Download homework assignment - Global Change Program

HOMEWORK ASSIGNMENT – The Importance of Tropical Rainforests
In lecture today, George assigned the following homework problem that is due on Friday
December 10th. Your assignment is to examine the following 2 statements using your
knowledge of ecosystems and biogeochemistry, and to come to some conclusions about the
validity of these statements:
(1) Tropical forests produce a lot of oxygen through photosynthesis, and if we cut down all
of the tropical forests, we would lose that oxygen production and we (as oxygen consuming
organisms) would be in trouble.
(2) If we burn all the tropical forests, we not only lose the oxygen that they produce each
year, but we would consume lots of oxygen from the atmosphere in the burning process and
then we would really be in trouble.
You will want to use the following concepts and relationships to help you:
A. Mass Balance:
Net change = INPUTS + OUTPUTS + Internal Change
This mass balance equation can be used to ask several questions. For example, if you were
interested in the effect of photosynthesis on the net change of oxygen in the atmosphere, then
the equation would be written as follows:
Net change =
Photosynthesis (the INPUT of O2 to the atm) + Outputs (in this case none) + Internal
change (in this case none)
If you were interested in the effects of burning on the net change of oxygen in the
atmosphere, then you would include the amount of burning into the equation as an OUTPUT,
because burning consumes and thus removes oxygen from the atmosphere. Again, in all of
these problems you should assume that the internal change in the atmosphere is zero.
(Remember that the concept of mass balance can be used without a specific equation – for
example in the “Michigan Theatre made 1 million dollars last night” case discussed in class.)
Residence time:
RT = (total amount) / (input or output rate)
Note that to calculate the residence time the system must be at "steady state", as discussed in
class. In addition, either the input or output of materials can be used in the denominator to
calculate residence time. For our current atmosphere, consider that we are at steady state
with respect to oxygen. Remember to interpret the residence time in light of the question
“what would it take to disturb or change this system?”
B. Equation of Photosynthesis and Respiration:
CO2 + H2O  CH2O + O2
The process that causes the forward reaction (left to right), which produces oxygen, is
photosynthesis and the processes that cause the reverse reaction, which consumes oxygen, are
respiration as well as burning.
Because all chemical reactions can be written in terms of the "number of atoms" that
participate in the reaction (the term often used by chemists is that a "number of moles" of one
compound react with a "number of moles" of another compound; a "mole" is equal to 6.022 x
1023 atoms). In the above reaction we see that in burning or respiration, one mole of O2 (or
two moles of O) reacts with a CH2O compound to produce one mole of CO2 (or one mole of
C). Because the assigned problem deals with the "weight" of oxygen and carbon in grams,
we need to convert from moles to grams. This is done using the atomic weight of the
substance, where a mole of C weighs 12 grams, and a mole of O weighs 16 grams (12 and 16
are the atomic weights of C and O, respectively – thus O2 would weigh 32 grams per mole).
Because C and O do not weigh the same amount, and you must find out given the above
reaction how much O is used in burning a certain amount of C, you must be able to convert
between the two using the following relationships:
(12 g/mol of C) / (32 g/mol of O2) = 0.375 g C / g O2 (read “g of Carbon per g of Oxygen”)
- or (32 g/mol of O2) / (12 g/mol of C) = 2.667 g O2 / g C
Numbers you will need to make the calculations to answer the question:
* Total mass of oxygen in the atmosphere = 1.19 x 1021 g O2
* Total "net" ecosystem production from global land photosynthesis = 1.06 x 1015 g O2/yr
(tropical forests are ~22% of this global total).
* Amount of C in all tropical forests = 206 x 1015 g C
* Amount of C in all land biomass = 560 x 1015 g C
That's it and good luck! Be sure to check that the "units" in your equations cancel properly,
or your answer will almost certainly be wrong.
Your answers should contain all of your work including the equations and the math, as well
as a brief description of what you did and what you found (e.g., “I calculated the residence
time by dividing the output rate from the atmosphere by the total stock in the atmosphere as
follows…”).