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STATES OF MATTER – TI-84 VERSION

Kinetic Molecular Theory (KMT)

  1. Gas particles move in constant, random, rapid motion.

  2. Collisions are elastic =- no loss of kinetic energy.

  3. No attractions or repulsions between ideal gas particles.

  4. Volume of particles negligible compared to container.

  5. Average KE depends only on temperature (Kelvin).

Formulas:

  • KE = 1/2 m v^2

  • KE avg = 3/2 n R T
    R = 0.0821 L atm mol^-1 K^-1 or 8.314 J mol^-1 K^-1

Gas Laws

  • Boyle: P1V1 = P2V2 (T constant)

  • Charles: V1/T1 = V2/T2 (P constant)

  • Gay Lussac: P1/T1 = P2/T2 (V constant)

  • Combined: P1V1/T1 = P2V2/T2

  • Ideal Gas: PV = nRT

  • Avogadro: V1/n1 = V2/n2

Gas Properties

  • Expansion: gases spread out to fill container.

  • Fluidity: gases flow =- considered fluids.

  • Density: very low compared to liquids or solids.

  • Compressibility: very high, easy to compress.

  • Diffusion: random mixing of gases.

  • Effusion: gas particles escape through tiny holes.

Graham’s Law: Rate1/Rate2 = (M2/M1)^(1/2)

Real vs Ideal Gases

  • Ideal: follows KMT perfectly.

  • Real: have volume and intermolecular forces.

  • Deviations happen at low temp and high pressure.

  • Close to ideal at high temp and low pressure.

Liquids

  • Particles in constant motion but closer together than gas.

  • Fluidity: yes, liquids flow.

  • Density: higher than gases, usually lower than solids.

  • Compressibility: very slight.

  • Diffusion: slower than gases, faster at higher T.

  • Surface tension: inward pull at surface.

  • Capillary action: rise in narrow tube (adhesion + cohesion).

Solids

  • Definite shape and volume.

  • Types: ionic, covalent network, metallic, molecular.

  • Amorphous = no regular structure (glass, plastic).

  • Least compressible, highest density, not fluid.

Phase Changes

  • Melting: solid to liquid

  • Freezing: liquid to solid

  • Vaporization: liquid to gas

  • Condensation: gas to liquid

  • Sublimation: solid to gas

  • Deposition: gas to solid

Energy formulas:

  • q = mCΔT (within a phase)

  • q = mΔHfus (melting/freezing)

  • q = mΔHvap (boiling/condensation)

Heating/Cooling Curve

  • Sloped lines = temp change, use q = mCΔT

  • Flat lines = phase change, use q = mΔH

  • Longer flat line = needs more energy.

Phase Diagrams

  • Triple point = all 3 phases coexist.

  • Critical point = end of liquid gas boundary.

  • Above critical temp = supercritical fluid.

Intermolecular Forces

  • London dispersion = weakest, all molecules.

  • Dipole dipole = polar molecules.

  • Hydrogen bonding = strongest, H bonded to N O or F.

  • Stronger IMF = higher boiling point, higher surface tension, lower vapor pressure.

Vapor Pressure and Boiling

  • Vapor pressure goes up as temperature goes up.

  • Boiling point = vapor pressure = external pressure.

  • Lower external pressure = lower boiling point.

Quick Facts to Memorize

  • Kelvin = Celsius + 273

  • 1 atm = 760 mmHg = 101.3 kPa

  • STP = 0 C = 273 K and 1 atm

  • 1 mole gas at STP = 22.4 L

Example Problems

  1. Boyle: P1 = 2 atm, V1 = 4 L, V2 = 2 L
    P2 = (P1V1)/V2 = (2*4)/2 = 4 atm

  2. KE particle: m = 3.3e-26 kg, v = 500 m/s
    KE = 1/2 mv^2 = 0.53.3e-26500^2 = 4.1e-21 J

  3. Graham’s Law: He vs O2
    Rate He/Rate O2 = (32/4)^(1/2) = (8)^(1/2) = 2.8