Foundations of General Chemistry: Matter, Measurement, and Atomic Structure

The Scientific Method

Overview

The scientific method is a systematic approach used in scientific investigation to acquire new knowledge and validate existing knowledge. It involves making observations, forming hypotheses, conducting experiments, analyzing data, and drawing conclusions.

• Hypothesis: A tentative explanation or prediction that can be tested by experiments.

  • Falsifiable: A hypothesis must be structured so that it can be proven false by evidence.

• Experiments: Controlled procedures carried out to test the validity of a hypothesis.

• Data Analysis: The process of interpreting experimental results to determine if they support or refute the hypothesis.

• Drawing Conclusions: Summarizing findings and determining the next steps, such as revising the hypothesis or conducting further experiments.

Scientific Laws and Theories

Definitions

• Scientific Law: A concise statement that describes a fundamental relationship or regularity of nature, often expressed mathematically. Example: The Law of Conservation of Mass.

• Scientific Theory: A well-substantiated explanation of some aspect of the natural world that is based on a body of evidence and has stood up to repeated testing.

States of Matter

Classification

Matter exists in different physical forms called states or phases. The three primary states are:

• Solid: Has a definite shape and volume. Particles are closely packed and vibrate in place.

  • Crystalline: Particles are arranged in a regular, repeating pattern (e.g., table salt, diamond).

  • Amorphous: Particles lack a long-range order (e.g., glass, plastic).

• Liquid: Has a definite volume but takes the shape of its container. Particles are close but can move past each other.

• Gas: Has neither definite shape nor volume. Particles are far apart and move freely.

Types of Matter

Classification

• Mixture: A physical combination of two or more substances.

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

  • Heterogeneous: Non-uniform composition (e.g., salad, sand in water).

• Pure Substance: Matter with a fixed composition.

  • Element: Cannot be broken down into simpler substances by chemical means (e.g., oxygen, gold).

  • Compound: Composed of two or more elements chemically combined in fixed proportions (e.g., water, carbon dioxide).

Properties and Changes of Matter

Properties

• Physical Properties: Characteristics observed without changing the substance's composition (e.g., color, melting point, density).

  • Example: Ice melting to water (change in state, not composition).

• Chemical Properties: Characteristics observed when a substance undergoes a chemical change (e.g., flammability, reactivity).

  • Example: Iron rusting (iron reacts with oxygen to form iron oxide).

Changes

• Physical Change: Alters the state or appearance but not the chemical composition.

  • Example: Boiling water, dissolving sugar in water.

• Chemical Change: Alters the chemical structure, resulting in new substances.

  • Example: Burning wood, digesting food.

Significant Figures

Rules and Applications

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

• Zeroes:

  • Interior (captive) zeroes: Always significant (e.g., 205 has three significant figures).

  • Leading zeroes: Never significant (e.g., 0.0025 has two significant figures).

  • Trailing zeroes: Significant only if there is a decimal point (e.g., 2.300 has four significant figures).

• Scientific Notation: Used to express very large or small numbers. Only significant digits are included.

  • Example: $6.02 \times 10^{23}$

• Rounding: Round to the correct number of significant figures based on the operation performed (addition/subtraction: least decimal places; multiplication/division: least significant figures).

Unit Conversions

Dimensional Analysis

• Cross-method (Factor-label method): A systematic approach to converting units using conversion factors.

  • Example: To convert 10 inches to centimeters: $10 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 25.4 \text{ cm}$

Law of Definite and Multiple Proportions

Definitions

• Law of Definite Proportions: A chemical compound always contains the same elements in the same proportion by mass.

• Law of Multiple Proportions: When two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.

The Structure of the Atom

Subatomic Particles

• Protons: Positively charged particles in the nucleus. The number of protons defines the atomic number ($Z$).

• Neutrons: Neutral particles in the nucleus. The number of neutrons can vary, resulting in isotopes.

• Electrons: Negatively charged particles surrounding the nucleus.

Isotopes

• Definition: Atoms of the same element with different numbers of neutrons.

• Number of Protons: Equal to the atomic number ($Z$).

• Number of Neutrons: $\text{Number of Neutrons} = \text{Mass Number} (A) - \text{Atomic Number} (Z)$

• Natural Abundance: The relative proportion of each isotope found in nature.

Reading the Periodic Table

Groups and Charges

• Groups: Vertical columns in the periodic table. Elements in the same group have similar chemical properties.

• Determining Ionic Charges: Main group elements often form ions with predictable charges based on their group number (e.g., Group 1 forms $+1$ ions, Group 17 forms $-1$ ions).

Ions

Types and Naming

• Cations: Positively charged ions (formed by losing electrons).

• Anions: Negatively charged ions (formed by gaining electrons).

• Polyatomic Ions: Ions composed of two or more atoms covalently bonded, carrying a net charge (e.g., $\text{NO}_3^-$, $\text{SO}_4^{2-}$).

• Determining Charge: For monatomic ions, charge is often based on group number. For polyatomic ions, charges are memorized or determined from formulas.

• Naming: Cations use the element name (e.g., sodium ion), anions use the root plus "-ide" (e.g., chloride ion). Polyatomic ions have specific names (e.g., sulfate, nitrate).

Formula Writing and Naming Compounds

Rules and Examples

• Formula Writing: Combine cations and anions in ratios that result in a neutral compound.

• Naming Compounds: Use systematic rules for ionic and molecular compounds.

  • Binary Ionic Compounds: Name cation first, then anion (e.g., NaCl: sodium chloride).

  • Transition Metals: Indicate charge with Roman numerals (e.g., FeCl2: iron(II) chloride).

  • Molecular Compounds: Use prefixes to indicate number of atoms (e.g., CO2: carbon dioxide).

In-Class Naming Examples

• KI: Potassium iodide

• Sr(NO3)2: Strontium nitrate

• Carbon tetrachloride: CCl4

• Hydrogen sulfate: HSO4- (as an ion) or H2SO4 (as sulfuric acid)

• Copper(II) oxide: CuO

• Co(NO3)2: Cobalt(II) nitrate

• CaCO3: Calcium carbonate

Sample Math Review

Practice Problems

• 3.5 - 2.396 = 1.104 (rounded to 2 significant figures: 1.1)

• 2.341 × 376 × 0.007 = 6.16 (rounded to 2 significant figures: 6.2)

• (7826 + 23 - 5.2) × 7.5 = 58,627.5 (rounded to 2 significant figures: 59,000)

• (5.95 × 3.7628) - 4.25 = 17.39766 - 4.25 = 13.14766 (rounded to 3 significant figures: 13.1)

Summary Table: Types of Matter

Type	Definition	Example
Element	Pure substance, one type of atom	O2, Fe
Compound	Pure substance, two or more elements chemically combined	H2O, CO2
Homogeneous Mixture	Uniform composition throughout	Saltwater, air
Heterogeneous Mixture	Non-uniform composition	Salad, granite

Additional info: Some explanations and examples were expanded for clarity and completeness based on standard General Chemistry curriculum.