Ideal gases

• • 1 mole of a substance contains 6.02 x 10^23 particles (atoms or molecules) and will have a mass equivalent to its molar mass in grams
• • The amount of a substance indicates the number of elementary entities (normally atoms or molecules) within a given sample of substance
• Mole --> the amount of substance that contains as many elementary entities as there are atoms in 0.012kg (12g) of carbon -12
• N = n x NA
• Kinetic theory of matter --> used to describe the behaviour of the atoms or molecules in an ideal gas
• The assumptions made in kinetic model for an ideal gas:

  • The gas contains a very large number of atoms or molecules moving in random directions with random speeds
  • The atoms or molecules of the gas occupy a negligible volume compared with the volume of gas
  • The collisions of atoms or molecules with each other & the container walls are perfectly elastic (no KE lost)
  • The time of collisions between the atoms or molecules is negligible compared to the time between collisions
  • Electrostatic forces between atoms or molecules are negligible expect during collisions
• • Atoms or molecules in a gas are always moving
  • When they collide with the walls of a container, it exerts a force on the particles, changing their momentum as they bounce off the wall
• • When a single atom collides with the container wall elastically, its speed doesn't change, but its velocity changes from +ums^-1 to -ums^-1
  • The total change in momentum is -2mu
  • F atom = the change in momentum / change in time taken where the change in momentum is -2mu and the change in time is the time between collisions with the wall.
  • The atoms also exerts an equal but opposite force on the wall --> Newton's 3rd law
• Pressure & volume:

  • If the temperature & mass of gas remain constant then the pressure p of an ideal gas is inversely proportional to its volume V
  • P is inversely proportional to v
  • PV = constant
• Pressure & temperature:

  • If the volume and mass of gas remain constant, the pressure p of an ideal gas is directly proportional to its absolute temperature T in kelvin
  • P is directly proportional to T
  • P/T = constant
• P1V1/T1 = P2V2/T2
• Equation of state of an ideal gas:

  • pV = nRT
• Root mean square speed:

  • The velocity ,c, of each atom or molecule in the gas is squared
  • The average of this squared velocity is found for all the gas particles
  • The square root of this value is taken to give the r.m.s speed / Crms
• • pV = 1/3Nmc^2
  • N = number of particles
  • m = mass of each particle
  • c^2 = mean square speed
• Maxwell - Boltzmann distribution:

  • Changing the temperature of the gas changes the distribution
  • The hotter the gas becomes, the greater the range of speeds
  • The most common speed & the r.m.s speed increases, and the distribution becomes more spread out
• Boltzmann constant:

  • Used to relate the mean kinetic energy of atoms or molecules in gas to the gas temperature
  • k = R/Na = 1.38 x 10^-23 JK^-1
  • pV = NKT
• Mean kinetic energy & temperature:

  • 1/3Nmc^2 = NkT
  • 1/3mc^2 = kT
  • 2/3(1/2mc^2) = kT
  • 1/2mc^2 = 3/2kT
  • Ek is directly proportional to T
• • At given temperatures the atoms or molecules on different gases have the same average kinetic energy
  • However as the particles have different masses their rms speeds will be different
• • Internal energy of a gas is the sum of the kinetic and potential energies of the particles inside the gas
  • No electrical potential energy in an ideal gas
  • All internal energy is in the form of kientic energy of the particles
• Boyle's Law:

  • Discovered the relationship p is inversely proportional to volume
  • If the pressure of a pressurised gas is slowly reduced, its volume increases
  • The gas must be in a sealed tube to ensure the amount of gas inside the tube remains fixed