HL IB Chemistry: Exhaustive Study Guide

Subatomic Particles and the Nuclear Model

• Subatomic Particles: Atoms are composed of protons, neutrons, and electrons. Due to their extremely small scale, their properties are measured using relative units instead of standard units like grams ($g$) or coulombs ($C$).

  • Relative Mass and Charge Table:
    | Particle | Relative Charge | Relative Mass |
    | :--- | :--- | :--- |
    | Proton | $+1$ | $1$ |
    | Neutron | $0$ | $1$ |
    | Electron | $-1$ | Negligible ($\frac{1}{1836}$ of a nucleon) |

• Atomic Anatomy:

  • Nucleus: A dense, positively charged center containing protons and neutrons (nucleons). Most of the atom's mass is concentrated here.

  • Electrons: Occupy the space outside the nucleus in a "cloud" or as orbiting particles. Atoms are held together by electrostatic attraction between the positive nucleus and negative electrons.

  • Atomic Symbols:

  • $Z$ = Atomic Number (number of protons). Defines the element.

  • $A$ = Mass Number (total protons + neutrons).

  • Neutrons can be found via $A - Z$.

• Isotopes: Atoms of the same element with the same number of protons and electrons but different numbers of neutrons. They share chemical properties but differ in physical properties (e.g., carbon-12 vs. carbon-14).

Relative Atomic Mass and Mass Spectrometry

• Relative Atomic Mass ($A_r$): Defined as the weighted average mass of an atom of an element compared to $\frac{1}{12}$ of the mass of an atom of carbon-12.

• Calculation: $A_r = \frac{\sum (\text{isotopic mass} \times \text{percentage abundance})}{100}$.

• Mass Spectrometry: An analytical technique used to determine isotopic composition.

  • Process: Vaporization → Ionization (forming positive ions) → Acceleration → Detection (based on mass-to-charge ratio, $m/z$).

  • Interpretation: The peak at the highest $m/z$ in a molecular spectrum represents the molecular ion ($M^+$), which provides the relative molecular mass ($M_r$).

Particulate Nature of Matter and State Changes

• Classification of Matter:

  • Elements: Substances made of one kind of atom.

  • Compounds: Two or more elements chemically combined in fixed ratios.

  • Mixtures: Elements and compounds interspersed but not chemically bonded.

  • Homogeneous: Uniform composition (e.g., air, bronze).

  • Heterogeneous: Non-uniform composition (e.g., concrete, orange juice with pulp).

• Separation Techniques:

  • Filtration: Separates insoluble solids from liquids.

  • Distillation: Separates liquids based on boiling point differences (Simple vs. Fractional).

  • Chromatography: Separates substances based on different solubilities and rates of adsorption.

• Kinetic Molecular Theory:

  • Solids: Fixed volume/shape, regular pattern, particles vibrate.

  • Liquids: Fixed volume, take shape of container, particles move/slide.

  • Gases: No fixed volume/shape, particles move randomly ($\approx 500 \text{ m/s}$), highly compressible.

• Temperature and Energy:

  • Absolute temperature ($K$) is directly proportional to the average kinetic energy ($E_k$) of particles.

  • $E_k = \frac{1}{2}mv^2$.

  • Kelvin Conversion: $T(K) = T(^{\circ}C) + 273$.

  • Absolute Zero ($0 \text{ K}$): The point where particles have zero kinetic energy.

Ideal and Real Gases

• Kinetic Theory Assumptions:

  1. Gas molecules move fast and randomly.

  2. Molecules themselves have negligible volume.

  3. No intermolecular forces (attraction/repulsion).

  4. Collisions are perfectly elastic (energy is conserved).

• Gas Laws:

  • Boyle’s Law: $P \propto \frac{1}{V}$ (at constant $T$).

  • Charles’s Law: $V \propto T$ (at constant $P$).

  • Gay-Lussac’s Law: $P \propto T$ (at constant $V$).

• Ideal Gas Equation: $PV = nRT$.

  • $P$ in Pascals ($Pa$), $V$ in cubic meters ($m^3$), $n$ in moles, $R = 8.31 \text{ J K}^{-1}\text{ mol}^{-1}$, $T$ in Kelvin ($K$).

• Real Gas Deviation: Gases deviate from ideal behavior at high pressure and low temperature because molecular volume and intermolecular forces become significant.

Electronic Configuration

• Electromagnetic Spectrum: Energy is related to frequency ($f$) and wavelength ($\lambda$) by $c = f\lambda$. High frequency (gamma/UV) equals high energy.

• Emission Spectra: When electrons drop from higher to lower energy levels, they emit light of specific frequencies, creating a line spectrum.

  • This proves that energy levels are quantized.

  • Hydrogen Series: Drops to $n=1$ (UV, Lyman), $n=2$ (Visible, Balmer), $n=3$ (Infrared, Paschen).

  • Convergence: Lines get closer at higher frequencies. The convergence limit at $n=\infty$ represents the point where the electron is removed (ionization).

• Orbitals and Subshells:

  • Principal energy levels ($n$) contain subshells ($s, p, d, f$).

  • Shapes: $s$ is spherical; $p$ is dumbbell-shaped ($p<em>x, p</em>y, p_z$).

  • Filling Rules:

  • Aufbau Principle: Fill lowest energy first ($4s$ fills before $3d$).

  • Hund’s Rule: Orbitals of the same subshell are filled singly first to minimize spin-pair repulsion.

  • Pauli Exclusion Principle: Max 2 electrons per orbital with opposite spins.

• Exceptions: Chromium ($[Ar] 3d^5 4s^1$) and Copper ($[Ar] 3d^{10} 4s^1$) to achieve more stable half-full or full $d$-subshells.

Periodic Trends

• Atomic Radius: Decreases across a period (higher nuclear charge), increases down a group (more shells).

• Ionic Radius: Cations ($+$) are smaller than their parent atoms; Anions ($-$) are larger.

• Ionization Energy (IE): Energy required to remove 1 mol of electrons from 1 mol of gaseous atoms.

  • Increases across a period; decreases down a group.

  • Discontinuities: Dips occur (e.g., between Be and B, or N and O) due to subshell shielding or spin-pair repulsion.

• Electronegativity: Ability of an atom to attract a bonding pair of electrons. Increases across a period, decreases down a group.

• Oxides:

  • Metallic oxides (left) are basic (e.g., $Na_2O$).

  • Aluminum oxide ($Al<em>2O</em>3$) is amphoteric.

  • Non-metallic oxides (right) are acidic (e.g., $SO<em>3, P</em>4O_{10}$).

The Mole and Stoichiometry

• The Mole: One mole is $6.02 \times 10^{23}$ particles (Avogadro’s constant, $L$ or $N_A$).

• Molar Mass ($M$): Mass of 1 mole of a substance ($g/mol$).

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

• Solutions: Concentration ($c$) = $\frac{n}{V}$.

• Avogadro’s Law: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

  • At STP, 1 mole of any gas occupies $22.7 \text{ dm}^3$.

Energetics and Thermodynamics

• Exothermic ($-\Delta H$): Energy released to surroundings. Stability increases.

• Endothermic ($+\Delta H$): Energy absorbed from surroundings.

• Specific Heat Capacity ($c$): $q = mc\Delta T$.

• Bond Enthalpy: $\Delta H_{rxn} = \sum \text{Bonds Broken} - \sum \text{Bonds Formed}$.

  • Breaking bonds is endothermic; forming bonds is exothermic.

• Hess’s Law: Total enthalpy change is independent of the route taken.

• Born-Haber Cycles: Used to calculate Lattice Enthalpy, the energy change to turn 1 mol of an ionic solid into gaseous ions.

• Entropy ($S$): Measure of disorder. Gases have higher entropy than liquids or solids.

• Gibbs Free Energy ($G$): $\Delta G = \Delta H - T\Delta S$.

  • For a reaction to be spontaneous, $\Delta G \leq 0$.

  • Related to Equilibrium: $\Delta G^{\theta} = -RT \ln K$.

Organic Chemistry

• Homologous Series: Compounds with the same functional group and general formula; physical properties change gradually (e.g., boiling point increases with chain length).

• Isomerism:

  • Structural: Same molecular formula, different connections.

  • Stereoisomerism:

  • Cis-trans: Occurs due to restricted rotation (double bonds or rings).

  • Enantiomers: Mirror images caused by a chiral carbon (4 different groups attached). Rotates plane-polarized light.

• Functional Groups: Alkanes, Alkenes, Alkynes, Alcohols, Aldehydes, Ketones, Carboxylic Acids, Esters, Amines, Amides, Nitriles.

• Spectroscopic Analysis:

  • Infrared (IR): Identifies functional groups by bond vibrations.

  • Proton NMR: Identifies hydrogen environments. Splitting (multiplicity) follows the $n+1$ rule (neighboring protons).

  • Mass Spec Fragmentation: Loss of small units (e.g., $18$ for $H<em>2O$, $15$ for $CH</em>3$).