Honors Chemistry: Chemical Composition, Stoichiometry, and Molecular Behavior

Chemical Composition and the Mole

• Conversion Factor: A ratio derived from the equality between two different units that must equal $1$. Examples include $\frac{4\,\text{quarters}}{1\,\text{dollar}}$, $\frac{100\,\text{cm}}{1\,\text{m}}$, and $\frac{1000\,g}{1\,kg}$.

• Dimensional Analysis: A mathematical technique using units to solve measurement problems.

• The Mole (mol): The SI unit for amount of substance. A mole is defined as the amount of substance containing as many particles as there are atoms in exactly $12\,g$ of Carbon-12.

• Avogadro's Number: Named for Amadeo Avagadro (also spelled Amedeo Avogadro in text), it equals $6.02 \times 10^{23}$. This counting unit is used for atoms, ions, or molecules due to their small size.

• Molar Mass: The mass of one mole of a pure substance, expressed in $g/mol$. It is numerically equal to the element's average atomic mass in atomic mass units ($\text{amu}$).

• Formula Mass: The sum of average atomic masses of all atoms in a compound's formula, expressed in $\text{amu}$.

• Chemical Formulas:

  • Empirical Formula: The simplest whole-number ratio of atoms in a compound.

  • Molecular Formula: The actual formula of a molecule; it is a whole-number multiple of the empirical formula.

• Hydrates: Compounds containing a specific number of water molecules within their crystal structure (e.g., $CuSO_4 \times 5H_2O$, copper (II) sulfate pentahydrate).

Stoichiometry and Chemical Reactions

• Stoichiometry: The numerical relationship between chemical quantities in a balanced equation, based on the Law of Conservation of Mass.

• Mole Ratio: A conversion factor relating the moles of any two substances in a balanced equation using their coefficients.

• Reaction Yields:

  • Theoretical Yield: The maximum amount of product calculated from the limiting reactant.

  • Actual Yield: The measured amount of product produced in a reaction.

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

• Reactant Types:

  • Limiting Reactant: The reactant that makes the least amount of product and is completely consumed.

  • Excess Reactant: The reactant not completely used up.

• Enthalpy (\text{\Delta}H_{\text{rxn}},): The thermal energy emitted (exothermic, negative \text{\Delta}H) or absorbed (endothermic, positive \text{\Delta}H) during a reaction at constant pressure.

Electrons in Atoms and the Periodic Table

• Light Characteristics: Light behaves as both a wave and a particle (dual nature).

  • Speed of Light ($c$): $3.00 \times 10^{8}\,m/s$.

  • Equation: $c = \lambda\nu$, where $\lambda$ is wavelength and $\nu$ is frequency.

  • Energy of a Photon: $E = h\nu$, where $h$ (Planck’s constant) is $6.626 \times 10^{-34}\,J \times s$.

• Atomic Models:

  • Bohr Model: Electrons orbit the nucleus in fixed, quantized circular energy levels ($n = 1, 2, 3...$). Light is emitted when electrons drop to lower energy levels.

  • Quantum-Mechanical Model: Electrons exist in orbitals—probability maps of where electrons are likely to be found. Models use principal quantum numbers ($n$) and lettered sublevels ($s, p, d, f$).

• Electron Configuration: The arrangement of electrons in an atom following the Aufbau Principle (lowest energy first), Pauli Exclusion Principle (opposite spins in an orbital), and Hund's Rule (fill empty orbitals of equal energy before pairing).

• Periodic Trends:

  • Atomic Radius: Decreases across a period (stronger nuclear pull); increases down a group (more energy levels).

  • Ionization Energy: The energy to remove an electron. Increases across a period; decreases down a group.

  • Electronegativity: An atom's ability to attract electrons in a bond. Fluorine is the most electronegative ($4.0$). Increases across a period; decreases down a group.

Chemical Bonding and Molecular Geometry

• Bond Types:

  • Ionic: Transfer of electrons between a metal and a nonmetal to form cations ($+\text{charge}$) and anions ($-\text{charge}$).

  • Covalent: Sharing of electrons between nonmetals. Bond Energy is required to break these bonds.

• Lewis Structures: Diagrams showing valence electrons as dots. Elements follow the Octet Rule (seeking 8 valence electrons), except $H$ and $He$ which seek 2.

• VSEPR Theory: (Valence-Shell Electron-Pair Repulsion) Predicts molecular shapes based on electron group repulsion.

  • Shapes: Linear ($180^{\circ}$), Trigonal Planar ($120^{\circ}$), Tetrahedral ($109.5^{\circ}$), Trigonal Pyramidal, and Bent.

• Polarity: Results from unequal electron sharing due to electronegativity differences, creating a Dipole Moment.

  • Pure Covalent: Equal sharing (electronegativities are identical).

  • Polar Covalent: Unequal sharing.

  • Ionic: Complete electron transfer.

Gases

• Kinetic-Molecular Theory: Gases are collections of particles in constant straight-line motion with negligible interactions and elastic collisions. Kinetic energy is proportional to temperature in Kelvins.

• Gas Laws:

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

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

  • Gay-Lussac's Law: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ (at constant $V$).

  • Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$.

  • Ideal Gas Law: $PV = nRT$, where $R = 0.0821\,\frac{L \times atm}{mol \times K}$.

• Dalton's Law of Partial Pressures: $P_{\text{total}} = P_1 + P_2 + P_3...$

• STP (Standard Temperature and Pressure): $0^{\circ}C$ ($273\,K$) and $1\,atm$. One mole of gas occupies $22.4\,L$.

Intermolecular Forces, Liquids, and Solids

• Properties:

  • Surface Tension: Tendency of liquids to minimize surface area.

  • Viscosity: Resistance of a liquid to flow.

• Phase Changes:

  • Vaporization/Evaporation: Endothermic conversion from liquid to gas.

  • Boiling Point: Temperature where vapor pressure equals external pressure.

  • Heat of Vaporization (\text{\Delta}H_{\text{vap}}): Energy to vaporize $1\,mol$ of liquid ($40.7\,kJ/mol$ for water).

  • Heat of Fusion (\text{\Delta}H_{\text{fus}}): Energy to melt $1\,mol$ of solid ($6.02\,kJ/mol$ for ice).

• Intermolecular Forces (Weakest to Strongest):

  1. Dispersion (London) Forces: Temporary dipoles in all atoms/molecules.

  2. Dipole-Dipole Forces: Exists in polar molecules.

  3. Hydrogen Bonding: Strong attraction when $H$ is bonded to $F, O, \text{or } N$.

  4. Ion-Dipole Forces: Mixture of ionic and polar compounds.

• Water Anomalies: Ice is less dense than liquid water due to the hexagonal hydrogen-bonded structure, acting as an insulator for aquatic life.

Solutions and Concentration

• Definitions: A solution is a homogeneous mixture of a Solute (minority) and a Solvent (majority).

• Solubility: Increases with temperature for solids; decreases with temperature for gases. Solubility of gases increases with pressure (Henry's Law).

• Saturation Levels: Saturated (holds maximum), Unsaturated (can hold more), Supersaturated (holds more than normal max).

• Concentrations:

  • Mass Percent: $\frac{\text{Mass Solute}}{\text{Mass Solution}} \times 100\%$.

  • Molarity (M): $\frac{\text{moles solute}}{1\,L\,\text{solution}}$.

• Dilution: $M_1V_1 = M_2V_2$.

• Colligative Properties: Properties depending on particle concentration: Freezing Point Depression, Boiling Point Elevation, and Osmotic Pressure.

  • Wood Frog Adaptation: Secretes glucose to act as intracellular antifreeze.

Acids and Bases

• Definitions:

  • Arrhenius: Acids produce $H^+$; Bases produce $OH^-$.

  • Bronsted-Lowry: Acids are proton donors; Bases are proton acceptors.

• Conjugate Pairs: A Conjugate Acid forms when a base gains a proton; a Conjugate Base remains after an acid donates a proton.

• Self-Ionization of Water: $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ at $25^{\circ}C$.

• Scales:

  • $pH = -\text{log}[H_3O^+]$ (<7 acidic, $7$ neutral, >7 basic).

  • $pOH = -\text{log}[OH^-]$ and $pH + pOH = 14.00$.

• Strong vs. Weak: Strong acids/bases ionize/dissociate completely. Weak ones only partially ionize and exist in equilibrium.

• Neutralization: Acid + Base $\rightarrow$ Salt + Water. A Titration uses this to find unknown concentrations via an equivalence point signaled by an indicator.

• Buffers: Solutions resisting pH changes containing significant amounts of a weak acid and its conjugate base (e.g., human blood).

Questions & Activities

• Cooking Analogy: Stoichiometry is compared to a pancake recipe: $1\,\text{cup flour} + 2\,\text{eggs} + 0.5\,\text{tsp baking powder} \rightarrow 5\,\text{pancakes}$. If you have $3\,\text{cups flour, } 10\,\text{eggs, and } 4\,\text{tsp baking powder}$, flour is the limiting reactant, allowing only $15\,\text{pancakes}$.

• James Bond Spy Gadget: A gold pen filled with acid could dissolve iron bars, though it would take more than one pen's volume. Gold is used because it does not react with the acid inside.

• Altitude and Ears: At high altitudes, lower external pressure causes internal ear pressure to push eardrums outward until yawning equalizes the pressure.

• Scuba Safety: Divers must never hold their breath while ascending to avoid lung expansion damage (Boyle's Law) and may use specialized gas mixes to avoid oxygen toxicity.

• Soap Mechanism: Soap molecules have a polar head and a nonpolar tail, allowing them to link polar water to nonpolar grease/oil for cleaning.