EPS5 - Problem Set 6 (40 points)
Due March 31, 2010
1. Carbon cycle concepts (10 Points)
(a) Briefly explain the following terms. Limit your answers to two sentences. (1 point each)
I. Carbon reservoir
II. Carbon flux (as in “the carbon flux from the atmosphere to the ocean”)
III. Residence time
(b) What explains the CO2 oscillations in the timeseries data shown below (reproduced from Figures 11.1 and 11.2 in the book)? Why is the oscillation greater at Mauna Loa than at the South
Pole Observatory? (2 points)
(c) Explain what happens when the partial pressure of CO2 in the ocean does not equal the partial
pressure of CO2 in the atmosphere (i.e., what happens if pCO2 in the atmosphere is higher than in
the ocean?). (2 points)
(d) How do oceanic concentrations of the carbonate ion, [CO2−
3 ], influence the ability of the ocean
2−
to absorb atmospheric CO2 ? If [CO3 ] in the ocean increased, would the capacity of the ocean to
take up atmospheric CO2 increase or decrease? How would the pH of the ocean change? (3 points)
2. Carbon reservoir residence times (10 Points)
Use the carbon cycle diagram below (reproduced from Fig. 11.8 in the textbook) to answer the
following questions.
(a) Calculate the residence time of CO2 in the atmosphere, the terrestrial (biosphere + soil) system,
and the entire ocean (surface + intermediate + deep). (2 points each)
(b) Which is a more permanent reservoir for sequestering CO2 out of the atmosphere, the land
(biosphere + soil) or the entire ocean system? (2 points)
(c) The figure represents a hypothetical steady-state for pre-industrial times. Current fossil fuel
emissions of carbon (in the form of CO2 ) represent the extraction of carbon from the very large
sediments reservoir. The rate at which CO2 is emitted to the atmosphere is greater than the rate at
which it is removed from the atmosphere, leading to accumulation of atmospheric CO2 . Does the
1
EPS5 - Problem Set 6 (40 points)
Due March 31, 2010
The Capacity of the Ocean as a Sink for Industrial CO2
The rate for removal to sediments is equal to 0.23 ! 109 tons
C yr –1. The probability, P, that a carbon atom is incorporated in
sediment on a particular visit to the ocean is given by:
615 G tons
Atmosphere
62
731 G tons
Biosphere
62
147
P=
60
60
0.23 × 109 tons C yr−1
= 0.0038
60.23 × 109 tons C yr−1
■
62
1238 G tons
Soil
842 G tons
Surface ocean
52
9
9744 G tons
Intermediate ocean
162
Example 11.8: Estimate the average number of times a carbon
atom visits the ocean before it is incorporated in sediments.
Calculate the total time spent by a carbon atom in the ocean before it is incorporated in sediments.
205
26,280 G tons
Deep ocean
0.23
90,000,000 G tons
Sediments
43
Answer: On each visit, the probability that the atom should be
incorporated in sediments is equal to the value derived above,
0.0038. The number of visits required to build this probability
up to 1 equals (0.0038)–1 = 263. The total time, T, spent by a
carbon atom in the ocean pending capture by sediments is obtained by multiplying the time per visit by the number of visits:
T = 611.9 yr × 263 = 160,930 yrs.
■
The time the atom spends in the ocean, 160,930 yrs, may be
compared with its integrated life in the combined atmosphereocean-biosphere-soil system: 171,087 yrs. It is clear that the avFigure 11.8 Composite model for the global carbon cycle,
erage carbon atom spends most of its life in the ocean. It flits back
combining data in Figures 11.5 and 11.6. Reservoir contents are
process of9 fossil fuel emission increase9 or decrease
theand
atmospheric
CO2 residence
time, assuming
–1
forth between the
ocean and atmosphere many times, with
in units of 10 tons C; transfer rates are in 10 tons C yr .
the rate
of carbon
removal
from
the atmosphere
remains
constant?
(2 visits
points)
brief
but frequent
to the terrestrial biosphere and soils. The
Carbon
is deposited
in sediment
both
as CaCO
3 and as organic
carbon atoms that constitute our flesh, bones, and blood, had
matter. There is a small release of CO2 in steady state from the
an earlier history in the atmosphere, biosphere, and ocean; we
ocean; this source is employed in weathering of crustal rocks.
3. Impacts of population increase on atmospheric
are in a realcarbon
sense part(10
of thePoints)
stuff of Earth.
The residence time of a carbon atom in the combined atThe current global population is about 6.7 billion people. A recent report by the United Nations
mosphere-ocean-biosphere-soil system is comparatively brief.
The
rate at which
is withdrawn
to sediments
is equalcould
to
estimated
thatcarbon
by 2100,
the global
population
beSince
as high
asexisted
14 billion
people
(World
Popu-years, it may
life has
on Earth
for close
to 4 billion
0.23
× 109in
tons
yr–1. The
residence
time, !,2004).
is givenHumans
therefore by
lation
2300,
United
Nations,
contribute
to
the
global
carbon
cycle
by
ingesting
be concluded that the sedimentary reservoir itself must be tran9
carbon as39,
food
Assume
for this time
problem
that each
person
The residence
for a carbon
atom in
the sediment, es350and
× 10releasing
tons C CO2 through exhalation.sitory.
!=
■
−1 = 171,087 yrs
9
timated
in
the
same
fashion
as
for
other
reservoirs
eats on average
of Cfood
0.23 × 101 kg
tons
yr per day, that 50% of that food is in the form of carbon, and that 100% above, is
of the carbon ingested as food is eventually released asabout
CO2390
. million years. The typical carbon atom, then, has cycled more than 10 times through the sedimentary compartment
(a) Calculate the mass of carbon currently consumed over
by humans
over
the course
year. (2
the course
of geologic
time. of
It isone
the motion
of the crustal
Example 11.6: Estimate the residence time for carbon in the ocean.
plates—the
internal
dynamics
of
Earth—that
provides
a solupoints)
tion
to
the
dilemma.
Sediments
are
transported
by
the
crustal
Answer: The carbon content of the ocean equals to 36,866 !
(b)
Calculate
the
estimated
mass
of
carbon
that
will
be
consumed
by
humans
over
the
course
of
9
plates;
over
the
course
of
time
they
are
either
uplifted
(returned
10 tons C. Carbon atoms leave the ocean, transferring to either
one
year in or2100.
(2 points)
to the surface) or subducted (withdrawn to the mantle). In the
the
atmosphere
sediments.
The combined loss rate is given by
9
9
–1
9
–1
latter case, they are cooked and carbon is vented to the atmos[(60 ! 10 ) + (0.23 ! 10 )] tons C yr = 60.23 ! 10 tons C yr .
(c) If the current mass of carbon in the atmosphere is 615
Gtons, as shown in the figure in Problem
phere as a component of volcanoes and hot springs. In the forThe residence time, !, is given by
1, what will be the percent increase in atmospheric carbon
due toisthe
increased
consumption
mer, carbon
exposed
to the food
weather,
where it can be eroded
36,the
866increased
× 109 C population? (2 points)
associated
with
and
returned
to
the
more
mobile
environments
of the atmos=
!=
■
612
yrs
60.23 × 109 tons C yr−1
phere, biosphere, and ocean. Without this overturning of the
(d) What are the possible fates for this extra carbon? (2 points)
crust, life might cease to exist on earth—all of the carbon in
surface reservoirs
tied up in the
(e) Should we be concerned about the increase in atmospheric
carbonwould
due tobeincreased
COcrust.
2 exhaExample
the probability
a carbon
atom inabout the impact of increased population on the
lation?11.7:
AreEstimate
there other
reasonsthat
to be
concerned
the ocean will be removed to sediments rather than released
carbon cycle? (2 points)
11.2 The Capacity of the Ocean as a Sink
into the atmosphere.
for Industrial CO2
Answer: The probability is determined by the relative magnitudes of
2
The preceding section sought to present a view of the carbon
the fluxes to the relevant reservoirs. The total removal rate is given
cycle in a steady state; sources and sinks were purposely balby the sum of the separate contributions, 60.23 ! 10 9 tons C yr –1.
anced for the individual reservoirs included in Figures 11.5,
EPS5 - Problem Set 6 (40 points)
Due March 31, 2010
4. Acidity of rainwater (10 Points)
In this problem, you will calculate the pH of rainwater in equilibrium with atmospheric CO2 ,
assuming there are no other significant dissolved gases or solutes, at an atmospheric pressure of 1
atm and a temperature of 10◦ C. The dissociation constants from the Table 11.2 in the textbook are
reproduced below:
α 4.42·10−2 mol L−1 atm−1
K1 7.93·10−7 mol L−1
K2 4.67·10−10 mol L−1
(a) Calculate the concentration of aqueous phase CO2 in the rainwater, assuming it is in equilibrium
with present-day atmospheric CO2 concentrations of approximately 390 ppm. (3 points)
(b) Calculate the associated concentration of [H+ ] ions. You can assume that [CO2−
3 ] is negligible
−
−
+
compared to [HCO3 ] such that [H ] ≈ [HCO3 ]. (3 points)
(c) What is the pH associated with this concentration of [H+ ] ions? (1 point)
(d) What approximate concentration of [HCO−
3 ] does this correspond to? (1 point)
(e) What is the associated concentration of [CO2−
3 ] in the rainwater? Is our assumption in part (b)
reasonable? (2 points)
3