Introductory Chemistry: Comprehensive Final Exam Review Notes

The Chemical World

The Scientific Method

The scientific method is a systematic approach to understanding the natural world through observation, experimentation, and analysis. It is foundational to all scientific inquiry and ensures that knowledge is based on evidence.

• Observation: Gathering information using the senses or instruments.

• Hypothesis: A tentative explanation for an observation, which can be tested by experiments.

• Experiment: A controlled procedure to test the hypothesis.

• Analysis and Conclusion: Interpreting data to determine if the hypothesis is supported or refuted.

• Revision: If results do not support the hypothesis, it is revised or a new hypothesis is formed.

Matter and Energy

Classification of Matter by Composition

Matter can be classified based on its composition into elements, compounds, and mixtures.

• Element: A pure substance made of only one type of atom (e.g., O2).

• Molecule: Two or more atoms chemically bonded together (e.g., O2, CO2).

• Compound: A substance composed of two or more elements in fixed, definite proportions (e.g., H2O).

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

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

Physical and Chemical Properties and Changes

Physical properties are observed without changing the substance's composition (e.g., color, boiling point). Chemical properties are observed only when a substance undergoes a chemical change (e.g., flammability).

• Physical changes: Changes in state or form without altering composition (e.g., melting, dissolving).

• Chemical changes: Formation of new substances (e.g., burning, rusting).

Measurement and Problem Solving

Significant Figures in Measurement

Significant figures reflect the precision of a measurement. The last digit is always an estimate, and measurements should always be recorded one place beyond the smallest marked unit.

• More significant figures indicate greater precision.

• Different measuring devices yield different numbers of significant figures.

Significant Figures in Calculations

• Multiplication/Division: The result has the same number of significant figures as the factor with the fewest significant figures.

• Addition/Subtraction: The result has the same number of decimal places as the measurement with the fewest decimal places.

Scientific Notation

Scientific notation expresses very large or small numbers in the form a × 10n, where a is a number between 1 and 10, and n is an integer.

• All digits in the decimal part are significant.

• Used to clarify significant zeros and simplify calculations.

SI (Metric) Units and Prefixes

The International System of Units (SI) uses base units and prefixes to indicate multiples or fractions of units. Common prefixes include kilo-, centi-, and milli-.

Unit (Dimensional) Analysis

Unit analysis is a method for solving problems by converting between units using conversion factors. It is essential for all types of chemistry calculations.

• Identify the starting unit and the desired unit.

• Apply conversion factors stepwise until the desired unit is reached.

Chemical Composition

Density

Density is the ratio of mass to volume and is used to identify substances and convert between mass and volume.

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

• Units: g/mL or g/cm3

• Can be used as a conversion factor in calculations.

Atoms and Elements

Atomic Notation

Atoms are identified by their atomic number (number of protons), mass number (protons + neutrons), and charge (protons - electrons). The atomic number determines the element's identity.

• Notation: AZX, where A = mass number, Z = atomic number, X = element symbol.

• Isotopes have the same atomic number but different mass numbers.

Valence Electrons and Ions

Valence electrons are the outermost electrons and determine chemical reactivity. Atoms gain or lose electrons to achieve a full outer shell, forming ions.

• Cation: Positive ion (lost electrons).

• Anion: Negative ion (gained electrons).

• Metals tend to lose electrons; nonmetals tend to gain electrons.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom. Electrons fill sublevels in order of increasing energy, following the periodic table structure.

• Use the periodic table to assign electrons to sublevels (s, p, d, f).

• Ions have the same electron configuration as the nearest noble gas.

Chemical Reactions

Balancing Chemical Equations

Balancing equations ensures the law of conservation of mass is obeyed. Each side of the equation must have the same number of each type of atom.

• Write correct formulas for reactants and products.

• Add coefficients to balance atoms.

• Balance more complex molecules first; leave H and O for last.

Types of Chemical Reactions

• Single Displacement: One element replaces another in a compound.

• Double Displacement: Exchange of ions between two compounds.

• Combustion: Reaction with O2 producing CO2 and H2O (for hydrocarbons).

Stoichiometry

Stoichiometry involves quantitative relationships in chemical reactions, using mole ratios from balanced equations to convert between amounts of reactants and products.

• Steps: Balance equation, convert given to moles, use mole ratio, convert to desired unit.

Theoretical Yield, Actual Yield, and Percent Yield

• Theoretical yield: Maximum amount of product predicted by stoichiometry.

• Actual yield: Amount actually obtained from the reaction.

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

Chemical Bonding

Lewis Dot Diagrams

Lewis dot diagrams represent valence electrons as dots around element symbols, showing how atoms bond to achieve full outer shells (octet rule).

• Count total valence electrons.

• Arrange atoms and connect with bonds.

• Distribute remaining electrons to satisfy octet rule.

• Use double/triple bonds if necessary.

Polarity of Bonds and Molecules

Bond polarity depends on the difference in electronegativity between atoms. Molecular polarity depends on both bond polarity and molecular shape.

• Nonpolar bonds: Equal sharing of electrons.

• Polar bonds: Unequal sharing, resulting in partial charges.

• Symmetrical molecules with identical surrounding atoms are nonpolar; asymmetrical or with different atoms are polar.

Isomers

Isomers are compounds with the same molecular formula but different structural arrangements, resulting in different properties.

Functional Groups in Organic Chemistry

Functional groups are specific groups of atoms within molecules that determine the chemical properties of organic compounds.

Liquids, Solids, and Intermolecular Forces

Phase Changes

Phase changes are transitions between solid, liquid, and gas states, involving energy changes but not chemical composition.

• Melting, freezing, vaporization, condensation, sublimation, deposition.

Solutions

Types of Solutions and Solubility

Solutions are homogeneous mixtures. Solubility depends on the nature of solute and solvent, temperature, and pressure.

• Gas in liquid: Solubility increases with pressure, decreases with temperature.

• "Like dissolves like": Polar solutes dissolve in polar solvents; nonpolar in nonpolar.

Measuring Concentration

• Mass percent: $\text{Mass percent} = \frac{\text{g solute}}{\text{g solute} + \text{g solvent}} \times 100\%$

• Molarity (M): $\text{Molarity} = \frac{\text{moles solute}}{\text{liters solution}}$

• Dilution: $M_1V_1 = M_2V_2$

Solution Stoichiometry

Volume and molarity can be used to calculate moles of solute, which are then used in stoichiometric calculations.

Acids and Bases

Properties of Acids and Bases

• Acids: Sour taste, dissolve metals, turn blue litmus red.

• Bases: Bitter taste, slippery feel, turn red litmus blue.

pH Scale

The pH scale measures the acidity or basicity of a solution. It is calculated as $\text{pH} = -\log[H^+]$.

• pH < 7: Acidic

• pH = 7: Neutral

• pH > 7: Basic

Buffers

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They contain a weak acid and its conjugate base.

Gases

Kinetic Molecular Theory and Properties of Gases

The kinetic molecular theory explains the behavior of ideal gases: constant motion, negligible volume, no intermolecular forces, and elastic collisions. Real gases behave ideally at high temperature and low pressure.

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and amount of gas:

$PV = nRT$

• P = pressure (atm), V = volume (L), n = moles, R = 0.0821 L·atm/(mol·K), T = temperature (K)

Gas Stoichiometry

At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 L. This relationship is used in stoichiometric calculations involving gases.

Radioactivity and Nuclear Chemistry

Types of Radioactive Decay

Radioactive decay involves the transformation of unstable nuclei into more stable ones, emitting particles or energy.

• Alpha decay: Emission of a helium nucleus (2 protons, 2 neutrons).

• Beta decay: Conversion of a neutron to a proton with emission of an electron.

• Positron emission: Conversion of a proton to a neutron with emission of a positron.

Half-Life Calculations

The half-life is the time required for half of a radioactive sample to decay. The amount remaining after a given time can be calculated by dividing the initial amount by 2 for each half-life elapsed.

• Example: If 88 mg of I-131 (t1/2 = 8 days) is ingested, after 24 days (3 half-lives), 11 mg remains.

Additional info: These notes cover all major topics in an introductory college chemistry course, including measurement, matter, atomic structure, chemical reactions, stoichiometry, bonding, solutions, acids and bases, gases, and nuclear chemistry. All images included are directly relevant to the adjacent explanations and reinforce key concepts.