Kinetic Molecular Theory of Gases - Download as PowerPoint by 7rDNI50


                    GASES                                     manometers
               Kinetic theory of gases
                                                        Units of pressure

                Behavior of gases

                                                            Partial pressure
                                                            of a gas
Pressure vs.      Pressure vs.      Temperature vs.
volume            temperature       volume

           Combined gas law                           Diffusion/effusion

               Ideal gas law
     Properties of Gases
• Very low density
• Low freezing points
• Low boiling points
• Can diffuse (rapidly and
  spontaneously spread out and mix)
• Flow
• Expand to fill container
• Compressible
 Kinetic Molecular Theory of
• Particles move non-stop, in straight lines.
• Particles have negligible volume (treat as
• Particles have no attractions to each other
  (no repulsions, either).
• Collisions between particles are “elastic”
  (no gain or loss of energy)
• Particles exert pressure on the container
  by colliding with the container walls.
           Kinetic Energy
• Energy due to motion
• KE = ½ mv2
• Temperature is a measure of average
  kinetic energy.
  – Temperature measures how quickly the
    particles are moving. (Heat IS NOT the
    same as temperature!)
  – If temperature increases, kinetic energy
• Which has greater kinetic energy: a 25
  g sample of water at 25oC or a 25 g
  sample of water at -15oC?
 Why use the Kelvin scale?
• In the Kelvin scale, there is an
  absolute correlation between
  temperature and kinetic energy.
  – As temperature in Kelvin increases,
    kinetic energy increases.
• Absolute zero: All molecular motion
  ceases. There is no kinetic energy.
  –0 K
 Kelvin-Celsius Conversions
• K = oC + 273.15

• oC = K – 273.15
 Kelvin-Celsius conversions
• The temperature of liquid nitrogen is
  -196oC. What is this temperature in
• Convert 872 Kelvin to Celsius
• Pressure = force/area
• Atmospheric pressure
  – Because air molecules collide with

• More collisions  greater pressure
        Pressure Units
• Atmosphere
• Pounds per square inch (psi)
• mm Hg
• Torr
• Pascal (Pa) or kilopascal (kPa)
1 atm = 14.7 psi = 760 mm Hg = 760
  torr = 101.3 kPa
• Torricelli-1643
• Air molecules collide
  with liquid mercury in
  open dish
• This holds the column
• Column height is an
  indirect measure of
  atmospheric pressure
    • Two types: open
      and closed
    • Use to measure the
      pressure exerted
      by a confined gas
      Chapter 15 Wrapup
• At the same temperature, smaller
  molecules (i.e., molecules with lower
  gfm) have faster average velocity.
• Energy flows from warmer objects to
  cooler objects.
• Plasma
  – High energy state consisting of cations
    and electrons
    • Found in sun, fluorescent lights
                  Boyle’s Law
• Pressure-volume
• For a sample of a
  gas at constant
  pressure and
  volume are
  inversely related.
• Equation form:
     P 1 V 1 = P2 V 2
        Charles’ Law
             • Volume-temperature
V1 V2
T1 T2
             • For a sample of a gas
               at constant pressure,
               volume and
               temperature are
               directly related.
             • Equation form:
                      V1 V2
                      T1 T2
        Guy-Lussac’s Law
• Pressure
• For a sample of a
  confined gas at
  constant volume,
  temperature and
  pressure are
  directly related.   P P2
                      T1 T2
       Combined Gas Law
• Sometimes, all three variables change
• This single equation takes care of the
  other three gas laws!

                P1V1 P2V2
                 T1   T2
    Dalton’s Law of Partial
• For a mixture of
  gases, the total      Ptot  P  P2  ...
  pressure exerted
  by the mixture is
  equal to the sum of
  the pressures
  exerted by the
  individual gases.
 Collecting a sample of gas
        “over water”
• Gas samples are
  collected by       Ptot  Pgas  PH 2O
  bubbling the gas
  through water
• If a question asks
  about something
  relating to a “dry      Ptot  Pgas  PH 2O
  gas”, Dalton’s Law
  must be used to      Table: Vapor Pressure of Water
  correct for the
  vapor pressure of
              Ideal Gas Law
• The number of
  moles of gas

                         PV  nRT
  affects pressure
  and volume, also!
  – n, number of moles
    •   nV
    •   nP
    •   P  1/V       Where R is the universal gas constant
    •   PT           R = 0.0821 L●atm/mol●K
    •   VT
     Ideal vs. Real Gases
• Ideal gas: completely obeys all
  statements of kinetic molecular
• Real gas: when one or more
  statements of KMT don’t apply
  – Real molecules do have volume, and
    there are attractions between molecules
     When to expect ideal
• Gases are most likely to exhibit ideal
  behavior at…
  – High temperatures
  – Low pressures
• Gases are most likely to exhibit real
  (i.e., non-ideal) behavior at…
  – Low temperatures
  – High pressures
    Diffusion and Effusion
• Diffusion
  – The gradual mixing of 2 gases due to
    random spontaneous motion
• Effusion
  – When molecules of a confined gas
    escape through a tiny opening in a
           Graham’s Law
• Thomas Graham (1805-1869)
• Do all gases diffuse at the same
    • Graham’s law discusses this quantitatively.
    • Technically, this law only applies to gases
      effusing into a vacuum or into each other.
               Graham’s Law
• Conceptual:
  – At the same temperature, molecules
    with a smaller gfm travel at a faster
    speed than molecules with a larger gfm.
     • As gfm , v 

• Consider H2 vs. Cl2
  Which would diffuse at the greater velocity?
          Graham’s Law
• The relative rates of diffusion of two
  gases vary inversely with the square
  roots of the gram formula masses.
• Mathematically:

               rate1     gfm2
               rate2     gfm1
   Graham’s Law Problem
• A helium atom travels an average
  1000. m/s at 250oC. How fast would
  an atom of radon travel at the same
• Solution:
  – Let rate1 = x   rate2 = 1000. m/s
  – Gfm1 = radon 222 g/mol
  – Gfm2 = helium = 4.00 g/mol
           Solution (cont.)
• Rearrange:
        x        gfm2
      rate2      gfm1

     x  rate2

• Substitute and evaluate:
                    m   4.00 g / mol
        x  1000.                     134 m / s
                    s   222g / mol
  Applications of Graham’s
• Separation of uranium isotopes
  – 235U
  – Simple, inexpensive technique
  – Used in Iraq in early 1990’s as part of
    nuclear weapons development program
• Identifying unknowns
  – Use relative rates to find gfm
            Problem 2
• An unknown gas effuses through an
  opening at a rate 3.16 times slower
  than that of helium gas. What is the
  gfm of this unknown gas?
• Let gfm2 = x rate2 = 1
      gfm1 = 4.00 rate1 = 3.16

• From Graham’s Law,
                rate1       gfm2
                rate      
                     2      gfm1

• Rearrange:        (rate1 ) 2
                                gfm1  gfm2
                    (rate2 )
         Solution, cont.
• Substitute and evaluate:

            (3.16 ) 2
                       4  39 .9 g / mol

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