kinetic-molecular theory - explains behavior of gases

• gases made up of large number of molecules in constant, random motion
• gas molecules are extremely tiny
• attractive/repulsive forces between gas molecules don’t really do anything
• energy transferred between molecules during collisions, but average kinetic energy stays the same (elastic collisions)
  • individual molecules have different speeds
• average kinetic energy directly proportional to absolute temperature
  • constant temperature >> constant average kinetic energy
• rms speed (u) - speed of molecule w/ average kinetic energy
  • average kinetic energy = 1/2 mu2
  • u = (3RT/molar mass)1/2

effusion - escape of gas molecules through a tiny opening

• Graham’s law - compares rates of effusion under identical conditions
  • shows that lighter gas effuses more rapidly
  • r1/r2 = (M2/M1)1/2
• diffusion - spread of substance throughout a space or 2nd substance
  • molecular collisions >> motion of gas molecules constantly changes >> diffusion is slow
  • mean free path - average distance a molecule moves between collisions

behavior of real gases - different than behavior of ideal gases

• ideal gas equation assumes that gas molecules take up no space, have no intermolecular forces
• less deviation w/ higher temperature, lower pressure
• gas volumes usually slightly greater than predicted by ideal-gas equation
• gas pressure usually slightly lesser than predicted by ideal-gas equation

van der Waals equation - takes into account the gas volume and attractive forces

• (P + n2a/V2)(V - nb) = nRT
• constants a, b different for each gas

Find the pressure in atm that O2 exerts at 70.6° C if 1.850 moles occupies 16.5 L.  

• Given:
  • a = 1.36 (L2 atom/ mol2)
  • b = 0.0318 (L/mol)
  • R = 0.08206 (L-atm/mol-K)
  • (P + n2a/V2)(V - nb) = nRT
• (P + (1.850)2(1.36)/(16.5)2)(16.5 - (1.850)(0.0318)) = (1.850)(0.08206)(343.6)
• P = [(1.850)(0.08206)(343.6)] / [(16.5 - (1.850)(0.0318))] - (1.850)2(1.36)/(16.5)2
• P = 3.16 atm