1.4 Measurements | Chemistry: Atoms First 2e

Learning Objectives

Explain the process of measurement and its three essential components
Identify basic SI base units for length, mass, temperature, and time
Use metric prefixes and powers of 10 for unit scaling and conversions
Calculate density using direct mass/volume measurements or water displacement

Core Concepts & Principles

Every measurement in chemistry provides three essential pieces of information:

Magnitude: A numerical value representing size.
Unit: A standard of comparison.
Uncertainty: An indication of precision limits.

The Danger of Missing Units

Numbers without units are meaningless or dangerous. For example, prescribing a medication dose of "100" without specifying milligrams (mg) versus grams (g) can easily result in a fatal overdose.

The International System of Units (SI Units)

The International System of Units (SI units) establishes fixed, globally accepted standards for fundamental physical properties.

Length: Measured in meters ( $\text{m}$ ).
Mass: Measured in kilograms ( $\text{kg}$ ).
Time: Measured in seconds ( $\text{s}$ ).
Temperature: Measured in kelvin ( $\text{K}$ ) or Celsius ( $\text{°C}$ ).

Metric units scale by powers of 10 using standardized prefixes (e.g., kilo- means $10^3$ , milli- means $10^{-3}$ , micro- means $10^{-6}$ ).

Derived Units: Volume and Density

Units for complex properties are derived from SI base units:

Volume: The space occupied by matter. Standard SI unit is the cubic meter ( $\text{m}^3$ ), though chemists commonly use liters ( $\text{L}$ ), milliliters ( $\text{mL}$ ), or cubic centimeters ( $\text{cm}^3$ ).
Density: The ratio of an object's mass to its volume. Typically expressed in $\text{g/cm}^3$ or $\text{g/mL}$ for solids and liquids, and $\text{g/L}$ for gases.

Core Rule of Density

Density is an intensive property characteristic of a substance. If an object's mass and volume are known, its density can be determined by simple division ( $d = m / V$ ).

Problem-Solving Routines & Methods

Density Formula

d = \frac{m}{V}

Calculates the density of a substance from its mass and volume.

Variables & Constants

d

=density;

m

=mass;

V

=volume

How to Calculate Density via Water Displacement

1
Measure the mass (m) of the solid object using an analytical balance.
2
Pour liquid into a graduated cylinder and record the initial water volume.
3
Submerge the object completely in the water and record the new, higher water volume.
4
Calculate volume (V) by subtracting initial volume from final volume.
5
Divide mass by volume (d = m / V) to find density.

Pro-Tip: Ensure completely trapped air bubbles are removed from submerged irregular objects to prevent volume measurement errors.

Practice & Concept Checks

Concept Check

What is the density of an iron block with a mass of 31.48 g that displaces 4.0 mL of water?

Concept Check

How many grams are in 3 kilograms? Express your answer using a power of 10.

Key Terms & Vocabulary

UnitsMeasurement

Standards of comparison used to give meaning to numerical measurements.

Example: Liters, grams, meters

International System of UnitsStandards

Globally agreed-upon system of seven base physical units, abbreviated as SI.

Example: The SI system used in scientific research worldwide.

SI unitsStandards

Standardized units established by international agreement (Le Système International d’Unités).

Example: Kilograms, meters, seconds

lengthProperties

Measure of one dimension of an object or distance between points.

Example: Measuring the height of a beaker in meters.

meter (m)SI Units

The standard SI base unit of length.

Example: 1 m = 39.37 inches

kilogram (kg)SI Units

The standard SI base unit of mass.

Example: 1 kg is approximately 2.2 pounds.

kelvin (K)SI Units

The standard SI base unit of temperature, with zero representing absolute zero.

Example: Water freezes at 273.15 K.

Celsius (°C)Temperature

Commonly used temperature scale where water freezes at 0 °C and boils at 100 °C.

Example: Normal human body temperature is 37 °C.

second (s)SI Units

The standard SI base unit of time.

Example: Measuring the duration of a chemical reaction.

VolumeProperties

The measure of the amount of space occupied by an object.

Example: A 2-liter soft drink bottle.

cubic meter (m3)Derived Units

The standard SI derived unit of volume, representing a cube with 1 m edges.

Example: m³

liter (L)Derived Units

A common unit of volume equal to one cubic decimeter (dm³).

Example: A 1-L graduated cylinder.

cubic centimeter (cm3)Derived Units

Volume of a cube with 1 cm edge length, equal to one milliliter.

Example: cm³

milliliter (mL)Derived Units

Volume unit equal to one-thousandth of a liter (10⁻³ L).

Example: 50 mL of hydrochloric acid.

densityProperties

The ratio of an object's mass to its volume (

d = m/V

Example: Gold has a density of 19.3 g/cm³.

ccDerived Units

Cubic centimeter; abbreviation frequently used in medical settings.

Example: A dose of 5 cc of medicine.