Gases; Ideal gas Law

• Pressure and Weather

  • high-pressure area (anticyclone) --> greater pressure
• Characteristics of Gases

  • not touching other molecules --> huge distance
  • fills the shape and size of their containers
  • most compressible state of matter
  • 2 gases mix evenly in the same container
  • lower density --> b/c of distance
• Gas Pressure

  • collisions on surfaces = pressure
  • pressure = Force/Area
• Barometer

  • measures atmospheric pressure
  • pressure = density * gravity * height
  • mercury is used --> denser
  • mercury is smaller in height
• Pressure at Higher Altitudes

  • pressure drops exponentially with altitude
  • surface = 1 atm
  • 5km = 0.5 atm
  • pressure (atm) decreases with altitude increase
• Manometer

  • measure pressure of gas --> use to find how much made
  • uses height of a liquid needed to counterbalance the pressure in the container
  • closed-tube
  • open-tube
• open-tube

  pressure of gas = pressure of atmosphere + pressure of mercury
• Pgas > Patm

  gas pushes up J

  Pgas = Patm + PHg
• Pgas = Patm

  • U
  • closed-tube
• Pgas < Patm

  • atm pushed down tube
  • Pgas = atm - PHg
• Boyle's Law

  • pressure increase, volume decreases
  • pressure decreases, volume increases
  • pressure is inversely proportional to volume
  • P(h) proportional to 1/V
  • P1V1 = P2V2
• pressure is the result of just hitting walls

  • Boyle's law: as volume decreases number of collisions increases with pressure
• Charle's Law

  • as volume increases temperature increases too
  • volume is proportional to temperature
  • linear correlation
  • low temperature = less kinetic energy = less collisions
  • high temp = more kinetic energy = more collisions
  • v = (constant) x T
  • V1/T1 = V2/T2
  • pressure is constant when gas occupies larger volume = collisions less frequent
• Avogadro's Law

  • number of moles (n) is proportional to volume
  • v = constant x n
  • v1/n1 = v2/n2
  • nature of the gas doesn't matter
• Ideal Gas Law

  • P is proportional to (nT)/V
  • PV =nRT
  • Density, d (g/L): d = m/v , d = (nM)/V = (PM)/RT
  • Moles, n: n = m/M (g/mol)
  • M = (dRT)/p
  • gas does better at high temp low pressure
• R is the gas constant

  • R for gases: (Latm)/molK
  • R for energy: J/(molK)
• Standard Conditions

  • Standard Temperature and Pressure (STP)
  • permit inter-comparison of measurements
  • standard pressure = 1 atm
  • standard temperature = 273.15 K
  • standard amount = 1 mol
• Standard molar volume

  • volume occupied by one mole of a substance at STP
  • v = (nRT/P)
  • v = 22.41 L
• SATP

  • standard ambient temperature
  • temperature: 298.15K
  • molar volume: 24.47 L
  • pressure = 1 atm
• Dalton's Law of Partial Pressures

  • V and T are constant
  • combining pressures: Pt = P1 + P2
• Partial Pressures and Mole Fraction

  • partial pressure: P1 = (n1RT)/V
  • mole fraction: X1 = (ni)/(nT)
  • partial pressure: Pi = XiPt
• Planetary atmospheres

  • Fractions (x): % = x * 100
  • parts per million by volume (ppmv): ppmv = x * 10^6
• Collecting a gas over water

  • start: Chemical reaction creates gas O2 pushes down water
  • partial pressure
  • collect O2 gas
  • total pressure = when volumes are equal
• Distribution of speed in a gas

  • N2 increase temp increases average speed increases
  • heavier = narrower\
• Kinetic Molecular Theory of Gases

  • gas is a collection of particles in constant motion
  • size of the particle is negligible (has mass not volume)
  • average kinetic energy of a particle is proportional to temperature in Kelvin
  • collision of one particle with another is (conserved) elastic (no loss of kinetic energy)
• KMT and the Ideal Gas Law

  • momentum p = m * velocity
  • F= m*a
  • Pressure = F/Area
  • Density = #/V
  • Ke = 1/2 m*v^2
• Temperature and Molecular Speeds

  • temperature is a measure of average kinetic energy of particles
  • avg Ke (g) = 3/2 RT
  • any temp: gases have same average Ke
  • lighter gas --> move faster, higher velocity/temp
  • heavier gas --> move slow, lower velocity/temp
• Mean Free Path

  • molecules in a gas travel in straight lines before they collide with another molecule or something
  • average distance molecules take before collision
  • MFP inversely proportional to pressure
• Ideal gas behavior

  • not attractions b/w gas
  • gas molecules do not take up space
  • P is proportional to Ke proportional T
• gas diffusion

  • gradual mixing of molecules of one gas with molecules of another gas
  • through kinetic properties
  • mixing of gases in and out
• gas effusion

  • process where gas moves from one compartment into another compartment
  • passing through small opening releasing one gas to mix to surroundings
  • opening size < MFP of the gas
• Deviations from Ideal Behavior

  • at STP, gases are described by ideal gas approximations
  • no attractions or repulsions between gas molecules
  • gas molecules do not take up space
  • at low temps and high pressure the assumptions don't work
  • gases can turn to liquids if cooled or compressed
  • high pressure = high volume
  • low temperature = low pressure