GROUP EXERCISE NUMBER TWO                        CHM 1045 -- Dr. Light

The Mole

Only students working together in a group may submit solutions to the
group exercises.  Each group should get together, discuss, and agree on
how the solution to the exercise should be done.  A group solution is
then written out and submitted, with all members of the group who
participated signing the front cover page.

The solution should be worked out neatly (preferably printed or
typewritten--at least make it legible), should contain a cover page
with the group name and signatures, and all pages should be stapled
together.

The solution is due at the end of class on Wednesday, February 21.




                           MOLES FOR NOLES 
                                  or 
                     How big is a mole, anyway?   
                                  or
                   In touch with your ancestors.    

     Argon is a stable element that is gaseous and makes up 0.94%
of the  atmosphere.  All the atoms in the atmosphere today have
been there since  the early development of the atmosphere.  What is
the likelihood that you  will breathe one or more atoms that passed
through the lungs of Julius  Caesar, Alexander the Great, or some
other historic notable?   To approach such a question, we sometimes
carry out what are referred to  as "back of the envelope"
calculations--i.e. we are not looking for precise answers as much
as estimates, and often assumptions have to be built into the
process, with us later deciding how the answer would change if the 
assumptions changed.  Have a go at this one.  There is not really
a "right"  answer.  What is important is your thinking and approach
in how you go  about combining assumptions with known quantities. 

     A suggested way of addressing the question is as follows.  If
someone takes one breath of air, and sufficient time elapses for
all the molecules in that breath to disperse uniformly throughout
the earth`s atmosphere, then how many breaths would a second person
have to take in order to inhale  at least one atom of Ar?  

Following are some needed data and some hints:

     Assume the height of the atmosphere is 20 km (its higher, but
contains  very little gas above that height).  You can calculate
the volume as the  volume of a shell obtained by subtracting the
volume of the sphere  representing the earth from the volume of the
sphere representing the earth  plus its atmosphere.  You can also
estimate the volume by multiplying the  surface area of the earth
by the height of the atmosphere.  (What are the  problems
associated with each way of estimating the volume?) (Later on when we
study gases in Chapter 10, we can explain another way to calculate the
quantity of gas in the atmosphere).
  
     The radius of the earth is 6.37 x 10^3 km.  The volume of a
sphere is  4/3ăr^3, and the surface area of a sphere is 4ăr^2.
    
     At the surface of the earth there are about 0.044 moles of a
gas in a volume of one liter.  Assume one breath is a volume of
about 0.5 liters.  In considering the distribution of atoms and
molecules throughout the atmosphere, assume the average molecular
density of the atmosphere to be one-half that value or about 0.022
moles of gas in a volume of one liter.