Dissolved Gases & Solubility

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.

In this exploration, you will study the hydration of carbon dioxide:

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.

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:

Similarly, if (and only if) the system is at equilibrium, then Q equals K and DG = 0. Thus,

which is a completely general result.

In conclusion, the following relations always hold:

The following hold only when the system is at standard state:

The following hold only when the system is at equilibrium:

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?

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.

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.

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

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?

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.