General Chemistry Study Guide: Chapters 1–3

Mathematical Operations and Functions

Addition, Subtraction, Multiplication, and Division

Mathematical operations are fundamental in chemistry for solving quantitative problems. Addition and subtraction are used to combine or compare values, while multiplication and division are essential for calculations involving ratios, rates, and conversions.

• Addition/Subtraction: Used for combining measurements or calculating differences.

• Multiplication/Division: Used for scaling values, calculating densities, and converting units.

• Example: If you add 2.5 g and 3.1 g, the sum is 5.6 g.

Significant Figures and Scientific Notation

Significant figures reflect the precision of a measurement. Scientific notation is used to express very large or small numbers in a compact form.

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

• Scientific Notation: Numbers are written as $a \times 10^n$, where a is a number between 1 and 10 and n is an integer.

• Example: 0.00045 can be written as $4.5 \times 10^{-4}$.

Atoms & Elements

Element Symbols, Names, and Classification

Each element is represented by a unique symbol and can be classified as a metal, nonmetal, or metalloid. The periodic table organizes elements based on their properties.

• Element Symbol: One or two letters representing an element (e.g., H for hydrogen).

• Classification: Metals are typically shiny and conductive, nonmetals are dull and insulating, and metalloids have properties of both.

• Example: Si (Silicon) is a metalloid.

Chemical Reactions

Classification of Matter

Matter can be classified as an element, compound, homogeneous mixture, or heterogeneous mixture.

• Element: Pure substance consisting of one type of atom.

• Compound: Substance formed from two or more elements chemically bonded.

• Homogeneous Mixture: Uniform composition throughout (e.g., saltwater).

• Heterogeneous Mixture: Non-uniform composition (e.g., sand and water).

Physical vs. Chemical Properties

Properties of matter are classified as physical or chemical.

• Physical Property: Can be observed without changing the substance (e.g., melting point).

• Chemical Property: Describes how a substance reacts (e.g., flammability).

• Example: Boiling water is a physical change; rusting iron is a chemical change.

Chemical Quantities & Aqueous Reactions

Unit Conversions and Metric Prefixes

Unit conversions are essential for expressing measurements in different units. Metric prefixes indicate multiples or fractions of base units.

• Metric Prefixes: Prefixes such as kilo-, milli-, and micro- represent powers of ten.

• Conversion Example: 1 kilometer (km) = 1,000 meters (m).

Prefix	Symbol	Multiple/Fraction
kilo	K	1,000 = $1 \times 10^3$
milli	m	0.001 = $1 \times 10^{-3}$
micro	\mu	0.000001 = $1 \times 10^{-6}$
nano	n	0.000000001 = $1 \times 10^{-9}$
pico	p	0.000000000001 = $1 \times 10^{-12}$
mega	M	1,000,000 = $1 \times 10^6$

English-Metric Equivalents

Conversions between English and metric units are often required in laboratory and real-world settings.

Quantity	English Unit	Metric Equivalent
Length	1 inch (in.)	2.54 cm
Mass	1 pound (lb)	454 g
Volume	1 quart (qt)	946 mL
Time	1 second (sec)	1.00 s

Density Calculations

Density is a physical property defined as mass per unit volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Example: If a substance has a mass of 10 g and a volume of 2 mL, its density is $5 \text{ g/mL}$.

The Percent Concept

Percentages are used to express ratios, concentrations, and yields in chemistry.

• Formula: $\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100\%$

• Example: If 20 g of salt is dissolved in 100 g of water, the percent salt is $\frac{20}{120} \times 100\% = 16.7\%$.

Intro to General Chemistry

Changes of Physical State

Substances can change between solid, liquid, and gas states through physical processes.

• Evaporation: Liquid to gas

• Condensation: Gas to liquid

• Melting: Solid to liquid

• Freezing: Liquid to solid

• Sublimation: Solid to gas

• Deposition: Gas to solid

Law of Conservation of Mass

The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction.

• Formula: $\text{Total mass before reaction} = \text{Total mass after reaction}$

• Example: If 10 g of reactants produce 10 g of products, mass is conserved.

Law of Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, only transformed.

• Example: Chemical energy in fuel is converted to heat and light during combustion.

Additional info: Academic context and explanations have been expanded for clarity and completeness. Tables have been recreated and images included only where directly relevant to the explanation.