Matter and Measurement: Quick Revision

A brief note on Matter and Measurement. Read it before a test. Try each question at the end before you open its answer.

Matter

• Matter is a solid, a liquid or a gas.
• A pure substance has a fixed composition: an element (one kind of atom) or a compound (elements in a fixed ratio by mass, with new properties).
• A mixture has substances in any ratio: homogeneous (the same all through) or heterogeneous (parts you can see).
• A physical property keeps the substance the same. A chemical property shows in a chemical change.

Units

• Seven SI base units: metre, kilogram, second, ampere, kelvin, mole and candela.
• Prefixes: milli is $10^{-3}$, micro is $10^{-6}$, nano is $10^{-9}$, kilo is $10^{3}$.
• $1\ \text{L} = 1\ \text{dm}^3 = 1000\ \text{cm}^3$, and $1\ \text{mL} = 1\ \text{cm}^3$.
• Density: $d = \dfrac{m}{V}$.
• Temperature: $T = t_C + 273.15$ in kelvin, with no degree sign. $t_F = 1.8\, t_C + 32$.

Significant figures

• Scientific notation: $N \times 10^{n}$ with $1 \le N < 10$.
• Zeros at the left never count. Zeros at the right count after a decimal point.
• Sums keep the fewest decimal places. Products keep the fewest significant figures.
• Round only the final answer. A dropped 5 leaves an even digit and raises an odd one.
• Precision: readings agree with each other. Accuracy: readings agree with the true value.

Unit factors

• A unit factor is a fraction equal to one, such as $\dfrac{1000\ \text{g}}{1\ \text{kg}}$.
• Choose it so that the unwanted unit cancels. Cube the factor for a volume.
• If the units of the answer are wrong, the setup is wrong.

A worked example

A pebble has a mass of $18.42\ \text{g}$. In a measuring cylinder it raises the water from $40.0\ \text{mL}$ to $46.8\ \text{mL}$. Find its density.

1. Volume. $46.8 - 40.0 = 6.8\ \text{mL} = 6.8\ \text{cm}^3$. A difference keeps one decimal place, so this has 2 significant figures.
2. Density. $\dfrac{18.42\ \text{g}}{6.8\ \text{cm}^3} = 2.7088\ \text{g/cm}^3$.
3. Round. The volume has 2 significant figures, so the density is $2.7\ \text{g/cm}^3$.

Practice with new numbers

A program to try

The program reports one measured volume in three units, each to 3 significant figures.

Mistakes to avoid

• Calling an alloy or air a compound. Both are homogeneous mixtures.
• A degree sign with kelvin. Write $300\ \text{K}$.
• Counting zeros at the left as significant.
• The sum rule for a product. Products keep significant figures, not decimal places.
• A factor upside down. The unit to remove goes on the bottom.

Check yourself

1. Is a gold bar an element, a compound or a mixture? And a cup of sweet tea?

2. A thermometer in a cold store reads $-18\ ^\circ\text{C}$. What is that in kelvin?

3. Which has more significant figures, $0.00720\ \text{m}$ or $72.0\ \text{m}$?

4. A balance always reads $0.20\ \text{g}$ too high, but its readings agree well. Is it precise, accurate, or both?

5. How many seconds are in $1.5\ \text{h}$?