General Chemistry 1 Principles and Formulas

Posted on Jan 19, 2026 in Chemistry

Fundamentals and Measurements

• SI Units: Mass (kg), Length (m), Time (s), Temperature (K), Amount (mol), Volume (m³ or L = 10^-3m³).
• Prefixes: Pico (10^-12), nano (10^-9), micro (10^-6), milli (10^-3), centi (10^-2), kilo (10³), mega (10⁶).
• Density: d = mass / volume. To convert g/cm³ to kg/m³, multiply by 1,000 (e.g., 6.353 g/cm³ = 6,353 kg/m³).
• Temperature Conversions: °F = (9/5)°C + 32; K = °C + 273.15 (e.g., 56.1°C = 133°F).
• Significant Figures:
  • Non-zero digits are always significant. Zeros between non-zeros are significant. Leading zeros are not significant. Trailing zeros are significant if a decimal point is present.
  • Addition/Subtraction: Round to the least number of decimal places.
  • Multiplication/Division: Round to the least number of significant figures.
  • Examples: 970.0 (4 sig figs), 0.0043 (2 sig figs), 502 (3 sig figs), 0.300 (3 sig figs).
• Scientific Notation: e.g., 52,030.2 m = 5.20302 × 10⁴ m.
• Conversion Factors: Use dimensional analysis (e.g., 550 mg = 5.5 × 10^-4 kg; 134 pm = 1.34 × 10^-10 m).

Atomic Structure and Matter

• Atomic Theory:
  • Dalton: Atoms are indivisible; atoms of the same element are identical.
  • Thomson: Discovered electrons via cathode rays; determined mass/charge ratio; proposed the Plum Pudding Model.
  • Rutherford: Gold Foil Experiment discovered the nucleus (dense and positive).
  • Modern Theory: Atoms consist of protons, neutrons, and electrons. Atomic Number (Z) = protons. Mass Number (A) = protons + neutrons.
• Isotopes: Atoms with the same Z but different A (e.g., ⁴¹⁰X and ⁴¹²Y are isotopes if they share the same Z).
• Average Atomic Mass: Weighted average = Σ (isotope mass × fractional abundance).
  • Example (Si): (27.976927 × 0.9223) + (28.976495 × 0.0467) + (29.973770 × 0.0310) = 28.085 amu.
• Electrons: Negative charge; lost electrons form cations (positive), gained electrons form anions (negative).
• Periodic Table:
  • Groups: 1A (Alkali Metals), 2A (Alkaline Earth Metals), 7A (Halogens), 8A (Noble Gases).
  • Periods: Row number corresponds to the n energy level.
  • Classification: Metals (left, conductive), Nonmetals (right, e.g., Br), and Metalloids.
  • Symbols: K (Potassium), Po (Polonium).
• Changes in Matter: Physical (no composition change) vs. Chemical (composition change, e.g., ripening fruit).
• Elements, Compounds, and Mixtures: Elements (single type of atom), Compounds (fixed ratio of atoms), and Mixtures (variable composition).

Compounds, Formulas, and Naming

• Molar Mass: Sum of atomic masses.
  • Examples: Al₂(SO₄)₃ = 342 g/mol; CaF₂ = 78 g/mol; Mg(OH)₂ = 58 g/mol.
• Naming Conventions:
  • Ionic: Cation + Anion (e.g., (NH₄)₂S is ammonium sulfide; MgF₂ is magnesium fluoride; Na₂O is sodium oxide; CoCl₂ is cobalt(II) chloride; PbO is lead(II) oxide).
  • Acids: HBr(aq) is hydrobromic acid; HClO₄ is perchloric acid.
  • Covalent: Use Greek prefixes (e.g., PCl₃ is phosphorus trichloride).
• Percent Composition: (Mass of element / Molar mass of compound) × 100. (e.g., Sucrose C₁₂H₂₂O₁₁: C = 144/342 × 100 = 42.1%).
• Empirical and Molecular Formulas: Derived from mass percentages or elemental masses.
• Charge Balance: In a formula like M₂X₃, the total positive and negative charges must balance to zero (e.g., if X is 2-, M must be 3+).
• Mass Ratios: e.g., CH₄ (C:H = 12:4 or 3:1); C₂H₂ (C:H = 24:2 or 12:1).

Stoichiometry and Chemical Reactions

• The Mole: 6.022 × 10²³ particles. Moles = mass / molar mass.
  • Examples: 4.68 mol NaBrO₃ = 707 g; 17.8 g Mg(OH)₂ = 0.305 mol.
• Atoms and Molecules: Oxygen atoms in 29.34 g Na₂SO₄: (29.34 / 142) mol × 4 O atoms × 6.022e23 = 4.976 × 10²³ atoms.
• Total Atoms: Compare moles × atoms per formula (e.g., 50g Li₂O ≈ 5.0 × 10²³ total atoms).
• Balancing Equations: Adjust coefficients to balance atoms (e.g., B₂O₃ + 6HF → 2BF₃ + 3H₂O).
• Stoichiometry: Use molar ratios. N₂ + 3H₂ → 2NH₃; 325g NH₃ requires (28/34) × 325 = 267g N₂.
• Limiting Reactant: The reactant that produces the least amount of product.
  • Example: 4Al + 3O₂ → 2Al₂O₃. With 3.06 mol Al and 3.68 mol O₂, Al is limiting. Excess O₂ = 1.385 mol (44.24g).
• Reaction Types: Precipitation (insoluble product), Acid-Base (H⁺ transfer), and Redox (electron transfer, change in oxidation number).
• Oxidation Numbers: I₂ = 0; Cl in HClO₄ = +7.
• Net Ionic Equations: Omit spectator ions. e.g., Pb²⁺ + 2Cl^– → PbCl₂(s). Spectators: Na⁺, NO₃^–.
• Solubility Rules: CaCO₃ is insoluble; NaCl, AgNO₃, and Na₃PO₄ are soluble.
• Acids and Bases: Strong acids include HNO₃, HCl, H₂SO₄, and HClO₄. Weak acids include HF and CH₃COOH. Bases produce OH^–.
• Ion Concentration: CoCl₂ → Co²⁺ + 2Cl^–. 0.27 mol CoCl₂ yields 0.81 mol total ions.
• Combustion: e.g., C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O; Carbon is oxidized.

Solutions and Molarity

• Molarity (M): Moles of solute / Liters of solution.
  • Examples: 1.495 mol LiOH in 0.75L = 1.99 M; 2.61g Na₂CO₃ in 0.25L = 0.0987 M.
• Mass of Solute: M × V(L) × Molar Mass. (e.g., 0.150 M NaCl in 0.275 L = 2.41 g).
• Conductivity: Strong electrolytes (NaOH, KBr, HClO₄) have high conductivity; non-electrolytes (CH₃CH₂OH) have none.
• Mole Calculation: 0.06285 L × 0.453 M HCl = 0.0285 mol.

Gas Laws and Kinetic Molecular Theory

• Pressure: 1 atm = 760 torr. (e.g., 466 torr = 0.613 atm).
• Gas Laws:
  • Boyle’s Law: P₁V₁ = P₂V₂ (constant T, n).
  • Charles’s Law: V₁/T₁ = V₂/T₂ (constant P, n).
  • Avogadro’s Law: V ∝ n (constant P, T).
  • Ideal Gas Law: PV = nRT (R = 0.0821 L·atm/mol·K).
  • Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂.
• STP (Standard Temperature and Pressure): 0°C (273 K), 1 atm. Molar volume = 22.4 L/mol.
• Gas Density: d = (P × Molar Mass) / (RT). Density of Ar at STP = 1.78 g/L.
• Effusion: Lighter gases effuse faster (e.g., H₂ > NH₃ > N₂ > O₂).
• Kinetic Molecular Theory: Gas particles are in constant motion, have negligible volume, and undergo elastic collisions.

Thermochemistry and Enthalpy

• Internal Energy: ΔE = q + w. (q > 0: heat absorbed; w < 0: work done by system).
  • Work: w = -PΔV. (e.g., ΔV = -5L, P = 0.8 atm, w = 405 J).
  • Energy Change: If q = 575 J and w = -425 J, ΔE = 150 J.
• Heat Capacity: q = m c ΔT (c_water = 4.184 J/g°C).
  • Example: 28.6g water heated from 22°C to 78.3°C: q = 6,730 J.
• Enthalpy (ΔH): Heat at constant pressure. Exothermic (ΔH < 0); Endothermic (ΔH > 0).
• Hess’s Law: The total enthalpy change is the sum of the ΔH of individual steps.
  • Example: WO₃ + 3H₂ → W + 3H₂O yields ΔH = 125.94 kJ.
• Bond Energy: ΔH = Σ(bonds broken) – Σ(bonds formed).
  • Example: N₂ + 3H₂ → 2NH₃; ΔH = 2253 – 2346 = -93 kJ.
• Energy Conversion: 802.3 kJ = 191.9 kcal (1 kcal = 4.184 kJ).

Quantum Theory and Atomic Structure

• Quantum Numbers:
  • n: Principal (size/energy).
  • l: Angular momentum (shape: s=0, p=1, d=2, f=3).
  • m_l: Magnetic (orientation, -l to +l).
  • m_s: Spin (±1/2).
• Orbitals: For n=4, there are 16 orbitals (1s + 3p + 5d + 7f).
• Pauli Exclusion Principle: No two electrons can have the same four quantum numbers.
• Aufbau Principle: Electrons fill the lowest energy orbitals first.
• Hund’s Rule: Electrons occupy orbitals singly with parallel spins before pairing.
• Electron Configurations: S: [Ne]3s²3p&sup4;; Te: [Kr]5s²4d¹&sup0;5p&sup4;; Ni: [Ar]4s²3d&sup8;.
• Valence Electrons: Electrons in the outermost ns, np, and (n-1)d shells.
• Paramagnetism: Presence of unpaired electrons (e.g., Fe³⁺ is paramagnetic).

Periodic Trends and Chemical Bonding

• Atomic Size: Decreases across a period, increases down a group (e.g., Ba > Ca).
• Ionization Energy (IE): Increases across a period, decreases down a group (e.g., Cl > Br > Na > Ca).
• Electronegativity: Increases across and up the table (Fluorine is the most electronegative).
• Bonding Types:
  • Ionic: Metal and nonmetal; electron transfer (e.g., SrF₂, CaCl₂).
  • Covalent: Nonmetals; electron sharing (e.g., HCl, CO, IBr).
  • Polar Covalent: Unequal sharing due to electronegativity differences (e.g., C-F).
• Lattice Energy: Increases with higher ionic charges and smaller ionic radii (e.g., MgO > NaI).
• Lewis Structures: Based on the Octet Rule. Formal Charge = Valence – (Non-bonding + 0.5 × Bonding).
• Ion Sizes: Anions are larger than their parent atoms; cations are smaller (e.g., P^3- > Cl^– > K⁺ > Ca²⁺).

Scientific Method and Laboratory Basics

• Scientific Method: Involves hypothesis, experimentation, and theory development.
• Titration: The end point is reached when the indicator changes color.
• Molar Mass of O₂: Always use 32.00 g/mol for diatomic oxygen.