Difficulty: Introductory | Prerequisites: None (this is foundational material)
Chapter 1 is the toolkit chapter: it gives you the measurement language, number-handling rules, and classification vocabulary that every later topic in CHM 11100 assumes you already have. If you cannot convert units, count significant figures, or tell a compound from a mixture, the stoichiometry and bonding chapters will be rough going. This material maps directly onto the first exam and reappears in nearly every problem set for the rest of the semester.
Learn the seven metric prefixes, how density and dimensional analysis work, and the rules for significant figures and scientific notation. Know how to classify matter (element, compound, pure substance, mixture) and distinguish physical from chemical properties. These basics underpin every calculation and concept that follows.
Metric prefixes (M, k, d, c, m, µ, n, p)
The standard multipliers attached to SI base units. M = mega (10⁶), k = kilo (10³), d = deci (10⁻¹), c = centi (10⁻²), m = milli (10⁻³), µ = micro (10⁻⁶), n = nano (10⁻⁹), p = pico (10⁻¹²). Think of these as the "exchange rates" between differently sized versions of the same unit.
Density
Mass per unit volume, d = m / V. Water's density at room temperature is 1 g/mL, which serves as the reference point for comparing other substances. In simple terms, density tells you how much stuff is packed into a given space.
Scientific notation
A way of writing very large or very small numbers as a coefficient (between 1 and 10) multiplied by a power of ten. For example, 0.00042 becomes 4.2 × 10⁻⁴. Think of it as a shorthand that keeps the significant digits visible and the zeros out of the way.
Significant figures (sig figs)
The digits in a measured value that carry meaning, including the last digit which is estimated. Zeroes can be tricky: leading zeroes are never significant, trailing zeroes after a decimal point always are. In simple terms, sig figs tell you how precisely something was actually measured.
Precision
How close repeated measurements are to each other. A set of measurements can be precise (tightly clustered) without being accurate. Think of it as consistency: you keep hitting the same spot, even if that spot is off-target.
Accuracy
How close a measurement is to the true or accepted value. You can be accurate on average but imprecise if your individual readings scatter widely. Think of it as correctness: you hit the bullseye, even if not every time.
Dimensional analysis (factor-label method)
A problem-solving technique that uses conversion factors to cancel units step by step until you reach the desired unit. In simple terms, you multiply by fractions that equal 1 (like 1000 m / 1 km) to hop between units without changing the value.
Pure substance
Matter with a fixed, definite composition. Includes elements (one type of atom) and compounds (two or more elements chemically bonded in a fixed ratio). In simple terms, every sample of a pure substance is identical at the molecular level.
Mixture
Two or more substances physically combined but not chemically bonded. Homogeneous mixtures (solutions) look uniform throughout. Heterogeneous mixtures have visibly distinct regions. Think of saltwater (homogeneous) versus a salad (heterogeneous).
Element
A substance that cannot be broken down into simpler substances by chemical means. Each element is defined by its number of protons. In simple terms, it is the simplest type of pure substance.
Compound
A pure substance made of two or more elements chemically bonded in a fixed ratio. Water (H₂O) is always two hydrogens and one oxygen. Think of it as a recipe with exact, non-negotiable proportions.
States of matter symbols: (s), (l), (g), (aq)
(s) = solid, (l) = liquid, (g) = gas, (aq) = aqueous (dissolved in water). These subscripts appear in chemical equations to show what physical form each substance is in.
Extensive property
A property that depends on the amount of matter present, such as mass, volume, or energy. Double the sample, double the value.
Intensive property
A property that does not depend on the amount of matter, such as density, temperature, or boiling point. A cup of water and a swimming pool have the same density.
Mass is measured with a balance. It is an intrinsic property of matter and does not change with location (unlike weight).
Volume of liquids is read from graduated cylinders or volumetric flasks. Irregular solids use water displacement.
Density = mass ÷ volume. Water at room temperature has a density of 1 g/mL. Objects with density greater than 1 g/mL sink in water; those with density less than 1 g/mL float.
To solve a density problem, rearrange d = m/V to isolate whatever variable is missing.
Scientific notation places one non-zero digit before the decimal point, then multiplies by 10 raised to some power.
Moving the decimal left increases the exponent; moving it right decreases the exponent.
When multiplying, add exponents. When dividing, subtract exponents.
Significant figures rules for measured quantities:
All non-zero digits are significant.
Zeroes between non-zero digits are significant (e.g. 205 has three sig figs).
Leading zeroes are never significant (0.0034 has two sig figs).
Trailing zeroes after a decimal point are significant (2.50 has three sig figs).
Trailing zeroes in a whole number without a decimal point are ambiguous; use scientific notation to be clear.
Sig figs in calculations:
Multiplication and division: the answer has the same number of sig figs as the input with the fewest sig figs.
Addition and subtraction: the answer has the same number of decimal places as the input with the fewest decimal places.
Precision vs accuracy: Precision is reproducibility (tight grouping). Accuracy is closeness to the true value (centred on the target). Data can be precise but inaccurate, accurate but imprecise, both, or neither.
Set up conversion factors so that unwanted units cancel and the desired unit remains.
The seven metric prefixes (M, k, d, c, m, µ, n, p) are the most commonly tested conversions.
Key metric-to-English conversions to memorise:
5 mL = 1 teaspoon
1 kg = 2.2 lbs
1 inch = 2.54 cm (exact)
Multi-step conversions chain several factors together. Write them out fully so you can see each unit cancel.
Pure substances have a fixed composition.
Elements contain only one kind of atom (e.g. O₂, Fe).
Compounds contain two or more elements in a fixed ratio (e.g. H₂O, NaCl).
Mixtures are physical combinations, not chemically bonded.
Homogeneous mixtures (solutions) look uniform (e.g. saltwater, air).
Heterogeneous mixtures have visibly different regions (e.g. sand in water, granite).
Know the names and symbols of the first 20 elements (H through Ca).
Atoms are the smallest unit of an element that retains its identity. Molecules are two or more atoms bonded together.
Solid (s): fixed shape, fixed volume, particles packed tightly in a regular arrangement.
Liquid (l): no fixed shape (takes the shape of the container), fixed volume, particles close together but free to slide.
Gas (g): no fixed shape, no fixed volume, particles widely spaced and moving rapidly.
Aqueous (aq): dissolved in water. This is not a separate state of matter but a label used in equations.
Physical properties can be observed or measured without changing the substance's identity (colour, melting point, density, odour).
Chemical properties describe how a substance reacts or transforms into new substances (flammability, reactivity with acid).
Physical changes alter appearance but not composition (melting ice, dissolving sugar).
Chemical changes produce new substances (burning wood, rusting iron).
Extensive properties depend on sample size (mass, volume, energy).
Intensive properties are independent of sample size (density, temperature, boiling point).
Density formula
d = m / V
Rearranged: m = d × V, or V = m / d
Metric prefix ladder (each step is a factor of 10 in the relevant direction)
Prefix | Symbol | Factor |
|---|---|---|
Mega | M | 10⁶ |
Kilo | k | 10³ |
Deci | d | 10⁻¹ |
Centi | c | 10⁻² |
Milli | m | 10⁻³ |
Micro | µ | 10⁻⁶ |
Nano | n | 10⁻⁹ |
Pico | p | 10⁻¹² |
Key metric-to-English conversions
Conversion | Value |
|---|---|
1 inch | 2.54 cm (exact) |
1 kg | 2.2 lbs |
5 mL | 1 teaspoon |
Density is how engineers decide whether a material will float or sink, and it is the principle behind hydrometers that test the sugar content of wine or the charge level of a car battery's acid. Significant figures matter in pharmaceutical dosing: reporting a drug concentration to the wrong number of decimal places can mean the difference between a therapeutic dose and a toxic one. Dimensional analysis is the same method NASA uses when converting between metric and imperial units for spacecraft components, and a famous unit-conversion error is what caused the loss of the Mars Climate Orbiter in 1999.
Students often assume all trailing zeroes are significant. They are significant only when a decimal point is present. The number 1500 is ambiguous (could be 2, 3, or 4 sig figs), but 1500. (with the decimal point) has four.
Students often confuse precision and accuracy. A balance that consistently reads 5.02 g for a sample that truly weighs 5.50 g is precise but not accurate.
Students often treat dimensional analysis as optional and try to do conversions "in their heads." Writing out the full factor-label setup is the single most reliable way to avoid unit errors on exams.
Students often think that homogeneous mixtures are pure substances because they look uniform. A solution like saltwater is uniform but still contains two substances that can be physically separated.
⚠️ Density problems (given two of d, m, V, solve for the third) are a near-certainty on Exam 1.
⚠️ Sig fig questions typically appear as "how many significant figures does this number have?" and as "report this calculation to the correct number of sig figs."
⚠️ Multi-step unit conversions using the seven metric prefixes are heavily tested. Practise chaining two or three conversion factors in a single problem.
⚠️ Knowing the first 20 elements (names and symbols) by heart is expected. These appear throughout the naming and bonding chapters too.
⚠️ Distinguishing between elements, compounds, and mixtures from molecular-level diagrams (pictures of atoms and molecules) is a common question format.
True or False: The number 0.00320 has three significant figures. (True)
True or False: Density is an extensive property. (False, it is intensive)
Fill in the blank: 1 km = ______ m. (1000)
True or False: Air is a heterogeneous mixture. (False, air is a homogeneous mixture)
Fill in the blank: In the expression d = m / V, if mass is in grams and volume is in mL, density is in ______. (g/mL)
Q: A metal block has a mass of 57.3 g and a volume of 6.5 mL. What is its density, reported to the correct number of significant figures?
A: d = 57.3 g / 6.5 mL = 8.8 g/mL (two sig figs, limited by 6.5 which has two).
Q: Convert 0.075 km to centimetres.
A: 0.075 km × (1000 m / 1 km) × (100 cm / 1 m) = 7500 cm, or 7.5 × 10³ cm.
Q: How many significant figures are in 1.0040?
A: Five. The 1, the two 4s (non-zero), the zero between 1 and 4 (captive), and the trailing zero after the 4 (after a decimal point) are all significant.
Q: Classify each as element, compound, or mixture: (a) table salt, (b) oxygen gas, (c) bronze.
A: (a) Compound (NaCl, fixed ratio of Na and Cl). (b) Element (O₂, only one type of atom). (c) Mixture (alloy of copper and tin, variable composition).
Q: A substance has a density of 0.78 g/mL. Will it float or sink in water?
A: It will float. Its density is less than 1 g/mL (the density of water).
Q: Is boiling point an extensive or intensive property? Explain.
A: Intensive. The boiling point of water is 100 °C whether you have a teaspoon or a swimming pool.
The classification of matter (elements, compounds, mixtures) feeds directly into Chapter 2, where you learn to name and write formulas for ionic and molecular compounds. You cannot name a compound correctly if you cannot first tell whether it is ionic or molecular. Sig figs and unit conversions reappear in every quantitative problem throughout the course, from stoichiometry to gas laws. The concept of density comes back when discussing molar volume and gas behaviour.
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