General Chemistry: Comprehensive Study Guide (Units 1–11)

Unit 1: Matter, Measurement, and Problem Solving

Classification of Matter and Chemical Changes

Matter is anything that has mass and occupies space. Understanding how matter is classified and how it changes is fundamental in chemistry.

• Physical Change: Changes that do not alter the chemical composition (e.g., melting, boiling).

• Chemical Change: Changes that result in the formation of new substances (e.g., combustion, rusting).

• Separation Techniques: Methods such as filtration, distillation, and chromatography are used to separate mixtures based on physical properties.

• Example: Separating salt from water by evaporation is a physical change; burning wood is a chemical change.

Measurement and Significant Figures

Accurate measurement and proper reporting of significant figures are essential for scientific communication.

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

• Reporting Measurements: Measurements should reflect the precision of the instrument used.

• Example: Reporting a volume as 1.50 mL (not 1.5 mL) if measured with a graduated cylinder marked to 0.01 mL.

Density and Calculations

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

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

• Application: Used to identify substances and solve problems involving mass and volume.

• Example: A beaker with 38.64 g of mass and 100.0 mL of liquid has a density of $\frac{38.64\,\text{g}}{100.0\,\text{mL}} = 0.3864\,\text{g/mL}$.

Unit Conversions

Converting between units is a key skill in chemistry.

• Dimensional Analysis: A method to convert units using conversion factors.

• Example: 157 miles × $1.61\,\text{km}/1\,\text{mile}$ × $1000\,\text{m}/1\,\text{km}$ × $100\,\text{cm}/1\,\text{m}$ = number of centimeters.

Unit 2: Atoms, Ions, and Atomic Theory

Atomic Structure and Experiments

Key experiments led to the modern understanding of atomic structure.

• Thomson's Cathode Ray: Discovered the electron; showed atoms contain negatively charged particles.

• Millikan's Oil Drop: Measured the charge of the electron.

• Rutherford's Gold Foil: Revealed the existence of a small, dense nucleus.

Isotopes and Atomic Mass

Isotopes are atoms of the same element with different numbers of neutrons.

• Atomic Number (Z): Number of protons.

• Mass Number (A): Number of protons plus neutrons.

• Isotopic Abundance: Atomic mass is a weighted average of isotopic masses.

• Example: Boron has isotopes $^{10}\text{B}$ and $^{11}\text{B}$; atomic weight reflects their relative abundance.

Ions and Notation

Ions are atoms or molecules with a net electric charge due to loss or gain of electrons.

• Cations: Positively charged ions (loss of electrons).

• Anions: Negatively charged ions (gain of electrons).

• Notation: $\text{Element}^{A}_{Z}$ (e.g., $^{23}_{11}\text{Na}$).

Unit 3: Molecules, Compounds, and Chemical Formulas

Naming Compounds and Formulas

Chemical compounds are represented by formulas that indicate the types and numbers of atoms present.

• Empirical Formula: Simplest whole-number ratio of atoms.

• Molecular Formula: Actual number of atoms in a molecule.

• Naming: Use systematic rules for ionic and molecular compounds (e.g., $\text{NH}_4\text{PO}_4$ is ammonium phosphate).

Acids and Bases in Water

Acids release $\text{H}^+$ ions in water; bases release $\text{OH}^-$ ions.

• Strong Acids: Completely ionize in water (e.g., $\text{H}_2\text{SO}_4$).

• Weak Acids: Partially ionize (e.g., $\text{H}_2\text{CO}_3$).

• Example: $\text{H}_2\text{CO}_3$ acts as an acid in water.

Ionic Compounds and Precipitation

Mixing solutions of ionic compounds can result in precipitation if an insoluble product forms.

• Solubility Rules: Used to predict formation of precipitates.

• Example: Mixing $\text{Na}_2\text{CO}_3$ and $\text{Pb(NO}_3)_2$ forms $\text{PbCO}_3$ precipitate.

Unit 4: Chemical Reactions and Stoichiometry

Balancing Chemical Equations

Chemical equations must be balanced to obey the law of conservation of mass.

• Steps: Adjust coefficients to ensure equal numbers of each atom on both sides.

• Example: $\text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O}$

Limiting Reactant and Yield

The limiting reactant determines the maximum amount of product formed.

• Theoretical Yield: Maximum possible product from limiting reactant.

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

• Example: If 3.0 g H$_2$ reacts with 7.0 g N$_2$ to form NH$_3$, calculate limiting reactant and yield.

Unit 5: Introduction to Solutions and Aqueous Reactions

Solubility and Precipitation

Solubility rules help predict whether a compound will dissolve or form a precipitate in water.

• Insoluble Compounds: e.g., $\text{Ag}_2\text{SO}_4$ is insoluble in water.

• Precipitation Reaction: Mixing solutions to form an insoluble product.

Acid-Base Titration

Titration is used to determine the concentration of an acid or base in solution.

• Formula: $M_1V_1 = M_2V_2$ (for monoprotic acids and bases)

• Example: Titrating 25.00 mL of 0.100 M HCl with NaOH.

Gas-Evolution and Neutralization Reactions

Some reactions produce gases or neutralize acids and bases.

• Gas-Evolution: e.g., $\text{Na}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{H}_2\text{O} + \text{CO}_2$

• Neutralization: Acid + Base $\rightarrow$ Salt + Water

Unit 6: Gases and Kinetic Molecular Theory

Gas Laws and Relationships

Gas behavior is described by several laws relating pressure, volume, temperature, and amount.

• Ideal Gas Law: $PV = nRT$

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

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

• Avogadro's Law: $V \propto n$ (at constant P and T)

Kinetic Molecular Theory

This theory explains the properties of gases in terms of particle motion.

• Postulates: Gases consist of particles in constant, random motion; collisions are elastic; volume of particles is negligible.

• Diffusion and Effusion: Rate depends on molar mass; lighter gases diffuse/effuse faster.

• Example: Helium effuses faster than oxygen.

Unit 7: Thermochemistry and Energy

Heat, Work, and Internal Energy

Thermochemistry studies energy changes in chemical reactions.

• Endothermic Process: Absorbs heat ($\Delta H > 0$).

• Exothermic Process: Releases heat ($\Delta H < 0$).

• Specific Heat Capacity: $q = m c \Delta T$

• Example: Calculating heat required to raise temperature of water.

Enthalpy and Calorimetry

Enthalpy ($\Delta H$) is the heat content of a system at constant pressure.

• Calorimetry: Experimental measurement of heat changes.

• Example: Dissolving NH$_4$NO$_3$ in water is endothermic; solution cools down.

Unit 8: Atomic Structure and the Quantum Mechanical Model

Electromagnetic Radiation and Atomic Spectra

Atoms absorb and emit energy in quantized amounts.

• Photon Energy: $E = h \nu$

• Frequency Calculation: $\nu = \frac{E}{h}$

• Emission Spectrum: Distinct lines due to transitions between energy levels.

Quantum Numbers and Electron Configuration

Quantum numbers describe the arrangement of electrons in atoms.

• Principal (n): Energy level

• Angular (l): Subshell shape (s, p, d, f)

• Magnetic (ml): Orientation

• Spin (ms): Electron spin

• Example: $n=3$, $l=2$, $m_l=+1$, $m_s=+\frac{1}{2}$

Unit 9: Periodic Properties of the Elements

Trends in the Periodic Table

Periodic trends help predict element properties.

• Atomic Radius: Decreases across a period, increases down a group.

• Ionization Energy: Increases across a period, decreases down a group.

• Electronegativity: Tendency to attract electrons; increases across a period.

• Example: Fluorine is the most electronegative element.

Isoelectronic Species and Oxidation States

• Isoelectronic: Species with the same number of electrons.

• Oxidation States: Many transition metals form multiple oxidation states.

Unit 10: Chemical Bonding I: Lewis Structures and Molecular Geometry

Lewis Structures and Bonding

Lewis structures represent valence electrons and predict molecular shapes.

• Octet Rule: Atoms tend to have eight electrons in their valence shell.

• Bond Types: Single, double, triple bonds.

• Example: $\text{CO}_2$ has two double bonds.

Molecular Geometry (VSEPR Theory)

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts shapes based on electron pair repulsion.

• Common Geometries: Linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral.

• Example: $\text{BF}_3$ is trigonal planar; $\text{SF}_6$ is octahedral.

Unit 11: Chemical Bonding II: Molecular Shapes, Valence Bond & MO Theory

Molecular Orbital Theory and Bond Order

Molecular orbital (MO) theory explains bonding in terms of atomic orbital combinations.

• Bond Order: $\text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2}$

• Paramagnetism: Molecules with unpaired electrons are paramagnetic (e.g., $\text{O}_2$).

• Example: $\text{He}_2^+$ has a bond order of 0.5.

Polarity and Dipole Moments

Molecular polarity depends on shape and bond polarity.

• Nonpolar Molecules: Symmetrical charge distribution (e.g., $\text{SF}_6$).

• Polar Molecules: Asymmetrical charge distribution (e.g., $\text{H}_2\text{O}$).

Additional info:

• This guide is based on a comprehensive set of multiple-choice questions and explanations, covering all major topics in a first-semester General Chemistry course.

• Each unit includes definitions, examples, and key formulas relevant for exam preparation.