Matter and Measurement
Before you can do chemistry, you need two things: a clear way to describe what matter is, and a reliable way to measure it. This page covers both — classification, states, properties, units, significant figures, conversions, and density.
Classification of Matter
- Element: a pure substance made of one kind of atom (e.g., Fe, O2). It cannot be broken down by chemical means.
- Compound: a pure substance of two or more elements chemically combined in a fixed ratio (e.g., H2O, NaCl). It can only be broken down by a chemical change.
- Homogeneous mixture: uniform throughout — one phase (e.g., salt water, air). Composition can vary.
- Heterogeneous mixture: not uniform — two or more phases you can see or separate physically (e.g., sand in water, oil and vinegar).
Separation follows the classification: mixtures separate by physical means (filtration, distillation, evaporation); compounds only by chemical means.
States of Matter
Solid: fixed shape and volume, particles locked in place. Liquid: fixed volume, takes the shape of its container, particles flow past each other. Gas: neither fixed shape nor fixed volume — it fills its container. (A fourth state, plasma, is ionized gas: lightning, the Sun.) Adding heat generally drives solid → liquid → gas; removing heat reverses it.
Physical vs Chemical Properties and Changes
A physical property is observed without changing what the substance is: colour, density, melting point, solubility. A chemical property describes how it reacts: flammability, acidity, rusting. Likewise, a physical change (melting, dissolving, cutting) changes form but not identity, while a chemical change (burning, rusting, cooking) makes new substances. Signs of a chemical change: colour change, gas produced, precipitate formed, heat or light released, or a new smell.
SI Units and Prefixes
The base SI units you will use most: length in metres (m), mass in kilograms (kg), time in seconds (s), temperature in kelvin (K), amount in moles (mol). Common prefixes: kilo- ($10^3$), centi- ($10^{-2}$), milli- ($10^{-3}$), micro- ($10^{-6}$), nano- ($10^{-9}$). Temperature: $K = °C + 273.15$; note that a change of 1 °C equals a change of 1 K.
Significant Figures
Significant figures (sig figs) record how precisely a measurement was made. The rules:
- All nonzero digits count: 42.7 has 3 sig figs.
- Zeros between nonzero digits count: 1004 has 4.
- Leading zeros never count: 0.00457 has 3 (4, 5, 7).
- Trailing zeros count only if a decimal point is present: 250.0 has 4, but 250 has 2 (unless written as $2.50 \times 10^2$).
- Exact numbers (counted items, defined conversions like 1 km = 1000 m) have unlimited sig figs.
Rounding: if the first digit dropped is 5 or more, round the last kept digit up; if it is 4 or less, leave it. In multiplication and division, the answer has as many sig figs as the least precise measurement; in addition and subtraction, as many decimal places as the least precise measurement.
Dimensional Analysis
Convert units by multiplying by conversion factors — fractions equal to 1, arranged so unwanted units cancel: $$\text{starting quantity} \times \frac{\text{new unit}}{\text{old unit}}$$ Chain factors for multi-step conversions, and always check that the final unit is the one you want.
Density
Density links mass and volume: $$d = \frac{m}{V}$$ It is an intensive property — it does not depend on how much you have. Common units are g/mL (or g/cm3) for solids and liquids. An object floats in a liquid if its density is lower than the liquid's.
Practice Problems
- Classify each as element, compound, homogeneous mixture, or heterogeneous mixture: (a) distilled water, (b) air, (c) iron filings, (d) salt water.
- A metal block has mass 125 g and volume 25.0 cm3. Calculate its density.
- Convert 72.0 km/h to m/s.
- How many significant figures are in 0.005040? Round 8.4567 to three significant figures.
Answers: 1. (a) compound (b) homogeneous mixture (c) element (d) homogeneous mixture 2. 5.00 g/cm3 3. 20.0 m/s 4. 4 sig figs; 8.46