Chemistry: Atoms First 2e · Essential Ideas
Measurements
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In 30 seconds
Chemistry is a quantitative science: almost every conclusion rests on measurements of Mass Amount of matter in an object (kg, g). Full entry →, Volume Space an object occupies (m³, L, mL). Full entry →, temperature, or amount. To communicate measurements unambiguously, scientists worldwide use the International System of Units (SI) — one set of base units for the fundamental quantities. This topic covers the SI base units, common derived units (volume, density, speed), the metric prefixes that scale units, and the conversion method called Dimensional analysis Unit-conversion method using conversion factors and unit cancellation. Full entry → (factor-label method). It ends with the Celsius, Kelvin SI temperature unit starting at absolute zero; K = °C + 273.15. Full entry →, and Fahrenheit temperature scales and how to convert between them.
The central skill is a reliable procedure: write the unit relationship, build a Conversion factor A fraction equal to 1 relating two units (e.g., 1000 m / 1 km). Full entry →, and cancel units. Master dimensional analysis now, and every later calculation — molar mass, stoichiometry, gas laws — becomes easier.
Why this matters
- Units are part of the answer. "The dose is 5" tells you nothing; "5 mg" tells you what to administer. In healthcare, unit errors are a recognized cause of medication errors, so unit literacy is a patient-safety skill.
- The world agrees on SI. Science, medicine, and most countries use metric units. Converting between units (mL to L, mg to g, °C to K) is a daily task in labs and clinics.
- Dimensional analysis is the universal converter. The same method converts metric prefixes, metric to other systems, and later moles to grams to molecules.
- Exam value: SI units, prefixes, and conversions appear on nearly every chemistry exam, and temperature conversions (especially °C ↔ K) are guaranteed questions.
The college version
Core Concepts
SI base units
The SI system defines seven base units, each measuring one fundamental quantity. For this course, the ones you will use most are:
| Quantity | SI base 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 |
Two conventions trap students: the kilogram, not the gram, is the SI Base unit A fundamental SI unit (m, kg, s, K, mol, A, cd). Full entry → of mass (grams are more convenient in the lab), and the kelvin takes no degree sign.
Metric prefixes
The metric system scales base units by powers of ten using prefixes. The most important ones for introductory chemistry:
| Prefix | Symbol | Factor |
|---|---|---|
| kilo- | k | 103 (1000) |
| deci- | d | 10-1 (0.1) |
| centi- | c | 10-2 (0.01) |
| milli- | m | 10-3 (0.001) |
| micro- | µ | 10-6 |
| nano- | n | 10-9 |
So 1 kilometer = 1000 m, 1 centimeter = 0.01 m, 1 milligram = 0.001 g, and 1 microliter = 10-6 L. Prefixes apply to any base or Derived unit A unit made by combining base units (m³, g/mL, m/s). Full entry →: mL, kg, µm, nm, and so on.
Derived units
Many quantities are combinations of base units. Volume — the amount of space an object occupies — is length cubed, with the SI unit m³; in the lab, liters (L) and milliliters (mL) are standard, with 1 mL = 1 cm³ exactly. Density is mass per volume (g/mL or kg/m3). Speed is length per time (m/s or km/h). You will build derived units throughout the course — for example, molarity (mol/L) and pressure (N/m²).
Dimensional analysis: converting units
Dimensional analysis converts units by multiplying by conversion factors — fractions equal to 1 that express the relationship between units. Because 1 km = 1000 m, both fractions below equal 1:
1000 m1 km and 1 km1000 m
You choose the orientation that cancels the unit you want to eliminate: (1) write the given quantity with its unit; (2) multiply by the conversion factor arranged so the starting unit cancels; (3) confirm the unit you want remains; (4) calculate. Units behave like numbers — they multiply, divide, and cancel.
Temperature scales
Temperature measures the average kinetic energy of particles. Three scales matter:
- Celsius (°C) — everyday science; water freezes at 0 °C and boils at 100 °C.
- Kelvin (K) — the SI scale, same degree size as Celsius but starting at absolute zero. Never negative and proportional to average kinetic energy, it is required in gas law calculations.
- Fahrenheit (°F) — common in the US for weather and cooking.
The conversion relationships are:
TK = T°C + 273.15
T°F = 95 T°C + 32
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Mass | Weight | Mass is the amount of matter (constant, kg/g). Weight is the gravitational force on it (changes with location, N). |
| Kelvin (K) | Degree Celsius (°C) | K = °C + 273.15. Kelvin has no degree sign, never goes negative, and is the SI unit used in gas laws. |
| Gram | Kilogram | The kilogram is the SI base unit of mass; the gram is a derived convenience (1 kg = 1000 g). |
| Liter | Cubic meter | m³ is the SI volume unit; the liter (1 L = 1000 cm³) is common in lab work. 1 mL = 1 cm³ exactly. |
| Metric prefix direction | — | "kilo" multiplies by 1000 (1 km = 1000 m); "milli" divides by 1000 (1 mL = 0.001 L). Getting the direction wrong reverses the answer by 10⁶. |
| Conversion factor orientation | — | 1 km/1000 m and 1000 m/1 km both equal 1 — choose the one that cancels the unit you want to eliminate. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Scientists use one shared ruler system called metric so that a chemist in Japan and a nurse in Brazil mean exactly the same thing by "5 grams." The prefixes are like LEGO pieces: "kilo" means a thousand, "milli" means a thousandth, so a kilometer is 1000 meters and a millimeter is a tiny thousandth of a meter. Converting units is like trading coins: 10 dimes = 1 dollar, so you swap the old unit for the new one, canceling out what you started with.
Worked example
Worked example 1 — metric prefix conversion. A lab procedure calls for 250 mL of solution, but your graduated cylinder is marked in liters. Convert 250 mL to liters.
Relationship: 1 L = 1000 mL. Build the conversion factor with mL on the bottom so it cancels:
250 mL × 1 L1000 mL = 0.250 L
The mL units cancel (they appear in numerator and denominator), leaving liters. Answer: 0.250 L.
Worked example 2 — two-step conversion. A marathon is 42.195 km; express it in centimeters.
First convert km → m using 1 km = 1000 m, then m → cm using 1 m = 100 cm:
42.195 km × 1000 m1 km × 100 cm1 m = 4,219,500 cm
Both starting units cancel in turn, leaving cm. Answer: 4.2195 × 106 cm.
Worked example 3 — temperature conversion. A patient's temperature is 39.0 °C; convert to kelvins and degrees Fahrenheit.
Kelvin first:
TK = T°C + 273.15
TK = 39.0 + 273.15 = 312.2 K
Then Fahrenheit:
T°F = 95 T°C + 32
T°F = 95(39.0) + 32 = 70.2 + 32 = 102.2 °F
A fever of 39.0 °C is 312.2 K and 102.2 °F — three scales, one temperature. Note the kelvin carries no degree sign.
Worked example 4 — density with derived units. A liquid sample of volume 25.0 mL has a mass of 19.5 g. Find its density.
density = mV = 19.5 g25.0 mL = 0.780 g/mL
The derived unit g/mL combines the mass base unit with the volume derived unit — exactly what dimensional analysis predicts when you divide g by mL.
Key takeaways
- SI base units: meter (length), kilogram (mass), second (time), kelvin (temperature), mole (amount), ampere (current), candela (luminous intensity). Kilogram, not gram, is the SI base unit.
- Key prefixes: kilo 103, deci 10-1, centi 10-2, milli 10-3, micro 10-6, nano 10-9.
- Volume: 1 L = 1000 mL; 1 mL = 1 cm³ exactly. SI volume unit is m³.
- Density = mass/volume, commonly g/mL or g/cm3.
- Dimensional analysis: multiply by a conversion factor arranged so unwanted units cancel; the surviving unit must match the one you want.
- Kelvin ↔ Celsius: TK = T°C + 273.15 (no degree sign on K).
- Fahrenheit: T°F = 95T°C + 32.
- Always write the unit with every number; a bare number is incomplete.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
What are the SI base units for length, mass, time, and temperature?
Show answer
Length: meter (m); mass: kilogram (kg); time: second (s); temperature: kelvin (K).
Convert 3.5 kg to grams.
Show answer
3.5 kg × 1000 g1 kg = 3500 g = 3.5 × 103 g.
Convert 0.045 L to milliliters.
Show answer
0.045 L × 1000 mL1 L = 45 mL.
Convert 25.0 °C to kelvins.
Show answer
TK = 25.0 + 273.15 = 298.2 K.
Convert 98.6 °F to °C. (Hint: rearrange the Fahrenheit formula.)
Show answer
Rearrange: T°C = 59(T°F - 32) = 59(98.6 - 32) = 59(66.6) = 37.0 °C.
A block has a mass of 54.0 g and a volume of 20.0 cm³. What is its density in g/cm³?
Show answer
density = 54.0 g / 20.0 cm3 = 2.70 g/cm3.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- SI
- International System of Units, the world's standard measurement system.
- Base unit
- A fundamental SI unit (m, kg, s, K, mol, A, cd).
- Derived unit
- A unit made by combining base units (m³, g/mL, m/s).
- Prefix
- A multiplier placed before a unit (kilo-, milli-, micro-).
- Conversion factor
- A fraction equal to 1 relating two units (e.g., 1000 m / 1 km).
- Dimensional analysis
- Unit-conversion method using conversion factors and unit cancellation.
- Kelvin
- SI temperature unit starting at absolute zero; K = °C + 273.15.
- Mass
- Amount of matter in an object (kg, g).
- Volume
- Space an object occupies (m³, L, mL).
Sources & references
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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