Notes
Classifying matter
- Solids have fixed shape and volume, liquids fixed volume only, gases neither.
- Pure substances are elements or compounds. Mixtures are homogeneous (solutions) or heterogeneous, and can be separated by physical means.
- Physical changes (melting, dissolving) keep the substance the same. Chemical changes (burning, rusting) make new substances; look for gas, color change, precipitate, heat or light.
Measurement
| Quantity | SI unit | Common prefixes |
|---|---|---|
| mass | kilogram (kg) | kilo $= 10^3$ |
| length | meter (m) | centi $= 10^{-2}$ |
| temperature | kelvin (K) | milli $= 10^{-3}$ |
| amount | mole (mol) | micro $= 10^{-6}$ |
- $K = °C + 273$, $1 \text{ mL} = 1 \text{ cm}^3$, and density $\displaystyle D = \frac{m}{V}$.
- Accuracy means close to the true value. Precision means repeated results agree.
Working with numbers
- Sig figs: leading zeros never count; trailing zeros count only with a decimal point.
- Multiply/divide: fewest sig figs. Add/subtract: fewest decimal places.
- Scientific notation: $a \times 10^n$ with $1 \le a < 10$. Add exponents to multiply, subtract to divide.
- Dimensional analysis: multiply by conversion factors so unwanted units cancel.
Topics in this unit
Each topic has its own short notes and practice.
Practice
Air is an even blend of gases. Pure water and NaCl are compounds, and sand with iron is heterogeneous.
Melting is a change of state, a physical change.
All the zeros are either between nonzero digits or trailing after a decimal, so all 5 digits count.
$m = D \times V = 0.80 \times 250 = 200$ g.
$\displaystyle 4.5 \text{ h} \times \frac{60 \text{ min}}{1 \text{ h}} \times \frac{60 \text{ s}}{1 \text{ min}} = 16{,}200$ s.
$9.36 \div 3.0 = 3.12$, rounded to 2 sig figs because 3.0 has 2.
Free response
Write your answer first, then open the scoring guide.
Free-response question
A student finds the density of an unknown metal cube. The cube has a mass of 43.56 g. She places it in a graduated cylinder, and the water level rises from 22.0 mL to 26.9 mL.
(a) Find the volume of the cube and its density, with correct significant figures.
Show the answer and scoring guide
Volume $= 26.9 - 22.0 = 4.9$ mL. Density $\displaystyle = \frac{43.56 \text{ g}}{4.9 \text{ mL}} = 8.889 \rightarrow 8.9$ g/mL, since 4.9 has only 2 sig figs.
Check off the points you earned:
(b) The density of copper is 8.96 g/mL. Calculate the percent error if the metal is copper.
Show the answer and scoring guide
Percent error $\displaystyle = \frac{|8.9 - 8.96|}{8.96} \times 100\% = 0.67\%$. The small error suggests the metal is likely copper.
Check off the points you earned:
(c) Convert the measured density to kg/L using dimensional analysis.
Show the answer and scoring guide
$\displaystyle 8.9 \frac{\text{g}}{\text{mL}} \times \frac{1 \text{ kg}}{1000 \text{ g}} \times \frac{1000 \text{ mL}}{1 \text{ L}} = 8.9$ kg/L. The two factors of 1000 cancel.
Check off the points you earned: