CHEM 200: Introduction to Matter, Energy, and Measurement (Chapter 1, Part 2)

Numbers and Chemistry

The Role of Numbers in Chemistry

Quantitative analysis is fundamental in chemistry, as many concepts and experiments rely on precise numerical data. Understanding how to measure, calculate, and interpret numbers is essential for accurate scientific work.

• Measurement: The process of obtaining the magnitude of a quantity relative to a standard unit.

• Calculated Quantities: Values derived from measured data using mathematical operations.

• Uncertainty in Measurement: All measurements have some degree of error or uncertainty, which must be considered in scientific analysis.

• Significant Figures: Digits in a measurement that are known with certainty plus one estimated digit.

• Dimensional Analysis: A method for converting between units using conversion factors.

Units of Measurement

SI Units (International System of Units)

The SI system (Système International d’Unités) is the standard system of measurement in science. Each physical quantity has a designated base unit.

Quantity	Name of Unit	Abbreviation
Length	Meter	m
Mass	Kilogram	kg
Temperature	Kelvin	K
Time	Second	s or sec
Amount of Substance	Mole	mol
Electric Current	Ampere	A or amp
Luminous Intensity	Candela	cd

Metric System Units

The metric system uses standard units for various physical quantities:

• Mass: gram (g)

• Length: meter (m)

• Time: second (s or sec)

• Temperature: degrees Celsius (°C) or Kelvin (K)

• Amount of substance: mole (mol)

• Volume: cubic centimeter (cc or cm3) or liter (L)

Metric System Prefixes

Prefixes are used to indicate multiples or fractions of units, making it easier to express very large or small quantities.

Prefix	Meaning	Example
peta-	1015	1 petawatt (PW) = 1 × 1015 watts
tera-	1012	1 terawatt (TW) = 1 × 1012 watts
giga-	109	1 gigawatt (GW) = 1 × 109 watts
mega-	106	1 megawatt (MW) = 1 × 106 watts
kilo-	103	1 kilowatt (kW) = 1 × 103 watts
deci-	10-1	1 deciwatt (dW) = 1 × 10-1 watt
centi-	10-2	1 centiwatt (cW) = 1 × 10-2 watt
milli-	10-3	1 milliwatt (mW) = 1 × 10-3 watt
micro-	10-6	1 microwatt (μW) = 1 × 10-6 watt
nano-	10-9	1 nanowatt (nW) = 1 × 10-9 watt
pico-	10-12	1 picowatt (pW) = 1 × 10-12 watt
femto-	10-15	1 femtowatt (fW) = 1 × 10-15 watt
atto-	10-18	1 attowatt (aW) = 1 × 10-18 watt
zepto-	10-21	1 zeptowatt (zW) = 1 × 10-21 watt

Mass and Length

Mass

Mass is a measure of the amount of matter in an object. The SI base unit for mass is the kilogram (kg).

• 1 kilogram (kg) = $1 \times 10^3$ grams (g)

Length

Length is the measure of distance. The SI base unit for length is the meter (m).

Volume

Definition and Units

Volume is not a base SI unit; it is derived from length ($m \times m \times m = m^3$). Common metric units for volume include the liter (L) and the milliliter (mL).

• 1 liter (L) = 1000 cubic centimeters (cm3) = 1 decimeter cubed (dm3) = $10^{-3}$ m3

• 1 mL = 1 cm3

Example: A cube 1 dm on each side has a volume of 1 L. A cube 1 cm on each side has a volume of 1 mL.

Laboratory Glassware for Measuring Volume

Various types of glassware are used to measure and deliver specific volumes in the laboratory:

• Beaker: Used for approximate volumes.

• Syringe: Delivers variable volumes.

• Burette: Delivers variable volumes with a stopcock to control flow.

• Pipette: Used to deliver a specific volume accurately.

Density

Definition and Formula

Density is a physical property defined as mass per unit volume. The SI unit for density is kg/m3, but g/cm3 or g/mL are commonly used in chemistry.

• Formula: $d = \frac{m}{V}$

• 1 g/cm3 = $10^{-3}$ kg / $10^{-3}$ dm3 = 1 kg/dm3 = 1 kg/L

Example: What is the mass of platinum metal with a density of 21.5 g/cm3 and a volume of 4.49 cm3?

• Calculation: $21.5\ \text{g/cm}^3 \times 4.49\ \text{cm}^3 = 96.5\ \text{g}$

Substance	Density (g/cm3)
Air	~0.0012
Balsa wood	~0.16
Ethanol	~0.79
Water	1.00
Ethylene glycol	1.11
Table sugar	1.59
Table salt	2.16
Iron	7.87
Gold	19.3