • Nonzero digits are always significant: 1–9 are significant.

  • Captive (sandwich) zeros between nonzero digits are significant: e.g., 4 0 5 has the zero significant.

  • Trailing zeros: significance depends on context.

  • Trailing zeros to the right of a decimal point are significant.

  • Trailing zeros not to the right of a decimal point are not necessarily significant.

  • Leading zeros are not significant: e.g., 0.0032 has two significant figures (3 and 2).

  • In scientific notation, all digits in the coefficient are significant.

• Examples from the lecture:

  • Digits: 3, 0, 9, 8, 2

  • 0 between 3 and 9 is a captive zero, thus significant.

  • A trailing zero without a decimal point is not significant (e.g., 30 has 1 significant figure).

  • A value like 0.0300 has three significant figures (3, 0, 0).

• Practical implication: determine the number of significant figures before reporting results.

Significant figures in arithmetic

• Addition and subtraction:

  • The result should have as many decimal places as the measurement with the fewest decimal places among those being added/subtracted.

  • Example: $54.139 + 13.2 = 67.339 <br>ightarrow 67.3$ (since 13.2 has only one decimal place).

• Multiplication and division:

  • The result should have the same number of significant figures as the measurement with the fewest significant figures among those involved.

  • Example: $54.139 imes 13.2$

  • 54.139 has 5 significant figures; 13.2 has 3 significant figures.

  • The result should have 3 significant figures.

• Rounding rules:

  • When dropping digits, if the first dropped digit is 5 or greater, round the last retained digit up; if it is 4 or less, leave it unchanged.

  • In scientific practice, rounding rules may be applied carefully to avoid bias in datasets; discussion to be continued in class.

Quick refresher: connecting ideas to practice

• In chemistry, you will work with measurements, conversions, and data interpretation daily.

• Build fluency with units, prefixes, and the concept of uncertainty to communicate results clearly.

• Practice with real data: identify if a change is physical or chemical; distinguish between elements, compounds, mixtures; and apply significant figures consistently.

Quick summary recap

• Matter types and classifications: solids, liquids, gases; mixtures (heterogeneous vs homogeneous) and pure substances (elements vs compounds).

• Physical vs chemical properties and changes; examples of each.

• Atoms, molecules, and bonds; diatomic gases (H₂, N₂, O₂) and their notation.

• Measurement components: number, unit, and uncertainty; SI base units and prefixes; derived units (area, volume).

• Density and critical equalities (e.g., 1 mL = 1 cm³).

• Significant figures: rules for identification and for arithmetic operations; proper rounding.

• Reading a graduated cylinder involves interpreting the meniscus and understanding uncertainty.

End of notes