Ch.E - Essentials: Units, Measurement, and Problem Solving

SI Units, Prefixes, and Conversions

Understanding and converting between units is fundamental in chemistry. The SI system uses base units and prefixes to express quantities at different scales.

• Common Prefixes:

  • Mega (M):

  • Kilo (k):

  • Centi (c):

  • Milli (m):

  • Micro (\mu):

  • Nano (n):

  • Pico (p):

• Key Conversions:

• Avogadro's Number: (particles per mole)

Conversion Methods:

• To convert to per particle: multiply by 1,000, then divide by .

• To convert per particle to : multiply by , then divide by 1,000.

• To convert to per atom: divide by , then by 1,000.

• Number of photons:

• Photons per second:

• Moles:

• Number of particles:

• Mass percent:

Significant Figures

• Multiplication/Division: Use the fewest significant figures among measured values.

• Addition/Subtraction: Use the fewest decimal places.

• Exact counts and defined conversions do not limit significant figures.

• Keep extra digits during calculations and round at the end.

Ch.2 - The Quantum-Mechanical Model of the Atom

Light and Quantum Theory

Light exhibits both wave-like and particle-like properties, which are central to quantum mechanics.

• Wavelength (), Frequency (), and Energy ():

  • Shorter → higher → higher

  • Longer → lower → lower

  • Visible light: approximately 400–750 nm (violet is shorter, red is longer)

• Key Equations:

• Wave Phenomena:

  • Constructive interference: waves reinforce each other

  • Destructive interference: waves cancel each other

  • Diffraction: waves spread around obstacles

  • Refraction: waves change direction due to speed change in different media

  • Standing waves: fixed patterns with nodes (points of zero amplitude)

• Important Scientists:

  • Planck: Energy is quantized ()

  • Einstein: Light consists of photons; explains photoelectric effect

  • Bohr: Electrons occupy discrete energy levels

  • de Broglie: Matter has wave properties ()

  • Schrödinger: Wavefunctions () describe atomic states

Photoelectric Effect and Matter Waves

• Electrons are ejected from a metal only if the incident light has a frequency above a threshold value.

• Below threshold frequency: no electrons ejected, regardless of intensity.

• Above threshold: kinetic energy of ejected electrons increases with frequency.

• Photon energy:

• de Broglie wavelength:

Ch.5 - Chemical Bonding I

Bohr Model and Atomic Spectra

• Energy changes in atoms:

  • : absorption

  • : emission

  • Photon energy is always positive:

• Energy levels:

  • Ground state:

  • First excited state:

  • Ionization limit: ,

  • As increases: electron is less tightly bound, energy is less negative, orbitals are larger

• Hydrogen-like species: Bohr equation applies to one-electron ions (e.g., H, He, Li)

• Energy gap scales with (atomic number squared)

• Effective nuclear charge () can be used for multi-electron atoms in approximations

• Ionization energy:

Ch.6 - Chemical Bonding II: Quantum Numbers and Orbitals

Quantum Numbers

• Principal quantum number (): (shell)

• Angular momentum quantum number (): to (subshell, shape)

  • : s

  • : p

  • : d

  • : f

• Magnetic quantum number (): to (orbital orientation)

• Spin quantum number (): or

Orbitals and Their Properties

• Number of orbitals per subshell:

• Number of orbitals per shell:

• Maximum electrons per shell:

• Subshell capacities:

  • s: 1 orbital, 2 electrons

  • p: 3 orbitals, 6 electrons

  • d: 5 orbitals, 10 electrons

  • f: 7 orbitals, 14 electrons

• Nodes:

  • Angular nodes:

  • Total nodes:

  • Radial nodes:

  • Radial peaks:

• Shapes:

  • s: spherical

  • p: two lobes

  • d: four lobes (except : two lobes and a ring)

• Wavefunction (): probability amplitude; is probability density

• Degeneracy: Orbitals with the same are degenerate in hydrogen-like atoms; in multi-electron atoms, subshells have different energies due to electron interactions

Ch.7 - Chemical Reactions and Chemical Quantities

Electron Configurations

• Filling order (up to Period 4): 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p

• Aufbau principle: fill lower-energy orbitals first

• Pauli exclusion principle: max two electrons per orbital, opposite spins

• Hund's rule: fill degenerate orbitals singly before pairing

• Valence electrons: highest for main-group elements; for transition metals, include outer s and d electrons as per course convention

• Magnetism:

  • Paramagnetic: at least one unpaired electron

  • Diamagnetic: all electrons paired

• Exceptions to memorize:

  • Chromium (Cr): [Ar] 3d5 4s1 (6 unpaired electrons)

  • Copper (Cu): [Ar] 3d10 4s1 (1 unpaired electron)

• Transition-metal cations: remove ns electrons before (n-1)d electrons

• Electron counting:

  • Neutral atom: electrons = atomic number

  • Positive ion: subtract electrons equal to charge

  • Negative ion: add electrons equal to magnitude of charge

Ch.3 - Periodic Properties of the Elements

Ion Charges and Naming

• Common Charges to Memorize:

  • Silver: Ag+

  • Zinc: Zn2+

  • Aluminum: Al3+

• Main-group monatomic ions:

  • Group 1: +1

  • Group 2: +2

  • Group 13: +3 (especially Al3+)

  • Group 15: -3

  • Group 16: -2

  • Group 17: -1

• Variable charges: Fe2+/Fe3+, Cu+/Cu2+, Sn2+/Sn4+, Pb2+/Pb4+

• Roman numerals: indicate the metal's charge (e.g., Iron(III) = Fe3+)

• Polyatomic ions to memorize:

  • Ammonium: NH4+

  • Hydroxide: OH-

  • Nitrate: NO3-

  • Nitrite: NO2-

  • Sulfate: SO42-

  • Sulfite: SO32-

  • Carbonate: CO32-

  • Hydrogen carbonate: HCO3-

  • Phosphate: PO43-

  • Chromate: CrO42-

  • Chlorate: ClO3-

  • Perchlorate: ClO4-

• Formula rules: Ionic compounds must have zero total charge; use parentheses for multiple polyatomic ions (e.g., Mg(NO3)2).

• Molecular naming prefixes: mono-, di-, tri-, tetra-, penta-, hexa-, hepta-, octa-, nona-, deca-

Periodic Trends and Exceptions

• Across a period (left to right):

  • Atomic radius decreases

  • First ionization energy increases

  • Electronegativity increases

  • Metallic character decreases

  • Effective nuclear charge increases

• Down a group:

  • Atomic radius increases

  • First ionization energy decreases

  • Electronegativity decreases

  • Metallic character increases

• Explanations: Greater holds electrons more tightly; shielding and penetration affect trends.

• Atomic and ionic radii: Cations are smaller, anions are larger than parent atoms; in isoelectronic series, more protons = smaller radius.

• Ionization energy: Removing electrons requires energy; large jump after valence electrons are removed marks core electron removal.

• First-ionization exceptions: Be > B, Mg > Al (p electron easier to remove); N > O, P > S (paired electrons are easier to remove).

• Electron affinity: Adding an electron is exothermic (negative energy); Cl has more negative first electron affinity than F.

• Electronegativity: Attraction for electrons in a bond; F is most electronegative.

Ch.10 - Ionic Bonding and Lattice Energy

Ionic Bonding and Lattice Energy

• Ionic solids form extended lattices, not discrete molecules.

• Stronger attraction (higher charge, smaller ions) = greater lattice energy and higher melting point.

• Forming a lattice releases energy (negative enthalpy); separating a lattice requires energy (positive enthalpy).

Born–Haber Cycle Steps

• Sublimation/atomization of metal

• Dissociation of nonmetal

• Ionization of metal

• Electron attachment to nonmetal

• Formation of ionic lattice

• Include all coefficients, correct electron-affinity steps, and reverse/multiply enthalpy as needed

Ch.4 - Molecules and Compounds

Lewis Structures

1. Count available valence electrons

2. Add electrons for negative charge; subtract for positive charge

3. Draw atom framework and single bonds

4. Complete terminal atom octets (except H)

5. Place remaining electrons on central atom

6. Form multiple bonds as needed

7. Check total electrons, octets, formal charges, and overall charge

• Hydrogen forms one bond, is always terminal

• Fluorine is always terminal

• Central atom is usually least electronegative

• Beryllium and boron are often electron-deficient

• Second-period atoms cannot expand octets; Period 3 and beyond can

• Odd-electron species are radicals

Formal Charge, Resonance, and Bond Properties

• Formal charge:

• Formal charges must sum to overall charge; prefer small values and negative charge on more electronegative atoms

• Resonance: move electrons, not atoms; actual structure is a resonance hybrid

• Bond order: higher order = shorter, stronger bond

• Single > double > triple (longest/weakest to shortest/strongest)

• Breaking bonds requires energy; forming bonds releases energy

Ch.13 - VSEPR: Shapes and Angles

VSEPR Theory

• Electron geometry counts bonds and lone pairs; molecular geometry describes atom positions

• Lone pairs repel more strongly than bonding pairs, compressing bond angles

• Lone pairs occupy equatorial positions in trigonal bipyramidal geometry

Ch.14 - Bond Polarity and Molecular Polarity

Bond and Molecular Polarity

• Bond dipole arises from difference in electronegativity; arrow points toward more electronegative atom

• Molecular polarity depends on both bond dipoles and molecular geometry

• Examples:

  • CO2: polar bonds, nonpolar molecule (dipoles cancel)

  • H2O: polar molecule (bent shape prevents cancellation)

  • CH2F2: polar molecule (tetrahedral, dipoles do not cancel)

  • XeF4: nonpolar molecule (square planar, dipoles cancel)

• Do not assume polar bonds or lone pairs always mean a polar molecule; consider 3D geometry

First Memorization Priorities

• Metric prefixes and unit conversions

• Quantum number values and subshell capacities

• Chromium: [Ar] 3d5 4s1

• Copper: [Ar] 3d10 4s1

• Silver: Ag+

• Zinc: Zn2+

• Common monatomic and polyatomic ion charges

• Remove outer s electrons before d electrons in transition-metal cations

• Ionization-energy exceptions

• Complete VSEPR shapes, angles, and lone-pair placement

• Absorption/emission and lattice-energy sign conventions

Additional info: For best results, practice explaining each concept in your own words and apply them to unfamiliar examples.