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13.2 Using Gas Laws to Solve Problems

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					13.2 Using Gas Laws to Solve
          Problems


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                                 http://www.phy.cuhk.edu.hk/contextual/heat/tep/trans/kinetic_theory.gif
              Today…
We are going to learn about:
    the ideal gas law
    partial pressure
    molar volume




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              The Ideal Gas Law
• Boyle’s Law   V = k (at constant T and n)
                    P
• Charles’s Law V = bT (at constant P and n)
• Avogadro’s Law V = an (at constant T and P)

    We can combine these equations to get
        The Ideal Gas Law




R = the universal gas constant= 0.08206 L atm
                                        mol K


Rearrange to get the Ideal Gas Law:
          PV = nRT
                PV = nRT

The ideal gas law involves all the important
 characteristics of a gas:
     P - Pressure (in atm)
     V - Volume (in L)
     n - number of moles
     T - Temperature (in K)



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              PV = nRT
Knowing any three of these properties is
                           describe the
 enough to completely an d a
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                the gas.
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The fourth property can be derived.
    Setbacks to Ideal Gas Law
A gas that obeys this equation is said to
  behave ideally.
However, in actuality, no gas is truly ideal.
Ideal Gas- A hypothetical gas that exactly
  obeys the ideal gas law.
Why do we use it?
  Most gases closely obey the ideal gas law at
  pressures of approximately 1 atm or lower,
  when the temperature is approximately 0oC
  or higher.

                   http://chemistry.boisestate.edu/people/richardbanks/inorganic/chemistry/gas_animation.gif
      Using the Ideal Gas Law
A sample of hydrogen gas, H2, has a volume of
  8.56 L at a temperature of 0oC and a pressure
  of 1.5 atm. Calculate the number of moles of
  H2 present in this gas sample.
     Using the Ideal Gas Law
A 2.50 mol sample of nitrogen gas has a
  volume of 5.50 L at a temperature of 27oC.
  Calculate the pressure of the nitrogen gas.
     Using the Ideal Gas Law
What volume is occupied by 0.250 mol of
 carbon dioxide gas a 25oC and 371 torr?
Ideal Gas and Changing Conditions
Suppose we have a 0.240-mol sample of ammonia gas
  at 25oC with a volume of 3.5 L at a pressure of 1.68
  atm. The gas is compressed to a volume of 1.35 L at
  25oC. Find the final pressure.
Ideal Gas and Changing Conditions
A sample of methane gas that has a volume of 3.8 L at
  5oC is heated to 86oC at constant pressure. Calculate
  its new volume.
     Using the Ideal Gas Law
The idea behind these exercises is to use the
 ideal gas law for all types of gas law
 problems.
We don’t have to ask, “Is this a Boyle’s Law
 problem or a Charles’s Law problem?”




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Dalton’s Law of Partial Pressures
 We just learned about the different
  properties of gases: pressure, volume,
  moles and temperature.
 But we’ve only been concerned about
  non-mixtures of gases.
 What happens if we mix different gases
  together?



                    http://www.nhn.ou.edu/~jeffery/course/c_energy/energyl/lec004/gas_001_kinetics.gif
Dalton’s Law of Partial Pressures
 Many important gases contain a mixture
   of components.
 Air = 78% N2, 21% O2, 0.93% Ar…
 Gaseous mixtures show that each
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   component behaves this p icture .
   the others.
 In other words, a given amount of oxygen
   exerts the same pressure in a 1.0-L
   container whether it is alone or in the
   presence of nitrogen or a different gas.

                       http://www.chemistryland.com/CHM107/AirWeBreathe/Comp/AirAtomsMolecules.jpg
  Dalton’s Law of Partial Pressures
For a mixture of gases in a container, the total pressure
  exerted is the sum of the partial pressures of the
  gases present.
      Ptotal = P1 + P2 + P3…

The partial pressure of a gas is the pressure that a gas
  would exert if it were alone in the container.
Each gas is responsible for only a part of the pressure.
Dalton’s Law of Partial Pressures
 Same container =
  same volume and temperature

 P1=n1RT/V    P2=n2RT/V                                P3=n3RT/V

 Ptotal = n1RT/V + n2RT/V…
        = (n1 + n2 …) (RT/V)
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        = ntotal (RT/V)


                                         https://reich-chemistry.wikispaces.com/file/view/P3.JPG/34106723/P3.JPG
     Practice with Partial Pressure
Mixtures of helium and oxygen are used in the “air”
  tanks of underwater divers for deep dives. For a
  particular dive, 12 L of O2 at 25oC and 1.0 atm and 46
  L of He at 25oC and 1.0 atm were pumped into a 5.0-L
  tank. Calculate the partial pressure of each gas and
  the total pressure in the tank at 25oC.
   Practice with Partial Pressure
A 2.0-L flask contains a mixture of nitrogen gas and
  oxygen gas at 25oC. The total pressure of the
  gaseous mixture is 0.91 atm, and the mixture is
  known to contain 0.050 mol of N2. Calculate the
  partial pressure of oxygen and the moles of
  oxygen present.
          Gas Stoichiometry
So far, we have seen how useful the ideal
   gas equation is.
It is useful for finding the number of moles of
   gas involved.
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This fact makes it possible to do
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   stoichiometric calculations for reactions
   involving gas.




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                  Practice
Calculate the volume of oxygen gas produced at 1.00
 atm and 25oC by the complete decomposition of 10.5
 g of potassium chlorate. The balanced equation for
 the reaction is:
            2KClO3  2KCl + 3O2
               Molar Volume
It is useful to define the volume occupied by 1 mol
    of a gas under certain conditions.
    1 mol of an ideal gas at 0oC (273 K) and 1 atm,
    has a volume of 22.4aL.
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Standard Temperature and Pressure (STP): 0oC
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    and 1 atm
Molar Volume of an ideal gas is 22.4 L at STP.
        22.4 L contains 1 mol of an ideal gas at STP.



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                 STP
A sample of nitrogen gas has a volume of
  1.75 L at STP. How many moles of N2
  are present?

				
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