Chemistry Basics: Matter, Measurement, and Significant Figures

Chemistry Basics: Matter and Measurement

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. Understanding how to identify and use significant figures is essential for accurate scientific calculations.

• Leading Zeros: Zeros that appear before any nonzero digit. Never significant.

• Captive Zeros: Zeros between nonzero digits. Always significant.

• Trailing Zeros: Zeros after all nonzero digits. Significant only if a decimal point is present.

Examples:

• 350g: 2 sig figs

• 0.00280: 3 sig figs

• 0.0083400: 5 sig figs

• 40000: 1 sig fig (unless specified otherwise)

Exact Numbers: Integers obtained by counting objects or by definition have infinite significant figures (e.g., 12 eggs, 24 students, 100 pennies).

Rounding Significant Figures

When rounding, keep only the required number of significant figures:

• 207.514 (to 3 sig figs) → 208

• 0.0036 (to 2 sig figs) → 0.0036

• 1.005 (to 3 sig figs) → 1.01

Significant Figures in Calculations

For multiplication and division, the answer should have the same number of significant figures as the measurement with the fewest significant figures.

• $815.94 \times 0.13 = 106.072$ → $110$ (2 sig figs)

• $8.52 / 2 = 4.26$ → $4.3$ (2 sig figs)

• $2003 \times 3.0 = 6009$ → $6000$ (2 sig figs)

Measurement and the Metric System

Metric System & Converting Units

The metric system uses prefixes to indicate multiples of ten. Conversion factors are used to change from one unit to another.

• 1 cm = 0.01 m

• 1 kg = 1000 g

• 1 L = 1000 mL

• 1 m = 100 cm

• 1 in = 2.54 cm

Example: How many cm are in 7.6 nm?

• Plan: nm → m → cm

• $7.6 \times 10^{-9} \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 7.6 \times 10^{-7} \text{ cm}$

Scientific Notation: Used to express very large or small numbers. Format: $n \times 10^x$, where $1 \leq n < 10$.

• 618,000 = $6.18 \times 10^5$

Dimensional Analysis

Dimensional analysis is a method to convert one unit to another using conversion factors.

• 1 in = 2.54 cm

• 1 lb = 453.6 g

• 1 oz = 28.34 g

• 1 L = 1.06 qt

• 1 hr = 60 min

• 1 min = 60 sec

Example: Convert 125g to oz:

• $125 \text{ g} \times \frac{1 \text{ oz}}{28.34 \text{ g}} = 4.41 \text{ oz}$

Matter and Its Properties

Definition of Matter

Matter is anything that has mass and occupies space. It can be classified by its physical state and composition.

• Solid: Closely packed, fixed shape, rigid, not easily compressed.

• Liquid: Closely packed but can move, takes the shape of its container, not fixed shape, not easily compressed.

• Gas: Far apart, not rigid, no fixed shape or volume, easily compressed.

Density

Density is the mass of a substance per unit volume.

• Formula: $d = \frac{m}{V}$

• Example: Mass = 15.5g, Volume = 6.01cm3

• $d = \frac{15.5 \text{ g}}{6.01 \text{ cm}^3} = 2.58 \text{ g/cm}^3$

Energy and Temperature

Energy

Energy is the ability to do work or cause change. It exists in different forms:

• Kinetic Energy: Energy of motion (e.g., rolling ball).

• POTENTIAL ENERGY: Stored energy (e.g., gasoline in a tank).

• Heat: Energy associated with movement of particles.

Units of Energy

• Joule (J), kilojoule (kJ), calorie (cal), kilocalorie (kcal)

• 1 cal = 4.184 J

• 1 kcal = 1000 cal

Example: 150 J of energy = $\frac{150}{4.184} = 36$ cal

Temperature Scales

• Celsius (°C): Water freezes at 0°C, boils at 100°C.

• Fahrenheit (°F): Water freezes at 32°F, boils at 212°F.

• Kelvin (K): Absolute temperature scale. 0 K is absolute zero.

Conversions:

• $°C = (°F - 32) \div 1.8$

• $°F = (°C \times 1.8) + 32$

• $K = °C + 273.15$

Example: Convert 95°F to °C:

• $(95 - 32) \div 1.8 = 35°C$

Absolute Zero: 0 K = -273°C

Summary Table: Common Metric Prefixes

Prefix	Symbol	Factor
kilo-	k	103
centi-	c	10-2
milli-	m	10-3
micro-	μ	10-6
nano-	n	10-9

Additional info:

• These notes cover foundational concepts from Ch.1 Chemistry Basics - Matter and Measurement, including significant figures, metric conversions, dimensional analysis, density, energy, and temperature scales.