Gas laws

• Ideal gas 


  gas that obeys the gas laws
• The three gas laws 


  Boyles law, Charles’ law, Pressure law
• Boyles law

  when temperature is constant, pressure is Inversely proportional to volume
• Charles‘ law

  When pressure is constant, Volume is directly proportional to temperature
• Pressure law

  When volume constant, Pressure is directly proportional to temperature
• Emperical


  From observations
• Work done = p∆V


  work done = pressure x change in volume
• Charles law eq


  V/T = k (constant)
• Pressure law equation 


  P/T = k (constant)
• derivation for Ideal gas equation

  1. pV/T = K
  2. pV/T = nR (K dependant on no. Moles; so number of moles x molar gas constant - 8.31)
  3. pV = nRT (rearranged)
  4. pV=NRT/Na (n= N/Na subbed into ideal gas equation)
  5. pV=NkT (sub Boltzman constant k=R/Na)
• Ideal gas equation 


  pV=nRT
• boltzman ideal gas eq

  pV=NkT
• What do the ideal gas graphs look like?

  graphs:

  
• Brownian motion 


  Random motion of larger particles in a fluid caused by collisions
• can use simple molecular model to explain gas laws
• Explain Boyles law

  P inversely proportional to volume at a constant temp. When Volume increases, molecules move further apart and collide less so pressure decreases.
• Explain Charles’ law

  Volume directly proportional to temperature at constant pressure. When temp increases, kinetic energy increases so speed increases, molecules move apart so volume increases.
• When pressure is constant, amount of collisions are constant
• Explain pressure law 


  Pressure directly proportional to temp at a constant volume. When temp increases, kinetic energy increases so collisions increase and at higher speeds, so pressure increases.
• Kinetic theory model is not emperical so is only based on theory
• Kinetic theory assumptions

  R - Random motion

  A - do not attract eachother ( no intermolecular forces)

  V - negligible volume

  E - Elastic collisions

  D - Duration of collisions negligible
• ideal gas follows gas laws perfectly, no intermolecular forces; no potential energy as PE is intermolecular; internal energy = the sum of kinetic energies
• pV = ⅓ Nm(Crms)²
• derive kinetic theory equation

  1. change in momentum 2mu
  2. time between collisions t = 2L/u
  3. Force (rate of change in momentum) F = 2mu/(2L/u) = mu^2/2L
  4. pressure = force/ area P=mu^2/Volume
  5. think about all particles p = m(u^2+ u2^2….)/Volume
  6. find mean of speeds and multiply by N for sum mesn speed. P=Nm(mean speed)^2
  7. think about all directions (as vectors x,y,z) speed is u in all directions. Mean speed same in all directions. mean speed squared (Crms)^2 same in all three directions. U^2 = ⅓ Crms^2 sub. pV=1/3Nm(Crms)^2
• Newton Straight raved

  1. Motion follows newton laws
  2. motion of collisions is straight lines
  3. RAVED assumptions
• Internal energy is the sum of the randomly distributed kinetic and potential energies of its molecules
• Ideal gas has no potential energy
• Internal energy for ideal gas Is equal to the kinetic energy
• boyles’ law is an isothermal change.
• If the temperature is hotter, the isotherm is further from origin of a P-V graph
• Experiment for boyles law: change the force sealed on gas syringe, calculate pressure exerted and subtract from atmospheric.
• Experiment for Charles’ law: measure height of trapped air bubble in capillary tube when temperature is changed. tube needs to be open at top to have constant pressure
• Pressure law experiment: change temp of gas in flask in water bath, pressure gauge used to measure pressurez
• N = n x Na
• If two out of three factors are being changed, use one of the 3 Gas laws.
• If all three factors are changing, p1v1/T1 = p2V2/T2
• If one factor staying constant then remove the factor that’s constant, eg it T constant, P1V1 = p2V2
• Kinetic theory only applies to ideal gasses
• Brownian motion can be seen with smoke particles being moved randomly due to colliding with air particles
• what does m stand for in kinetic theory equation?

  Mass Of one molecule ( as Nm = total mass of gas)