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Chemical Bonding - Lesson 1 - Derivation of the Ideal Gas Law

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Chemical Bonding - Lesson 1 - Derivation of the Ideal Gas Law Powered By Docstoc
					     Derivation of the                                  We have now identified the models of
                                                   how we look at atoms and molecules,
      Ideal Gas Law                                studied reactions they undergo and have
                                                   learned how energy is involved in these
                                                   processes. Now we will turn our study to
                                                   the different phases in which matter exists.
                                                       You will find that these units on
                                                   phases of matter and the kinetic-molecular
                                                   theory will be quite extensively tested in the
                                                   multiple-choice section of the national AP
                                                   exam; especially the unit on gases. Be
                                                   forewarned.
                       Get out AP equation sheet




     Characteristics of Gases
1. Non metallic compounds
                                                       Factors the Influence
2. Simple formulas w/ low M.W.                            Gas Behavior
3. A.k.a. Vapors for substances that are
    normally (s) or (l) at room temp.               •Temperature (T)
4. Expand to fill their container                      = The indirect measure of the
5. Highly compressible                                 average kinetic energy of a
6. Form homogeneous mixtures
                                                       collection of particles (on the
7. Relatively far apart (behave                        Kelvin scale, K)
    independent of other molecules)




•Volume (V)                                         •Pressure (P)
  = The total space of a container that
                                                       = The measure of the number of
  gases occupy due to the free random
  motion of the gas molecules                          collisions between gas particles
  (reported in liters, L)                              and a unit area of the walls of its
                                                       container (reported in KPa or
•Number of moles (n)                                   atm)
  = The total number of gas                               P=F/A    having the units (N/m2)
  molecules in a collection of
  particles. (reported in moles, mol)                        1N/m2 = 1 Pascal (Pa)




                                                                                                    1
                                                                                                     8
Pressure of air is measured                        Pressure
                                                   Pressure
  with a BAROMETER                             Column height measures
                                                Column height measures
                                                  pressure of the
                                                  pressure of the
                                                  atmosphere
                                                  atmosphere
                                               •• 1 standard atm
                                                  1 standard atm
                                                 = 760 mm Hg
                                                 = 760 mm Hg
                                                 = 760 torr
                                                 = 760 torr
 (developed by Torricelli in 1643)               = 29.92 inches Hg
                                                 = 29.92 inches Hg
                                                 = 14.70 psi
                                                 = 14.70 psi
Hg rises in tube until force
                                                 = about 34 feet of water
                                                 = about 34 feet of water
 of Hg (down) balances the
                                               •• SI unit is PASCAL, Pa,
                                                  SI unit is PASCAL, Pa,
 force of atmosphere
                                                 – where 1 atm = 101.325 kPa
                                                 – where 1 atm = 101.325 kPa
 (pushing up).




                           Aneroid Barometer   In order to measure the pressure
                                                 exerted by an enclosed gas, scientist
                                                 use a device called an manometer.
                                               Two types of manometers:
                                                 1. Open-end manometer- used for gas
                                                    pressures near 1 atm.
                                                 2. Closed-end manometer- used for
                                                    gas pressures greatly over or under
                                                    1 atm.




1.The pressure of a gas is                       The Classical Gas Laws
  measured at 49.0 torr in an
  open-end manometer. Describe
                                                 •Boyle’s Law
  this pressure in the units of
  atmospheres and describe the                        The volume of a
  mercury level in the manometer                 fixed quantity of gas at
  in respect to the pressure of the              constant temperature is
  gas and the atmosphere.                        inversely proportional           Robert Boyle
                                                 to the pressure               (1627-1691). Son of
                                                                                  Earl of Cork,
                                                                                    Ireland.




                                                                                                         2
           (L, atm)         •Boyle’s Law
                                   The volume of a        2. Baby George was given a 4.53 dm3
         V = 1/P            fixed quantity of gas at         helium filled metallic balloon on a
                            constant temperature is
         VP = k             inversely proportional to        bright, sunny day when the
                            the pressure                     barometric pressure was 768 torr.
       V1P1 = V2P2
                                                             That night a storm front moved in
                                  y=mx+b                     and the pressure dropped to 732 torr.
                                         1                   What is the expected volume of the
                             V = m          + b
                                         P                   balloon at these new barometric
                                           k                 conditions?
                             or       V =
                                           P




                                                                                                      (L, K)
  •Charles’ Law
                                                                                                    V = k’ T
       The volume of
                                                                                               V1/ T1 = V2/ T2
  a fixed amount of
  gas maintained at
  constant pressure is
  proportional to its         Jacques Charles (1746-
                               1823). Isolated boron       •Charles’ Law
  absolute                      and studied gases.
                                                                 The volume of a fixed amount of gas maintained at
  temperature.                      Balloonist.
                                                           constant pressure is proportional to its absolute temperature.




                                              He
                                                          3. Baby George received a larger 6.19
             Y=mx+b                                          dm3 helium filled metallic balloon
       5
             V=mT+b                                 CH4      on top of Pike's Peak at noon when
       4      V = k’ T                                       the temperature was 200C. That
                                                             night, the temperature dropped to -
V(L)




       3                                           H2O
                                                             100C. What volume did the balloon
       2                                           H2        occupy at that temperature?
       1                                           N2O

             -200     0           200
                          T(0C)




                                                                                                                            3
            Avogadro’s Law
• The volume of a gas at constant temperature
                                                       Avogadro’s
  and pressure is directly proportional to the
  number of moles of the gas.
                                                       Hypothesis
• Mathematically, this means   V = kn
                                                  At constant temperature and
                V1/ n1 = V2/ n2                     pressure, equal volumes of gases
                                                    contain equal number of particles
                                                  It was found that one mole of any
                                                    gas occupies a volume equal to
                                                    22.414 L at STP, or 0oC and 1 atm
                                                    (Avagadro’s law)




         Y=mx+b                                           Ideal-Gas Equation
         V=mn+b
          V = k’’ n                                • So far we’ve seen
                                                     that V ∝ 1/P (Boyle’s law)
V                                                          V ∝ T (Charles’s law)
                                                           V ∝ n (Avogadro’s law)
                                                   • Combining these, we
                                                     get              nT
                                                                      V∝
                                                                            P
                   n




          Ideal-Gas Equation                           “R” is the ideal gas constant
                                                  describing the volume of one mole of a gas
   The relationship            nT                 at 1 atm and 0oC
                       V∝                                                    L ⋅ atm
                               P                         R = 0 . 0821
                                                                            mol ⋅ K
   then becomes                nT
                       V=R                                                L ⋅ kPa
                               P                            = 8.314
                                                                         mol ⋅ K
    or
         PV = nRT                                                          L ⋅ torr
                                                            = 62.36
                                                                           mol ⋅ K
With the addition of a proportionality constant             = 8.314          J
(R).                                                                       mol • K




                                                                                               4
 4. A sample of hydrogen gas has            Relevance of the Ideal Gas Law
   a volume of 8.56 L at a                     The Ideal gas law provides a
   temperature of 0oC and a                constant set of conditions to which we
   pressure of 1.5 atm. Calculate          can compare any gas sample.
   the mass of hydrogen present                However, if any one variable is
   in the sample.                          held constant, the combined gas law
                                           can be utilized, where:

                                               P1V1/ n1T1 = P2V2/ n2T2




5. A sample of diborane gas (B2H6), a
   substance that burst into flame when
   exposed to air, has a pressure of 345
   torr at a temperature of –15.0oC and
   a volume of 3.48 L. If the conditions
   changed the temperature to 36.0oC
   and the pressure to 468 torr, what
   will be the volume?




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