General Chemistry I: Comprehensive Study Guide and Key Concepts

Chapter 1: Matter, Measurement & Problem Solving

Scientific Method

The scientific method is a systematic approach to research and discovery in science. It involves several key steps:

• Observation: Gathering data and noticing phenomena.

• Hypothesis: Proposing a tentative explanation or prediction.

• Experiment: Testing the hypothesis through controlled investigation.

• Theory: A well-substantiated explanation based on repeated experiments.

• Law: A statement describing consistent natural phenomena.

Types of Matter

Matter can be classified based on its composition:

• Element: Pure substance consisting of one type of atom (e.g., Silver).

• Compound: Substance composed of two or more elements chemically combined (e.g., NaCl, Sucrose).

• Homogeneous Mixture: Uniform composition throughout (e.g., Kool-aid, Bronze).

• Heterogeneous Mixture: Non-uniform composition (e.g., Salad dressing).

Chemical Change: Alters the composition of matter (e.g., Iron rusts). Physical Change: Does not alter composition (e.g., Gasoline vaporizes).

Significant Figures

Significant figures reflect the precision of a measured or calculated quantity. Rules include:

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant; trailing zeros after a decimal are significant.

When performing calculations, round the result to the correct number of significant figures based on the operation (multiplication/division: fewest sig figs; addition/subtraction: fewest decimal places).

Scientific Notation

Used to express very large or small numbers, maintaining correct significant figures. Example: $4.00 \times 10^5$.

Units and Unit Conversions

Unit conversions are essential for solving chemistry problems. Use conversion factors to switch between units (e.g., meters to kilometers, inches to centimeters). The density equation is:

$d = \frac{m}{v}$

where d is density, m is mass, and v is volume.

Chapter 2: Atoms & Elements

Atomic Structure

Atoms consist of protons (positive), neutrons (neutral), and electrons (negative). Isotopes are atoms of the same element with different numbers of neutrons. The number of protons defines the element; electrons determine chemical behavior.

To calculate average atomic mass:

$\text{Average atomic mass} = \sum (\text{isotope mass} \times \text{fractional abundance})$

Naming Compounds

• Ionic Compounds: Metal + nonmetal; may include polyatomic ions (e.g., CaO, Al2(SO4)3).

• Binary Molecular Compounds: Nonmetal + nonmetal (e.g., PCl5).

• Acids: Contain H; binary acids (e.g., HCl), oxoacids (e.g., HNO3).

Cation: Positively charged ion; Anion: Negatively charged ion.

Mole and Molecular Weights

The mole is a counting unit (Avogadro's number: $6.02 \times 10^{23}$). Molar mass is the mass of one mole of a substance. Use the following relationships:

• Atoms/molecules ↔ moles ↔ grams

Empirical and Molecular Formulas

The empirical formula gives the simplest whole-number ratio of atoms; the molecular formula gives the actual number of atoms in a molecule. To determine empirical formula, convert mass percentages to moles and simplify ratios.

Chapter 4: Chemical Reactions & Chemical Quantities

Balancing Equations

Chemical equations must be balanced to obey the law of conservation of mass. Adjust coefficients to ensure equal numbers of each atom on both sides.

Stoichiometry

Stoichiometry involves calculating quantities of reactants and products using balanced equations. Key steps:

• Balance the equation.

• Convert given quantities to moles.

• Use mole ratios to find unknowns.

Limiting Reactant, Theoretical and Percent Yield

The limiting reactant is consumed first and determines the amount of product formed. The theoretical yield is the maximum possible amount of product. Percent yield is calculated as:

$\text{Percent yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$

Chapter 5: Introduction to Solutions and Aqueous Reactions

Solution Calculations

Molarity (M) is moles of solute per liter of solution:

$M = \frac{\text{moles of solute}}{\text{liters of solution}}$

Dilution calculations use:

$M_1V_1 = M_2V_2$

Solution Chemistry

• Precipitation reactions: Formation of an insoluble solid from two solutions.

• Acid-base reactions: Acid donates H+, base donates OH-.

• Oxidation-reduction (redox) reactions: Transfer of electrons between species.

Strong electrolytes dissociate completely; weak electrolytes only partially.

Ionic Equations

Reactions in solution can be written as:

• Molecular equation: All species as compounds.

• Complete ionic equation: All strong electrolytes as ions.

• Net ionic equation: Only species undergoing change.

Acid-Base Reactions

Strong acids/bases ionize completely; weak acids/bases do not. Neutralization produces water and a salt.

Oxidation-Reduction Reactions

Assign oxidation numbers to identify electron transfer. The oxidizing agent is reduced; the reducing agent is oxidized.

Chapter 8: The Quantum-Mechanical Model of the Atom

Electromagnetic Radiation

Light has both wave and particle properties. Key relationships:

• Speed of light: $c = 2.998 \times 10^8$ m/s

• Wavelength and frequency: $c = \lambda \nu$

• Energy of a photon: $E = h\nu$

As wavelength decreases, frequency and energy increase.

Bohr Theory

Electrons occupy quantized energy levels. When an electron absorbs energy, it moves to a higher level; when it returns, it emits light of a specific wavelength. The Balmer series describes visible emissions as electrons fall to n=2.

Quantum Numbers

• Principal quantum number (n): Energy level (1, 2, 3...)

• Angular momentum quantum number (l): Shape of orbital (0=s, 1=p, 2=d, 3=f)

• Magnetic quantum number (ml): Orientation (−l to +l)

• Spin quantum number (ms): +1/2 or −1/2

No two electrons in an atom can have the same set of four quantum numbers (Pauli Exclusion Principle).

Chapter 9: Periodic Properties of the Elements

Electron Configuration Principles

• Aufbau Principle: Electrons fill lowest energy orbitals first.

• Hund’s Rule: Electrons occupy degenerate orbitals singly before pairing.

• Pauli Exclusion Principle: No two electrons have the same four quantum numbers.

Write electron configurations using the periodic table and noble gas shorthand.

Periodic Trends

Properties of elements show trends across periods and down groups:

Property	Trend Down a Group	Reason Down a Group	Trend Across a Period	Reason Across a Period
Atomic Radii	Increases	Outer shell size increases	Decreases	Effective nuclear charge increases
First Ionization Energy	Decreases	Valence electrons farther from nucleus	Increases	Effective nuclear charge increases
Electron Affinity	No definite trend		Becomes more negative	Effective nuclear charge increases
Metallic Character	Increases	Ionization energy decreases	Decreases	Ionization energy increases

Chapter 10: Chemical Bonding I: The Lewis Model

Types of Bonds

• Ionic: Transfer of electrons (metal + nonmetal).

• Covalent: Sharing of electrons (nonmetal + nonmetal).

• Metallic: Delocalized electrons among metal atoms.

Lewis Dot Structures

Show valence electrons as dots around atomic symbols. Used to represent molecules and polyatomic ions, including lone pairs and multiple bonds.

Electronegativity and Bond Polarity

Electronegativity is the ability of an atom to attract electrons in a bond. It increases across a period and decreases down a group. The difference in electronegativity determines bond polarity and dipole moment.

Formal Charge and Resonance

Formal charge helps determine the most stable Lewis structure:

$\text{Formal charge} = \text{valence electrons} - (\text{lone pair electrons} + \frac{1}{2}\text{bonding electrons})$

The best structure has the smallest formal charges and negative charges on the most electronegative atoms. Resonance structures differ only in electron placement.

Exceptions to the Octet Rule

• Electron-deficient: Boron, aluminum compounds.

• Expanded octets: Phosphorus, sulfur, arsenic, bromine, iodine can have more than 8 electrons.

Chapter 11: Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts molecular geometry based on electron pair repulsion. Five basic geometries are determined by the number of electron pairs around the central atom. Lone pairs cause greater repulsion and distort geometry.

Valence Bond Theory and Hybridization

• Hybridization: Mixing of atomic orbitals to form new hybrid orbitals (sp3, sp2, sp, sp3d, sp3d2).

• σ (sigma) bonds: Single bonds; π (pi) bonds: Additional bonds in double/triple bonds.

Chapter 6: Gases

Gas Laws

Describe the relationships between pressure, volume, temperature, and amount of gas:

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

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

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

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

• Ideal Gas Law: $PV = nRT$