Chemistry Unit 1: Matter, Measurement & Math Skills

Quick-reference study sheet

1. Classification of Matter

Matter

Pure Substance

Element

One type of atom

e.g. Fe, O₂, Cu

Compound

2+ elements, fixed ratio

e.g. H₂O, NaCl, CO₂

Mixture

Homogeneous

Uniform; 1 visible phase

e.g. saltwater, air, brass

Heterogeneous

Non-uniform; 2+ phases

e.g. sand + water, salad

Separation Techniques

Technique	Separates	Based On
Filtration	Solid from liquid (heterogeneous)	Particle size
Distillation	Liquids in solution (homogeneous)	Boiling point
Chromatography	Dissolved pigments / substances	Polarity / solubility
Evaporation	Dissolved solid from liquid	Volatility / boiling point
Magnetism	Magnetic solid from mixture	Magnetic properties

2. Physical vs. Chemical Properties

Physical Property

Chemical Property

Observed without changing chemical identity

Color, odor, texture, luster
Melting point & boiling point
Density, mass, volume
Hardness (Mohs scale)
Electrical & thermal conductivity
Solubility, malleability, ductility
State of matter at room temperature

Describes ability to become a new substance

Flammability
Reactivity with acids or water
Toxicity
Ability to rust (oxidize)
Ability to decompose
pH / acidity / basicity
Radioactivity

3. Physical & Chemical Changes; Intensive & Extensive Properties

Physical Change

Chemical Change

No new substance; identity preserved; usually reversible

Cutting, crushing, tearing
Melting, freezing
Boiling, condensing
Dissolving sugar in water

New substance(s) formed; often irreversible

Burning, rusting
Cooking an egg
Souring of milk
Explosion

Signs: gas, precipitate, light/heat, color change, odor

Intensive Property

Extensive Property

Does NOT depend on sample size

Density
Temperature
Melting / boiling point
Color, hardness
Specific heat capacity

Use to identify substances

DOES depend on amount of matter

Mass, weight
Volume
Length / area
Total energy

Change when sample is divided or combined

4. States of Matter & Phase Changes

Solid

Fixed shape & volume

Tightly packed; vibrate in place; strong forces

Liquid

Fixed volume; takes container shape

Close together; slide past each other; moderate forces

Gas

No fixed shape or volume

Far apart; move rapidly; weak/negligible forces

Phase Changes — absorb energy (endothermic) or release energy (exothermic)

Solid → Liquid: Melting (absorbs energy)

Liquid → Solid: Freezing (releases energy)

Liquid → Gas: Vaporization/Boiling (absorbs)

Gas → Liquid: Condensation (releases)

Solid → Gas: Sublimation (absorbs; e.g. dry ice)

Gas → Solid: Deposition (releases; e.g. frost)

Plasma = 4th state; ionized gas at extremely high temperature (e.g. lightning, stars)

5. SI Units & Metric Prefixes

SI Base Units

Quantity	Unit	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Amount of substance	mole	mol
Electric current	ampere	A
Luminous intensity	candela	cd

Common Derived Units

Quantity	Unit / Symbol
Volume	L, mL, cm³
Density	g/mL or g/cm³
Speed	m/s
Force	N = kg·m/s²
Energy	J = kg·m²/s²
Pressure	Pa = N/m²
Concentration	mol/L (molarity, M)

Metric Prefixes (memorize kilo through milli at minimum)

Prefix	Symbol	Power of 10	Decimal Value
giga	G	10⁹	1,000,000,000
mega	M	10⁶	1,000,000
kilo	k	10³	1,000
hecto	h	10²	100
deka	da	10¹	10
(base unit)	—	10⁰	1
deci	d	10^-1	0.1
centi	c	10^-2	0.01
milli	m	10^-3	0.001
micro	μ	10^-6	0.000 001
nano	n	10^-9	0.000 000 001
pico	p	10^-12	0.000 000 000 001

6. Accuracy, Precision & Significant Figures

Accuracy vs. Precision

Accuracy: how close a measurement is to the true/accepted value

Precision: how close repeated measurements are to each other (reproducibility)

Precise but inaccurate = consistent results that miss the true value

Accurate but imprecise = correct on average, but scattered

Good measurements are both accurate AND precise

Significant Figure Rules

All nonzero digits are significant. (456 → 3 sig figs)
Zeros between nonzero digits are significant. (4006 → 4 sig figs)
Leading zeros are NOT significant. (0.0023 → 2 sig figs)
Trailing zeros WITH a decimal point ARE significant. (3.00 → 3 sig figs)
Trailing zeros WITHOUT decimal are not significant — (100 → 1 sig figs).

Sig Figs in Calculations & Rounding

× and ÷ :

Keep the FEWEST sig figs of all values.

4.56 × 1.4 = 6.384 → 6.4 (2 sig figs)

+ and − :

Keep the LEAST number of decimal places.

12.11 + 18.0 = 30.11 → 30.1 (1 decimal place)

Rounding rule: digit to be dropped ≥ 5 → round up; < 5 → round down (leave as is).

7. Scientific Notation

M × 10ⁿ

where 1 ≤ M < 10, and n is a positive or negative integer

Standard → Scientific Notation

93,000,000 = 9.3 × 10⁷
(moved decimal 7 places left → n is positive)
0.000045 = 4.5 × 10^-5
(moved decimal 5 places right → n is negative)

Scientific Notation → Standard

6.02 × 10²³: move decimal 23 places right
1.6 × 10^-19: move decimal 19 places left

8. Dimensional Analysis (Unit Conversion)

Multiply by conversion factors (fractions equal to 1). Set them up so unwanted units cancel diagonally. Continue until only the desired unit remains.

Given × desired unitgiven unit = Answer in desired unit

Example: Convert 5.00 km to cm

Identify given: 5.00 km; identify target unit: cm
Set up factors: 5.00 km × 1000 m1 km× 100 cm1 m
Cancel: km cancels km, m cancels m → cm remains
Calculate: 5.00 × 1000 × 100 = 5.00 × 10⁵ cm

Common Conversion Factors

1 km = 1000 m

1 m = 100 cm

1 cm = 10 mm

1 kg = 1000 g

1 g = 1000 mg

1 L = 1000 mL

1 mL = 1 cm³

1 nm = 10^-9 m

K = °C + 273.15

9. Density Calculations

Density

d = mV

Mass

m = d × V

Volume

V = md

Units: g/mL (liquids & solutions), g/cm³ (solids), g/L (gases). Note: 1 mL = 1 cm³ exactly.

Example: A sample has mass 52.0 g and volume 20.0 mL. Find density.

Write formula: d = m / V
Substitute: d = 52.0 g20.0 mL
Answer: d = 2.60 g/mL (3 sig figs)

⚠ Water displacement:Volume of an irregular solid = V_final − V_initial (read from graduated cylinder). Water density = 1.00 g/mL at 4 °C. Objects denser than water sink; less dense objects float.

10. Percent Error

% error =|measured − accepted|accepted× 100%

Absolute value bars ensure the result is always positive. Also called percent deviation.

Example: You measured density as 8.90 g/mL; accepted value is 8.96 g/mL.

Difference: |8.90 − 8.96| = 0.06
% error = 0.068.96 × 100%
Answer: 0.67%

Low % error (< 5%)

Close to accepted value → good accuracy. Check procedure for ways to reduce it further.

High % error (> 5%)

Check for systematic error, faulty equipment, parallax, or procedural mistakes.