Units
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Topic Summary & Highlights
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Core Concept
Purpose: Units provide a standardized framework to express quantities and ensure measurements are consistent, comparable, and easily understood worldwide.
Consequences of Unit Errors:
Mars Climate Orbiter loss (1999): $125 million mistake due to metric/imperial confusion
Laboratory safety hazards from incorrect concentrations
Failed experiments and wasted materials
Practice Tips
Ignoring units completely - Always write units with every number!
Mixing unit systems - Don't combine metric and imperial
Incorrect prefix conversions - Remember: kilo = ×1000, milli = ÷1000
Forgetting to convert - Match units before calculating
Wrong derived unit combinations - Check that units make sense
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Definition
Units provide a standardized framework to express quantities and ensure that measurements are consistent, comparable, and easily understood.
Various types of units are used to represent different types of quantities. Some commonly used units include:
SI Units: The International System of Units (SI) is the most widely used system of measurement in science, including chemistry. It provides a standardized set of units for fundamental quantities such as length (meter, m), mass (kilogram, kg), time (second, s), temperature (kelvin, K), amount of substance (mole, mol), and more.
Derived Units: Derived units are formed by combining base units. For example, volume is derived from the base unit of length, resulting in units such as cubic meter (m³) or liter (L).
Metric Prefixes: Metric prefixes are used to indicate decimal multiples or submultiples of a unit. For example, kilo- (k) represents a factor of 1000, so 1 kilogram (kg) is equal to 1000 grams (g).
Seven Base SI Units
| Quantity | Unit Name | Symbol | Example |
|---|---|---|---|
| Length | meter | m | 1.5 m test tube |
| Mass | kilogram | kg | 0.5 kg of sodium |
| Time | second | s | 30 s reaction time |
| Temperature | kelvin | K | 298 K room temp |
| Amount of substance | mole | mol | 2.0 mol of gas |
| Electric current | ampere | A | 0.5 A electrolysis |
| Luminous intensity | candela | cd | Light measurements |
Common Derived Units
| Quantity | Derived Unit | Symbol | Base Unit Combination | Example |
|---|---|---|---|---|
| Volume | cubic meter | m³ | m × m × m | 0.025 m³ |
| liter | L | dm³ (0.001 m³) | 2.5 L solution | |
| Concentration | molar | M | mol/L | 0.1 M NaCl |
| Velocity | meter per second | m/s | m ÷ s | 340 m/s sound |
| Energy | joule | J | kg⋅m²/s² | 1000 J heat |
| Pressure | pascal | Pa | kg/(m⋅s²) | 101,325 Pa atm |
| Density | kg per cubic meter | kg/m³ | kg ÷ m³ | 1000 kg/m³ water |
Metric Prefixes
Purpose: Indicate decimal multiples or submultiples of units
| Prefix | Symbol | Factor | Decimal | Example |
|---|---|---|---|---|
| kilo- | k | 1,000 | 10³ | 1 kg = 1,000 g |
| centi- | c | 0.01 | 10⁻² | 1 cm = 0.01 m |
| milli- | m | 0.001 | 10⁻³ | 1 mL = 0.001 L |
| micro- | µ | 0.000001 | 10⁻⁶ | 1 µm = 0.000001 m |
| nano- | n | 0.000000001 | 10⁻⁹ | 1 nm = 0.000000001 m |
$\boxed{\text{EXAMPLE PROBLEM}}$
Convert 3.5 kilograms (kg) to grams (g).
$3.5 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}}$ = 3,500 g
$\boxed{\text{EXAMPLE PROBLEM}}$
Convert a car's speed of 90 kilometers per hour (km/h) to meters per second (m/s).
$$90 \frac{\text{km}}{\text{h}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{60 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ s}} = \frac{90 \times 1000}{60 \times 60} \frac{\text{m}}{\text{s}} = \frac{90000}{3600} \frac{\text{m}}{\text{s}} = \mathbf{25 \frac{\text{m}}{\text{s}}}$$
Best Practices/ Study Tips
Always Remember:
Write units with every measurement
Carry units through all calculations
Check that final units make sense
Convert to consistent units before calculating
Use appropriate prefixes for readability
Unit Conversion Strategy:
Identify what you have and what you need
Set up conversion factor (new unit/old unit)
Multiply and cancel units
Check that answer makes sense
