General Chemistry I: Core Concepts and Problem-Solving Study Guide

Chapter 1: Matter, Measurement, and Problem Solving

States and Classification of Matter

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

• States of Matter:

  • Solid: Definite shape and volume; particles are closely packed in a fixed arrangement.

  • Liquid: Definite volume but no definite shape; particles are close but can move past each other.

  • Gas: No definite shape or volume; particles are far apart and move freely.

• Classification by Composition:

  • Pure Substances: Have a fixed composition. Can be elements (single type of atom) or compounds (two or more elements chemically combined).

  • Mixtures: Physical combinations of two or more substances. Can be:

    • Homogeneous: Uniform composition (e.g., salt water).

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

Atoms, Molecules, and Properties

• Atom: The smallest unit of an element that retains its properties.

• Molecule: Two or more atoms bonded together.

• Physical Change: Alters appearance, not composition (e.g., melting ice).

• Chemical Change: Alters composition, forming new substances (e.g., rusting iron).

• Physical Properties: Can be observed without changing composition (e.g., color, density).

• Chemical Properties: Describe reactivity and ability to form new substances (e.g., flammability).

Measurement and Calculations

• Scientific Notation: Expresses numbers as a product of a coefficient and a power of ten.

• Significant Figures: Digits that carry meaning in a measurement.

  • Multiplication/Division: Result has as many significant figures as the measurement with the fewest.

  • Addition/Subtraction: Result has as many decimal places as the measurement with the fewest decimal places.

• SI Units and Prefixes: Standard units for scientific measurement (e.g., meter, kilogram, second). Prefixes indicate powers of ten (e.g., kilo-, milli-).

• Unit Conversion: Use conversion factors to change units.

• Dimensional Analysis: A method to solve problems using units as a guide.

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

Chapter 2: Atoms and Elements

Laws of Chemical Combination

• Law of Conservation of Mass: Mass is neither created nor destroyed in a chemical reaction.

• Law of Definite Proportions: A 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 ratios of the masses of the second element that combine with a fixed mass of the first element are small whole numbers.

Atomic Structure and Isotopes

• Atom: Consists of a nucleus (protons and neutrons) and electrons.

• Atomic Number (Z): Number of protons in the nucleus.

• Atomic Mass (A): Total number of protons and neutrons.

• Chemical Symbol: One- or two-letter abbreviation for an element.

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

• Determining Subatomic Particles:

  • Protons = Atomic number (Z)

  • Neutrons = Mass number (A) - Atomic number (Z)

  • Electrons = Protons (for neutral atoms); adjust for charge in ions

• Ions: Atoms or molecules with a net charge due to loss or gain of electrons.

• Monoatomic Ions: Ions formed from single atoms; main group elements form predictable charges.

The Periodic Table

• Groups: Vertical columns; elements in a group have similar properties.

• Periods: Horizontal rows.

• Metals, Nonmetals, Metalloids: Classified by physical and chemical properties.

Atomic Mass and the Mole Concept

• Average Atomic Mass: Weighted average of isotopic masses based on natural abundance.

  • $\text{Average Atomic Mass} = \sum (\text{Fractional Abundance} \times \text{Isotopic Mass})$

• Mole: Amount of substance containing $6.022 \times 10^{23}$ entities (Avogadro's number).

• Conversions:

  • Moles to atoms: $\text{Moles} \times 6.022 \times 10^{23} = \text{Number of atoms}$

  • Atoms to moles: $\text{Number of atoms} \div 6.022 \times 10^{23} = \text{Moles}$

Chapter 3: Molecules and Compounds

Types of Elements and Compounds

• Atomic Element: Exists as single atoms (e.g., Ne, Fe).

• Molecular Element: Exists as molecules (e.g., O2, N2).

• Molecular Compound: Composed of nonmetals; molecules held by covalent bonds (e.g., H2O).

• Ionic Compound: Composed of cations and anions; held by ionic bonds (e.g., NaCl).

Nomenclature

• Writing Formulas: Use charges to balance ionic compounds.

• Naming Compounds:

  • Binary Ionic Compounds (Type I): Metal forms only one cation (e.g., NaCl: sodium chloride).

  • Binary Ionic Compounds (Type II): Metal forms more than one cation; use Roman numerals (e.g., FeCl2: iron(II) chloride).

  • Molecular Compounds: Use prefixes (e.g., CO2: carbon dioxide).

  • Acids: Name depends on anion (e.g., HCl: hydrochloric acid).

  • Polyatomic Ions: Compounds containing ions like NO3-, SO42-.

Calculations Involving Compounds

• Formula Mass: Sum of atomic masses in a formula unit.

• Molar Mass: Mass of one mole of a substance (g/mol).

• Mass Percent: $\text{Mass \% of X} = \frac{\text{Mass of X in 1 mol compound}}{\text{Molar mass of compound}} \times 100\%$

• Conversions: Mass ↔ moles ↔ number of molecules.

Chapter 4: Chemical Reactions and Chemical Quantities

Chemical Equations and Stoichiometry

• Writing and Balancing Equations: Ensure the same number of each atom on both sides.

• Stoichiometry: Quantitative relationships in chemical reactions.

  • Mole-to-mole conversions: Use coefficients from balanced equations.

  • Mass-to-mass conversions: Convert mass to moles, use mole ratio, then convert to mass.

  • Limiting Reactant: The reactant that is completely consumed first.

  • Theoretical Yield: Maximum amount of product possible.

  • Percent Yield: $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

Types of Reactions

• Combustion Reactions: Substance reacts with O2 to form CO2 and H2O (for hydrocarbons).

• Alkali Metal Reactions: Alkali metals react vigorously with water and halogens.

• Halogen Reactions: Halogens react with metals and hydrogen to form salts and acids.

Chapter 5: Introduction to Solutions and Aqueous Solutions

Properties and Concentrations of Solutions

• Solution: Homogeneous mixture of solute and solvent.

• Molarity (M): $\text{Molarity} = \frac{\text{Moles of solute}}{\text{Liters of solution}}$

• Dilution Equation: $M_1V_1 = M_2V_2$

Solubility and Electrolytes

• Soluble Compounds: Dissolve in water; insoluble do not.

• Electrolytes: Substances that conduct electricity in solution (strong, weak, nonelectrolytes).

Chemical Equations in Solution

• Molecular Equation: Shows all reactants and products as compounds.

• Total Ionic Equation: Shows all strong electrolytes as ions.

• Net Ionic Equation: Shows only species that change during the reaction.

Types of Aqueous Reactions

• Precipitation: Formation of an insoluble product.

• Acid-Base: Transfer of H+ ions.

• Gas Evolution: Formation of a gas product.

• Oxidation-Reduction (Redox): Transfer of electrons.

Oxidation States and Agents

• Oxidation State: Assigned to atoms to track electron transfer.

• Oxidizing Agent: Causes oxidation; is reduced.

• Reducing Agent: Causes reduction; is oxidized.

Chapter 6: Gases

Gas Properties and Laws

• Gas Pressure: Force exerted by gas particles per unit area.

• Pressure Units: atm, mmHg, torr, Pa.

• Simple Gas Laws:

  • Boyle's Law: $P_1V_1 = P_2V_2$ (at constant T, n)

  • Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (at constant P, n)

  • Avogadro's Law: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ (at constant P, T)

• Ideal Gas Law: $PV = nRT$

• Dalton's Law of Partial Pressures: $P_{\text{total}} = \sum P_i$

• Gas Density: $\text{Density} = \frac{PM}{RT}$

• Standard Temperature and Pressure (STP): 0°C (273.15 K) and 1 atm; 1 mol gas = 22.4 L at STP.

Kinetic-Molecular Theory

• Gases consist of particles in constant, random motion.

• Collisions are elastic; no energy is lost.

• Volume of particles is negligible compared to container.

• No intermolecular forces between particles.

Chapter 7: Thermochemistry

Energy and Thermodynamics

• First Law of Thermodynamics: Energy cannot be created or destroyed, only transferred.

• Internal Energy (ΔE): $\Delta E = q + w$ (q = heat, w = work)

• Heat and Temperature Change: $q = mC\Delta T$ (m = mass, C = specific heat, ΔT = temperature change)

• Thermochemical Equations: Show enthalpy change (ΔH) with reaction.

• Hess's Law: The enthalpy change for a reaction is the sum of enthalpy changes for individual steps.

• Standard Enthalpy of Formation (ΔHf°): Enthalpy change for forming 1 mol of a compound from its elements in standard states.

Chapter 8: The Quantum-Mechanical Model of the Atom

Electromagnetic Radiation and Atomic Models

• Wavelength (λ), Frequency (ν), and Speed (c): $c = \lambda \nu$

• Photon Energy: $E_{\text{photon}} = h\nu$ (h = Planck's constant)

• Bohr Model: Electrons orbit nucleus in quantized energy levels (applies to hydrogen atom).

• Quantum Mechanical Model: Electrons exist in orbitals defined by quantum numbers:

  • n: Principal quantum number (energy level)

  • l: Angular momentum quantum number (shape)

  • ml: Magnetic quantum number (orientation)

  • ms: Spin quantum number (spin direction)

Chapter 9: Periodic Properties of the Elements

Electron Configurations and Periodic Trends

• Electron Configuration: Distribution of electrons among orbitals.

• Periodic Table Structure: Arranged by increasing atomic number; groups and periods reflect electron configurations.

• Periodic Trends:

  • Atomic Radius: Increases down a group, decreases across a period.

  • Ionization Energy: Decreases down a group, increases across a period.

  • Electronegativity: Increases across a period, decreases down a group.

• Metals, Nonmetals, Metalloids: Classified by position and properties.