Much of the chemisry of natural waters is actually determined
by the dissolution of atmospheric gases, especially CO2
and O2, but as we have already seen, NOx and SOx also have
great consequences on natural water systems. Let's start with
carbon dioxide as an example.
What Conditions Favor CO2 Transfer
From the Atmosphere to the Ocean?
Chemists often need to know whether a reaction is spontaneous
by a quantitative measure. They do this by developing an expression
called the equilibrium constant. A reaction is at equilibrium
when the ratio of the products and reactants is constant with
time. Though it can appear that the reaction between reactants
has ceased at equilibrium, the product and reactant molecules
continue to react. At equilibrium, the rate of formation of
the products is equal to the rate of formation of reactants.
Thus, we write the reaction with a double-headed arrow to indicate
that forward and reverse reactions are simultaneously occurring
at equal rates. In this exploration, you will learn about the
relation between Gibbs energy and the equilibrium constant.
This relation, which is one of the most important applications
of Gibbs energy, will allow you to quantitatively predict how
many moles of products and reactants exist in a system at equilibrium.
Background
In this exploration, you will study the hydration of carbon
dioxide:
CO2(g) <=> CO2(aq)
Using the calculated Gibbs energy one can predict the concentration
of gaseous CO2 that dissolves in water
at equilibrium with the gas phase. A more negative Gibbs energy
indicates greater CO2 solubility in water.
A more positive Gibbs energy indicates lower CO2
solubility in water. The ratio of the amount of product (CO2(aq)) to the amount reactant (CO2(g))
is called the reaction quotient (Q). All gas concentrations
are expressed as pressures (in atmosphere) and all aqueous solutes
are expressed in molar concentration (M). If the system is at
equilibrium, then the ratio Q equals K, where K is called the
equilibrium constant. Though Q and K are identical in form,
they have the same numerical value only when the system is at
equilibrium. It is understood that all concentrations and pressures
in the reaction quotient and the equilibrium constant are actually
ratios of the actual pressure or concentration to the standard
pressure (1 atm.) or the standard concentration (1 M). Thus,
the equilibrium constant has no units associated with it.
Q = [CO2(aq)] / PCO2
K = [CO2(aq)]eq / PCO2 eq
The subscript "eq" represents the concentration
or pressure of each molecule at equilibrium.
We determine the spontaneous direction of the reaction by
comparing the ratio of Q/K.
Q > K: reaction goes spontaneously to the left (forms more
reactants)
Q < K: reaction goes spontaneously to the right (forms
more products)
Q = K: reaction is at equilibrium
To reiterate, a constant ratio of products and reactants does
not mean that molecules are not reacting. Rather, it means the
rate of the forward and reverse reactions are equal. The concept
of a forward and reverse reaction occurring at equal rates is
called dynamic equilibrium. Molecules constantly react, but
the concentration ratios do not change. If the ratio (Q) is
not constant over time, the mixture is not at equilibrium. At
equilibrium, the specific CO2 molecules in the gas and liquid
phase are always changing, but the ratio (K) of the concentration
of aqueous CO2 and pressure of gaseous CO2 remains constant.
The thermodynamic variable that relates to the reaction quotient
(Q) is the Gibbs energy (DG). Negative DG values indicate the
reaction is spontaneous in the forward direction; positive DG
values indicate the reaction is spontaneous in the reverse direction.
It is easy to confuse thermodynamic variables as they are subtly
differentiated by superscripts and subscripts. Thus, you must
make sure you do not mistake DG (Gibbs energy) for DG (standard
Gibbs energy). The relation between the two is:
DG = DG
+ RT ln Q
Since the standard state conditions are at one atmosphere
pressure and one molar concentration, Q must equal one at standard
conditions. Thus, if all reactants and products are at their
standard states, DG = DGo.
DG = DG
+ RT ln 1 = DG
Similarly, if (and only if) the system is at equilibrium,
then Q equals K and DG = 0. Thus,
DG = DGo
+ RT ln Q
0 = DGo + RT ln K
DGo = - RT ln K
which is a completely general result.
In conclusion, the following relations always hold:
DG = - RT ln K
DG = DGo
+ RT ln Q
The following hold only when the system is at standard state:
DG = DGo
Q = 1
The following hold only when the system is at equilibrium:
DG = 0
Q = K
Gathering Information
Your instructor may decide to demonstrate the properties of
pop (soda) under different conditions. If not, base your answers
and discussion on your real world experience.
What happens when you open up a bottle of pop (soda)?
What happens when you heat an open can of pop (soda)?
How do these observations relate to Gibbs energy?
Working with Information
1. Write the equilibrium constant expression for the
hydration of CO2 using pressure and concentration
units as appropriate.
2. Different groups should calculate DG
and then the equilibrium constant at one of the following temperatures:
1C, 15C, 25C or 30C using the appropriate values in the appendices.
Your instructor will assign a temperature.
T (C) DG K
1
15
25
30
3. Compare your group values with those of other groups
at different temperatures.
Making the Link
1. Do the values of the equilibrium constants as a function
of temperature make sense based upon every day experience? Think
back to the demonstration.
2. If global warming is real, the Earth's mean temperature
could increase by 3- 5C. What does this imply about the levels
of CO2 in the atmosphere versus the oceans.
Would you consider this a negative or positive feedback for
global warming?
3. Set up systems models for the CO2
hydration equilibrium.
4. Determine which aspects of your model would be temperature
dependent?
How Much CO2 is Dissolved in the
World's Oceans?
The oceans represent a potentially large sink for carbon dioxide.
In this exploration you will estimate the amount of CO2 that can partition into the world's oceans
with a quantitative Henry's Law calculation.
Gathering Information
The following information is available from John Harte's Consider
a Spherical Cow:
Ice-free area of the oceans
Pacific: 1.66x10^14 m2
Atlantic: 0.83x10^14 m2
Indian: 0.65x10^14 m2
Arctic: 0.14x10^14 m2
Volume of the world's oceans: 1.35x10^18 m3
Mass of the world's oceans: 1.4x10^21 kg
Fresh surface water: 1.26x10^17 kg
Working with Information
1. Using any relevant values from the information above and
the last session, calculate the amount of CO2 that can dissolve
in the planetary oceans. Assume the entire volume of the oceans
is in equilibrium with the atmosphere.
2. Is it a reasonable approximation to assume that CO2 is in equilibrium with all the planetary
water? Why or why not?
3. The Henry's constant for fresh water is 0.0339 at 25C.
Is CO2 more or less soluble in fresh
water than in ocean water? Hypothesize why the difference may
occur.
4. What percent of CO2 is dissolved
in fresh water compared with ocean water? Is it reasonable to
ignore fresh water CO2?
5. What is the average density and depth of the world's oceans?
Making the Link
The oceans are not well mixed. There are three "layers"
that scientists use to clasify the different depths: the surface
layer, the mixed layer, and the deep layer.
1. Suppose you were on board a cruise ship with scientists
measuring total inorganic carbon. Would you expect the concentration
to be the same in all geographic areas? Explain.
2. Assuming that equilibrium is maintained with just the mixed
layer, calculate the amount of dissolved CO2 in the oceans.
Volume of mixed layer = 2.7x10^16 m3
Mean depth of mixed layer = 75 m
3. One estimate for the total inorganic carbon in the world's
oceans is 3.91x10^19 g. How does this compare with your calculations?
Hypothesize why differences might exist.
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