⚡ Chapter 1: Properties & States of Matter

Matter is anything that has mass and takes up space (volume). Light, heat, sound, and energy are NOT matter — they have no mass and take up no space.

Mass vs. Weight

Mass = amount of matter; measured in kg or g; never changes. Weight = gravitational force on that mass; changes with gravity. On the Moon (1/6 Earth gravity) your mass stays the same but you weigh 1/6 as much. A brick of gold has the same mass on Earth and the Moon — only its weight differs.

The SI (metric) base unit of mass is the kilogram (kg). The SI unit of force (including weight) is the Newton (N).

Physical vs. Chemical Properties

Physical properties can be observed or measured without changing the substance: color, density, melting point, boiling point, hardness, viscosity, malleability, ductility, electrical and thermal conductivity, solubility, specific gravity, mass, volume, length, odor, luster.

Chemical properties describe how a substance reacts and forms a new substance: flammability, reactivity with acid, tendency to rust/corrode. Flammability is a chemical property, NOT a physical one.

Intensive vs. Extensive Properties

Intensive (intrinsic) properties do NOT depend on amount: density, color, boiling point, melting point, specific heat, hardness, conductivity, specific gravity. Cut a gold bar in half — each half still has density 19.3 g/cm³.

Extensive properties DO depend on amount: mass, volume, weight, length, energy, thermal energy. Two gold bars have twice the mass of one. Mass and volume are extensive; density is intensive.

Physical Changes vs. Chemical Changes

A physical change does NOT create a new substance — only form, size, or state changes: cutting, melting, freezing, boiling, evaporation, sublimation, deposition, bending, dissolving, magnetizing, vaporizing ethanol. Note: dissolving and phase changes are physical even though they may look dramatic.

A chemical change DOES create a new substance with new properties: burning (combustion), rusting (Fe→Fe₂O₃), frying an egg, burning toast, electrolysis, effervescence from a reaction. Signs that suggest (but don't prove) a chemical change: color change, gas production/bubbling, energy change (heat/light), precipitate formation, irreversibility.

A change in SIZE alone (cutting, grinding) is purely physical — it can't even suggest a chemical change. Steel turning red when heated is physical (glow = thermal emission, not new chemical). Iron rusting IS chemical — new substance (rust) forms. Burning toast IS chemical — new compounds form (Maillard reaction).

Irreversible changes: burning and effervescence (from chemical reactions) are irreversible. Dissolving, melting are reversible (physical).

Conservation of Mass

The Law of Conservation of Matter: during any chemical reaction, the total number of atoms is unchanged. Atoms are only rearranged. So the total mass of products equals the total mass of reactants. A glass of ice water weighs the same after the ice melts (300 g stays 300 g).

Density

Density = mass ÷ volume (unit: g/cm³ or g/mL). Density is intensive — it does NOT change with sample size. 1 cm³ of water ≈ 1 gram (density = 1.0 g/cm³). An object sinks if its density > the fluid; floats if less.

Special water facts: water is MOST dense at 4°C (3.98°C). Below 4°C, density decreases as hydrogen bonds form the open ice lattice. Ice (0.92 g/cm³) is less dense than liquid water — that's why ice floats. Density order: water at 1°C < water at 4°C < iron < gold.

Specific Gravity

Specific gravity (SG) = density of substance ÷ density of water at 4°C (1.000 g/cm³). SG is dimensionless (no units). SG numerically equals density in g/cm³. A hydrometer reading 1.0 means the liquid has the same density as water.

Thermal Energy & Specific Heat

Thermal energy = mass × specific heat × temperature. At the same temperature, a more massive object has more total thermal energy. Specific heat is the energy needed to raise 1 g of a substance by 1°C — this IS intensive. Specific heat ranking (highest to lowest): water > aluminum > silver. Water's high specific heat is why oceans moderate climate and why it takes so long to heat or cool. A concrete floor conducts heat away from your foot faster than a wooden floor even at the same temperature, making it feel colder.

Classification Tree

All matter → Pure Substance (fixed composition) or Mixture (variable composition, physically combined).
Pure Substance → Element (one atom type, can't be broken down chemically) or Compound (two+ elements, chemically bonded, fixed ratio).
Mixture → Homogeneous (uniform, same throughout = solution) or Heterogeneous (non-uniform, visible parts).

Elements

118 known elements on the periodic table. Each element is made of one type of atom. Examples: gold (Au), oxygen (O₂), iron (Fe), carbon (C), hydrogen (H₂), nitrogen (N₂), sulfur (S₂), mercury (Hg), bromine (Br₂). About 80+ elements are metals — so most periodic table darts hit a conductor/solid.

Compounds

Two or more elements chemically bonded in a fixed ratio. Only separated by chemical reactions, NOT physical means. Properties differ completely from component elements. Examples: water (H₂O), table salt (NaCl), carbon dioxide (CO₂), HCl, ammonia (NH₃), sodium sulfide (Na₂S), sucrose (C₁₂H₂₂O₁₁).

The smallest unit of a compound that retains its chemical properties is a molecule. The smallest unit of a covalent compound is also a molecule.

Compounds that conduct electricity when dissolved or molten form ionic bonds (metals + nonmetals: Na⁺ and Cl⁻). Compounds that don't ionize in solution, like sucrose, are covalent (molecular) and do NOT conduct. NaCl: solid = no conductance (ions locked); molten or dissolved = conducts (free ions). Active metals (alkali metals like Na, K) readily give up electrons to form ionic compounds — they lose their valence electrons most easily.

Ionic vs. Covalent Bonds

Ionic bonds: between metals and nonmetals; electrons transferred. Ionic compounds: high melting points (NaCl melts at 801°C), conduct when molten or in solution (dissociation into cations + anions), form crystalline lattices. Ionic compounds are NOT soluble in all cases — see solubility rules. Na₂S, NaCl are ionic. CCl₂₀ and PCl₂₃ are covalent (formed between nonmetals).

Covalent bonds: between nonmetals; electrons shared. Lower melting points than ionic solids. Often soluble in nonpolar solvents. Sucrose dissolved in water does NOT conduct electricity.

Mixtures

Physical blend; each component retains its properties; variable composition; separated by physical methods.

• Homogeneous mixture (solution): uniform throughout; e.g., saltwater, air, vinegar (acetic acid + water), lemonade, gasoline, steel, rubbing alcohol, ethanol-water mixture, 14K gold bracelet (alloy), sterling silver (92.5% Ag + 7.5% Cu — copper is the solute).
• Heterogeneous mixture: non-uniform, parts visible; e.g., concrete, salad, trail mix, pizza, sand + gravel, soil.

Solutions, Colloids & Suspensions

Solution: particles <1 nm; clear; don't settle; don't scatter light. Example: saltwater, vinegar, ethanol-water (miscible liquids mixed = solution).
Colloid: particles 1–1000 nm; don't settle (Brownian motion keeps them up); may scatter light (Tyndall effect). Example: milk, fog, Jell-O, aerosol sprays.
Suspension: particles >1000 nm; settle over time; must be shaken (e.g., orange juice with pulp, muddy water, the “drink that needs shaking” in competition). A drink that settles = suspension.

Emulsion: a mixture of two immiscible liquids (e.g., oil and water) where one is dispersed in the other as droplets. Over time, an emulsion separates into two distinct liquid layers (unlike a colloid).

Solubility & Solutions

Saturated solution: maximum solute dissolved at given T and P — can't dissolve more. Unsaturated: could dissolve more. Supersaturated: holds more than theoretical maximum (unstable).

Adding NaCl to water: raises boiling point (boiling-point elevation) and lowers freezing point (freezing-point depression). Both are colligative properties — depend on number of solute particles, not identity. Other colligative properties: vapor pressure lowering, osmotic pressure. Adding ethylene glycol (antifreeze) to car radiator: lowers freezing point AND raises boiling point.

Henry's Law: solubility of a gas in liquid increases with pressure. Solids and liquids: pressure has almost no effect on their solubility. Temperature: for most solids, solubility increases with temperature; for gases, solubility decreases with temperature.

Most soluble in water at 25°C: polar/ionic compounds (AlCl₃ ~700 g/L). Least soluble: nonpolar molecules like N₂. “Like dissolves like”: polar dissolves polar, nonpolar dissolves nonpolar. Iodine dissolves in ethanol — ethanol is the solvent.

Dissociation: ionic compounds split into cations and anions in solution. Best conductors: saturated ionic solutions (most ions). A saturated NaCl solution conducts better than unsaturated NaCl.

Solution Concentration Calculations

• Mass percent (% w/w) = (mass solute ÷ mass solution) × 100. 300 g of 20% NaCl solution contains 300 × 0.20 = 60 g NaCl.
• Weight/volume percent (% w/v) = (mass solute [g] ÷ volume solution [mL]) × 100. 20 g glucose in 1000 mL = 2% w/v.
• Molarity (M) = moles solute ÷ liters solution. NaCl (MW = 23+35 = 58 g/mol): 116 g in 1 L = 116/58 = 2 M. 10 L of 0.8 M solution of MW=100: need 10 × 0.8 × 100 = 800 g.
• Dilution: M₁V₁ = M₂V₂. To make 2 L of 1 mM from 0.1 M: V₁ = (0.001 × 2000)/0.1 = 20 mL.

Separation Techniques

• Filtration: separates solid from liquid (sand from water, suspended particles from liquid). Best for suspensions.
• Distillation: separates miscible liquids by different boiling points (best for miscible liquids). Fails if two substances have the same boiling point. Depends on boiling point.
• Chromatography (paper): separates by solubility differences; most commonly used for that purpose.
• Centrifugation: separates by density (blood separation, cream from milk).
• Magnetism: separates magnetic from non-magnetic (iron filings from sand).
• Reverse osmosis: converts salt water to fresh water (used in submarines).
• Evaporation/crystallization: recovers dissolved solid from solution.

Allotropes

Allotropes are different structural forms of the same element. Carbon allotropes: diamond (3D tetrahedral lattice, hardest natural substance), graphite (flat hexagonal layers, lubricant, conducts electricity), graphene (single carbon layer), fullerene/C₮₀ (buckyball), lonsdaleite (hexagonal diamond), nanofoam. Diamond is harder than graphite because of 3D tetrahedral covalent network (sp³) vs. graphite's flat sp² layers that slide. Non-amorphous carbon allotropes: diamond and graphite. Amorphous carbon: vitreous carbon, nanofoam, carbon black. Allotropes of oxygen: O₂ (dioxygen) and O₃ (ozone).

Allotrope pairs: diamond & graphite (carbon), O₂ & O₃ (oxygen). NOT allotropes: diamond & quartz (different elements).

Diatomic Elements

Seven elements naturally exist as diatomic molecules: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂ (HOFBrINCl or “Have No Fear Of Ice Cold Beer”). Sulfur is NOT diatomic — it forms S₂₀ rings. Nitrogen has an extremely stable triple bond (N≡N, 945 kJ/mol).

Metals, Metalloids, Nonmetals

Metals (majority of periodic table): shiny/lustrous, malleable, ductile, good conductors of heat and electricity, lose valence electrons to form positive ions (cations), tend to have high melting/boiling points. Best electrical conductor: silver (1st) > copper (2nd) > gold (3rd). Least magnetic among common metals: titanium (paramagnetic — not ferromagnetic). Ferromagnetic metals: iron, nickel, cobalt. Magnetic AND conductive: iron nail, steel can. Tungsten has the highest melting point (3,422°C) — used in light bulb filaments. Most metals are solid at room temperature.

Nonmetals: brittle (not malleable), dull (not shiny), poor conductors (insulators), gain electrons to form anions. Examples: nitrogen, sulfur, selenium, carbon, oxygen, halogens, noble gases.

Metalloids: properties between metal and nonmetal; semiconductors. Examples: silicon (Si) — the most important semiconductor; germanium (Ge), arsenic (As), antimony (Sb), boron (B), tellurium (Te), polonium (Po). Identify: silicon = metalloid, sodium = metal, neon = nonmetal. Semiconductors conduct electricity somewhat — better than insulators, worse than conductors.

Insulators have tightly bound electrons that cannot move. Distilled water = excellent insulator (no free ions, very high resistivity). Salty water = excellent conductor.

Noble gases (Group 18): He, Ne, Ar, Kr, Xe, Rn — stable outer energy level (full valence shell), very unreactive.

Acid-Base Basics & pH

pH = −log[H⁺]. pH < 7 = acidic (sour taste — Kate's sour juice is likely acidic). pH > 7 = basic/alkaline. pH = 7 = neutral. Vinegar pH ≈ 2.4–3.4 (acidic). Sodium bicarbonate, soapy water, ammonia = basic. Neutralize basic NaOH spill: use citric acid (safe, weak acid — NOT concentrated H₂SO₂⁴). The pH scale quantifies basicity/acidity.

Atomic History

Democritus first theorized (ancient Greece) that everything is made of physically indivisible atoms. John Dalton developed the first modern atomic theory in 1803.

Three Subatomic Particles

Charged particles: protons and electrons. Neutrons = neutral. Proton mass ≈ neutron mass (differ by 0.1%). Atom's ability to react = determined by valence electrons. Element's identity = determined by number of protons (atomic number).

Key Numbers

• Atomic number (Z) = # protons. Defines the element. Molybdenum Z=42 means every Mo atom has 42 protons. Never changes for an element.
• Mass number (A) = protons + neutrons (always a whole number, also called nucleon number).
• Neutrons = mass number − atomic number.
• In a neutral atom: # electrons = # protons.
• Atomic weight (on periodic table) = weighted average of all natural isotopes. Reflects total of protons + neutrons (approximately). “Atomic weight of an element most nearly reflects total number of protons + neutrons.”

Isotopes

Same element (same # protons), different # neutrons → different mass numbers. Examples:

• Carbon-12: 6p + 6n; Carbon-14: 6p + 8n — used in radiocarbon dating
• Boron-10: 5p + 5n; Boron-11: 5p + 6n — differ by one neutron
• Gold-197: 79p + 118n (197 − 79 = 118 neutrons)
• Helium nucleus: 2 protons (add a proton + 2 neutrons to H₂ = He)
• Nitrogen common isotope: Z=7, A=14, so 7 neutrons
• Na neutral atom (Z=11, A=23): 11p, 12n, 11e
• Lithium: atomic mass 6.941 amu, two stable isotopes (⁻⁶Li and ⁻⁷Li). Li-7 has 4 neutrons.

As atomic mass increases, more neutrons are needed to hold the nucleus together (strong nuclear force). C-14 beta-minus decay: a neutron → proton + electron, so neutrons go from 8 → 7 (and atomic number increases from 6 to 7 = nitrogen).

Valence Electrons & Reactivity

Elements in the same group (column) have the same number of valence electrons — this is why they have similar properties. Noble gases (Group 18) have a FULL outer shell — they are the most stable and unreactive. Active metals (alkali metals, Group 1) have 1 valence electron and lose it readily.

Electronegativity: increases up and right on periodic table. Fluorine = most electronegative element of all. Among C, B, Na, Rb: C > B > Na > Rb. Chloride ion (Cl⁻) is LARGER than chlorine atom (Cl) because adding an electron increases repulsion, expanding the electron cloud.

Electron Shells & Insulator/Conductor Distinction

Shell 1: max 2e⁻. Shell 2: max 8e⁻. Shell 3: max 18e⁻. In metals, outer electrons are loosely held and free to move — excellent conductors. In insulators, electrons are tightly bound — they can't move. Semiconductors (metalloids like silicon) are between: some free electrons, conductivity adjustable by doping.

Kinetic Molecular Theory (KMT)

All particles are in constant motion. Temperature measures the average kinetic energy of particles. Higher T = faster particles. At absolute zero (0 K = −273°C) all motion theoretically stops. Kinetic energy order: solid < liquid < gas < plasma. A more massive object at the same temperature has MORE total thermal energy (but same average KE per particle).

Gas pressure increases with temperature because molecules move faster and strike walls more frequently and forcefully (Gay-Lussac explanation).

Four States Compared

Solid Details

Strongest intermolecular attractions — particles held in fixed positions, only vibrate. Crystalline solids: ordered geometric lattice (salt, diamond, ice, sugar, snow, metals). Amorphous solids: random arrangement (glass, rubber, wax, plastic, charcoal). Glass is amorphous. Most solids: definite shape and volume, nearly incompressible, volume SHRINKS when becoming solid (most substances contract on freezing — water is the exception). Ionic solids (NaCl): high melting points (NOT low).

Liquid Details

Particles close but slide past each other — definite volume, no definite shape. Best distinguishing property between liquid and gas: density (liquids much denser). Liquids are nearly incompressible — this is why hydraulic systems work. “All liquids are resistant to compression.”

Surface tension: cohesive forces at liquid-air interface create a “skin”. Allows water striders to walk on water, metal wire to float on water, liquid drops to be spherical (rounded). Water has the greatest surface tension of common liquids at room temperature. Caused by hydrogen bonding in water.

Viscosity: resistance to flow (internal friction). Molasses > honey > water (high viscosity = slow flow). Temperature increases → viscosity of liquids decreases (particles move faster, less friction).

Adhesion: water sticking to other surfaces. Cohesion: water sticking to itself (surface tension).

Water molecules are dipoles (polar). At all temperatures, water molecules continuously evaporate from and condense into the liquid — dynamic equilibrium. Warm air holds MORE water vapor (higher vapor pressure of water at higher T).

Water at higher altitude: lower atmospheric pressure → boils at a LOWER temperature (e.g., ≈90°C on Mt. McKinley/Denali). Increasing atmospheric pressure on water → would raise its boiling point.

Gas Details

Particles far apart, rapid random motion, no attraction, fill any container. Highly compressible. Gas exerts uniform (isotropic) pressure on ALL walls — unlike liquid hydrostatic pressure. Pressure increases with depth in liquids but a gas in a closed container exerts the SAME pressure on all walls. At a given temperature, gas velocity is inversely proportional to molecular mass (lighter = faster). A gas with double the mass moves at 1/√2 the speed.

Properties that DON'T affect fluid pressure at a point: container width/shape (only depth, density, and gravity matter for hydrostatic: P = ρgh). Properties that increase in a closed container when T rises: pressure (more wall collisions), kinetic energy.

Plasma Details

Gas heated so intensely that electrons are stripped from atoms → ionized gas of positive ions + free electrons. Conducts electricity. Responds to electromagnetic fields. Most common state in the universe (stars!). On Earth: lightning, neon signs, fluorescent lights, aurora borealis, fire (debated). A powered fluorescent light has: solid (glass, electrodes), plasma (ionized mercury vapor = light source) — but NOT liquid.

Near absolute zero, atoms can coalesce into a Bose-Einstein condensate — a fifth state of matter. Gases in a fluorescent tube with ionized mercury and krypton/xenon: if you breathe heavy noble gases like xenon or krypton your voice would get DEEPER (heavier gas = slower sound = lower resonant frequency; opposite of helium which makes voice higher).

Fluid States

The three fluid states of matter: gas, liquid, and plasma. (Fluids flow; solids don't.)

Special Properties of Water

Water is the ONLY common substance on Earth that naturally exists in all three common states (solid, liquid, gas). Maximum density at 4°C. Ice expands when freezing — water volume increases below 4°C. Hydrogen bonding gives water its unique properties: high specific heat, high surface tension, high heat of vaporization.

Solid Types (Exam Question!)

Which pairs of solid types and properties are correctly matched?

• Crystalline: ordered lattice, definite melting point (e.g., NaCl, diamond, ice, sugar, metals)
• Amorphous: random arrangement, range of melting temps (e.g., glass, rubber, plastic)
• Ionic (NaCl): high melting point, conducts when molten/dissolved, brittle
• Covalent network (diamond, quartz): very high melting point, hard, don't conduct
• Metallic: conducts electricity as solid (unlike ionic), malleable, ductile
• Molecular covalent: lower melting points, often soft (sucrose)

Fluid Mechanics Basics

Pascal's principle: pressure applied to enclosed fluid transmits equally throughout — basis of hydraulic lifts (multiplies force by using larger area piston). Bernoulli's principle: faster-moving fluid has lower pressure (explains how airplane wings generate lift, why soda cans blown between move TOWARD each other, not apart). Hydrostatic pressure P = ρgh; container WIDTH has no effect. Sound waves require a medium — cannot travel through vacuum (space is silent). Sound waves are longitudinal; light waves are transverse — only light can be polarized. Mass of sound: sound carries energy, NOT mass — mass is NOT a property of sound waves.

The Six Phase Changes

All phase changes are physical changes (chemical identity unchanged). All phase changes are reversible. Dry ice (CO₂) at atmospheric pressure: sublimes directly from solid to gas — this is sublimation. Snowflakes form by deposition (water vapor → ice directly). CO₂ depositing (gas to solid) IS a phase change.

Temperature Stays Constant During Phase Changes

This is the most tested fact. When a substance is MELTING (or any phase change): energy is absorbed but temperature does NOT rise — all energy goes into breaking intermolecular bonds. If you stick a thermometer into a melting frozen slurry (lemonade ice): the temperature reads constant (NOT rising) as long as ice remains. A perfectly insulated box with melting ice: the air temperature will get COOLER (ice absorbs heat from the air). After all ice melts, temperature can rise again.

Heating Curve

• Sloped segments: temperature rises within a state (kinetic energy increasing)
• Flat plateaus: phase change; T = constant; energy = breaking/forming bonds (potential energy)
• Water: 1st plateau at 0°C (melting/freezing); 2nd plateau at 100°C (boiling/condensing)

Latent Heat

Heat of fusion (Hᵣ) = energy to melt 1g of solid at its melting point. For water: Hᵣ = 334 J/g. The “change in enthalpy for ice to become water at 0°C.” Heat of vaporization (Hᵥ) = energy to vaporize 1g of liquid at boiling point. For water: Hᵥ = 2,260 J/g. Vaporization requires ~6.8× more energy than melting (because you completely separate particles).

Why sweating cools you: evaporation of sweat absorbs 2,260 J/g of heat from your skin. Why steam burns are worse than boiling water burns: steam releases that 2,260 J/g as it condenses.

Exothermic phase changes (release energy): water freezes, water condenses (also: precipitation). Endothermic phase changes (absorb energy): ice melts, water boils, sublimation.

Entropy

Entropy measures disorder/randomness in a system. Higher disorder = higher entropy. Gas has highest entropy; solid has lowest. Processes that increase entropy: melting, boiling, dissolving, expanding gases. Process that DECREASES entropy: precipitation (dissolving disorder → ordered solid lattice). Entropy of system decreases when a solid precipitates from solution.

Vapor Pressure & Boiling Point

Vapor pressure: pressure exerted by vapor above a liquid in a closed container. Increases with temperature. A liquid boils when its vapor pressure equals the surrounding atmospheric pressure. At higher altitude (lower atm. pressure) water boils at a LOWER temperature. Factors that do NOT affect vapor pressure: volume of container (vapor pressure depends only on T and the substance, NOT container volume). Adding solute LOWERS vapor pressure (Raoult's law) — colligative property.

At the critical point on a pressure-volume diagram, liquid and gas phases are no longer distinct. A triple point is where solid, liquid, and gas coexist.

Boiling vs. Evaporation

Bubbles in boiling water come from water vapor forming (liquid → gas). Evaporation occurs at ALL temperatures (even below boiling) — water molecules at the surface have enough energy to escape. Warm air holds more water vapor (higher T = higher saturation vapor pressure).

Melting Points Reference (for ordering questions)

Increasing melting/boiling point order: ammonia boils (−33°C) < water boils (100°C) < tin melts (232°C) < iron melts (1538°C) < tungsten melts (3422°C). Increasing melting points: oxygen (−219°C) < water (0°C) < iron (1538°C). Evaporation rate at room temp (fastest first): acetone > water > aluminum.

Summary Table

Boyle's Law

P and V are inversely proportional at constant T: if you double the pressure, volume halves. “Volume of a gas is inversely proportional to pressure” = Boyle's Law. Real-life: syringe, scuba diving (air in lungs compresses at depth), bicycle pump. Charles's Law is the one that assumes constant pressure for a temperature change (isobaric).

Charles's Law

V and T (Kelvin) are directly proportional at constant P: double the Kelvin temperature, volume doubles. Hot air balloon rises because heated air expands, becomes less dense, creates buoyancy. Balloon dipped in liquid nitrogen (very cold) → shrinks dramatically. “Most useful for determining change in volume with temperature change” = Charles's Law.

Gay-Lussac's Law

P and T (Kelvin) are directly proportional at constant V (rigid container). “Most useful for temperature changes in a fixed-volume container” = Gay-Lussac's. Car tires get warmer → pressure increases. Aerosol cans + fire = dangerous (Gay-Lussac). Isobaric process = constant pressure — uses Charles's Law.

Ideal Gas Law: PV = nRT

R = 0.0821 L·atm/(mol·K). At STP (0°C = 273 K, 1 atm): 1 mole ideal gas = 22.4 L. So 4 moles = 89.6 L. Ideal gas behavior is best approximated by: small, nonpolar molecules (H₂ is most ideal at room temp). Real gases deviate most from ideal at: high pressure, low temperature (molecules close together, intermolecular forces matter).

Dalton's Law

Total pressure in a gas mixture = sum of all partial pressures. Each gas in a mixture acts as if it's alone. Air: ~78% N₂, ~21% O₂, ~1% Ar — each has a partial pressure proportional to its mole fraction. Formula: Pₜₒₜₐˡ = P₁ + P₂ + P₃ + …

Graham's Law

Rate of effusion/diffusion ∝ 1/√M. Lighter gas = faster. “Lighter gases diffuse more quickly” = Graham's Law. H₂ (M=2) effuses 4× faster than O₂ (M=32): √(32/2) = 4. Helium balloon deflates faster than air-filled balloon. Gas velocity at given T inversely proportional to molecular mass. Effusion = gas under pressure escapes through a tiny hole (much smaller than mean free path).

Pressure Units

1 atm = 101,325 Pa = 760 mmHg = 14.7 psi (≈15 psi). The SI unit of pressure is the Pascal (Pa = N/m²). Other pressure units: atm, mmHg (torr), bar, psi. Ampere = electric current. Becquerel = radioactivity. Ohm = resistance. These are NOT pressure units.

Van der Waals / Intermolecular Forces

Nonpolar molecules (N₂, hydrocarbons) are liquefied by Van der Waals (London dispersion) forces — temporary dipole attractions. These are the weakest intermolecular forces. Strongest IMF hierarchy: hydrogen bonding (N-H, O-H, F-H) > dipole-dipole > Van der Waals/London dispersion. Hydrogen bonding explains water's high boiling point, surface tension, and unusual density behavior.

Brownian Motion

Brownian motion (pedesis): random motion of tiny particles suspended in a fluid, caused by constant random collisions from fast-moving fluid molecules. Named for Robert Brown (1827); explained by Einstein (1905). Most directly related to KMT (kinetic molecular theory). Colloids stay suspended partly because Brownian motion prevents settling.

Special Gas Situations

• Balloon at higher altitude: lower atmospheric pressure → balloon expands (Boyle's Law). Volume increases.
• Gas in rigid cylinder compressed: volume decreases, particles collide more often → pressure increases.
• Gas heated at constant volume: pressure increases and kinetic energy increases (Gay-Lussac). Temperature increases in a closed constant-volume container → pressure MUST increase.
• Isobaric process: constant pressure — described by Charles's Law (most useful for volume–temperature changes at constant P).
• O₂ + H₂ reaction: 1L O₂ + 2L H₂ → 2L H₂O gas (water vapor). Final:initial pressure ratio = 2:3 (3L total → 2L product at same T and P).
• Gas sample at 10L, 27°C (300K): at what T is it 5L? Charles: 5/T₂ = 10/300 → T₂ = 150 K = −123°C.
• Balloon P problem: 1L → 5L, T constant → Boyle: P₂ = 1×1/5... wait: P₁V₁ = P₂V₂ → if V multiplied by 5 at constant P₁=10 atm → P₂ = 10/5 = 2 atm.
• At STP (0°C, 1 atm): 1 mol ideal gas = 22.4 L. 4 mol = 89.6 L.