Matter & Measurement
Middle SchoolWhat chemistry studies, and how it counts
Matter is anything that has mass and occupies volume. Chemistry classifies matter along two independent axes. By composition, matter is either a pure substance (fixed composition — an element or a compound) or a mixture (two or more substances physically combined). Mixtures are homogeneous (uniform throughout, i.e. a solution) or heterogeneous (visibly non-uniform).
- Element — cannot be broken into simpler substances by chemical means (e.g. Fe, O₂).
- Compound — two or more elements chemically bonded in fixed ratio (H₂O, NaCl); separable only by chemical reaction.
- Physical change — no new substance; identity preserved (melting ice). Chemical change — bonds break and form, new substances appear (rusting).
Every measurement carries a unit and an uncertainty. The seven SI base units include the metre (m), kilogram (kg), second (s), kelvin (K), and mole (mol). A measured quantity is meaningful only when its precision is stated honestly through significant figures.
Why we obsess over units and digits
A number without a unit is chemically meaningless: "5" could be grams, moles, or degrees. Dimensional analysis — carrying units through a calculation like algebra and cancelling them — is the single most reliable check that a calculation is set up correctly. If the units of your answer come out wrong, the method is wrong, no matter what the arithmetic says.
Significant figures encode how well you know a value. Reporting a mass as 4.5 g claims you know it to a tenth of a gram; 4.500 g claims a thousandth. Overstating precision is a form of lying about your instrument. The rules: all non-zero digits count; zeros between non-zeros count; leading zeros never count; trailing zeros count only if a decimal point is present. In multiplication and division, the answer takes the fewest significant figures of any input; in addition and subtraction, it takes the fewest decimal places.
Worked example — density of an irregular solid
A metal nugget has mass 39.15 g. Dropped into a graduated cylinder holding 20.0 mL of water, the level rises to 25.0 mL. Identify the likely metal.
- Find the volume by displacement: V = 25.0 − 20.0 = 5.0 mL = 5.0 cm³.
- Apply the definition of density: ρ = m / V.
- Substitute: ρ = 39.15 g ÷ 5.0 cm³ = 7.83 g cm⁻³.
- Round to significant figures: the volume (5.0) has 2 sig figs, so ρ ≈ 7.8 g cm⁻³.
- Compare with reference densities: iron is 7.87 g cm⁻³. The nugget is almost certainly iron.
Displacement works only for solids that sink and do not dissolve or react with water. For a floating solid you must weigh it down or use a non-reacting liquid of known density.
Classify each: filtered seawater, brass, oxygen gas, table salt.
Filtered seawater — homogeneous mixture (salt dissolved in water). Brass — homogeneous mixture (an alloy of copper and zinc). Oxygen gas O₂ — pure substance (an element). Table salt NaCl — pure substance (a compound).
How many significant figures are in 0.00420, 100, and 100.0?
0.00420 has 3 (leading zeros don't count; the trailing zero after the decimal does). 100 is ambiguous — written plainly it has 1 sig fig; to show 3 write it as 1.00 × 10². 100.0 has 4 (the decimal point makes all trailing zeros significant).
Convert 72 km h⁻¹ to m s⁻¹ using dimensional analysis.
Multiply by unit-conversion factors chosen so unwanted units cancel:
The kilometres and hours cancel, leaving metres per second — a built-in confirmation the setup was right.
A block is 2.00 cm × 3.00 cm × 4.00 cm and has mass 216 g. Will it float in water?
Volume = 2.00 × 3.00 × 4.00 = 24.0 cm³. Density = 216 g ÷ 24.0 cm³ = 9.00 g cm⁻³. Since 9.00 > 1.00 g cm⁻³ (water), it sinks.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1A metal block has mass 54.0 g and volume 20.0 cm3. Find its density.
- Density = mass / volume.
- Density = 54.0 g / 20.0 cm3.
- Divide: 54.0 / 20.0 = 2.70.
Example 2Report 12.0 mL + 3.45 mL to the correct significant figures.
- Add the values: 12.0 + 3.45 = 15.45.
- For addition, round to the fewest decimal places (12.0 has one).
- Round 15.45 to one decimal place.
Now you try
Work each one out first, then tap to reveal the worked answer.