# 9 Gibbs free energy in aquatic environments

## 9.1 Energy in chemical reactions

As previously described, redox reactions power life by releasing energy when electrons move from one compound or element to another. These reactions can yield different amounts of energy to the lifeform depending on the reagents involved. The total energy yield of a reaction is captured by the concept of Gibbs free energy $$\Delta G$$. You may have come across the idea of Gibbs free energy when thinking about whether or not a reaction will proceed spontaneously where:

• $$\Delta$$G < 0 will be a spontaneous reaction
• $$\Delta$$G > 0 will be non-spontaneous (requires energy input).

And for a general review of Gibbs free energy you can go here. And watch the video below that explains energy yield in the context of electrochemistry (batteries)

But we are really focused on the Gibbs free energy yield in living systems.

### 9.1.1 Standard Gibbs free energy

Over decades scientists have figured out the standard gibbs free energy of formation for a very long list of elements and compounds. We can use these free energy estimates of compounds to estimate the total energy yield of a reaction using the following equation:

$$G^o = {\sum}\Delta G_{products} - {\sum}\Delta G_{reactants}$$

Where $$G^o$$ is the standard free energy yield of a reaction at $$25^o$$ and 1 atmosphere pressure with 1 mole of that substance. We can use the above equation to estimate how much energy a microbe may get out of a reaction. For example the reaction: $$3NO_{(g)} -> N_2O_{(g)} + NO_{2(g)}$$ with $$\Delta G_f^o$$ (standard gibbs free energy of formation values of):

• $$NO_{(g)}$$ = 86.55 kJ/mol

• $$N_2O_{(g)}$$ = 104.18 kJ/mol

• $$NO_{2(g)}$$ = 51.29 kJ/mol

Plugging these numbers into the equation we get

$$\Delta G^o = (1 * 104.18 kJ/mol + 1 * 51.29 kJ/mol) - (3 * 86.55)$$

$$\Delta G^o = -104.18 kJ$$

Knowing that final standard free energy yield gives us a sense of how much energy a lifeform can get out of a redox reaction. But these numbers are at standard state. What about non-standard temperatures or concentrations?

## 9.2 Non-standard $$\Delta G$$ yield

The above equation gives the standard free energy yield with 1 mole of each reactant at $$25^o$$C and 1 atmosphere pressure. Of course, almost all reactions in nature will not be at standard conditions like these. To calculate this “actual” Gibbs free energy in the environment we need to use one last equation. If we had the generic chemical reaction: $$aA+bB = cC+dD$$

Then we would estimate the actual gibbs free energy yield of a reaction as:

$$\Delta G = \Delta G^o + RT ln\left(\frac{([C]^c*[D]^d)}{([A]^a*[B]^b)}\right)$$

Where $$\Delta G^o$$ is the standard free energy yield of a reaction (calculated above), R is the universal gas constant $$R = 0.008314 \frac{kJ}{mol K}$$ and K is temperature in Kelvin $$K= Temp^oC + 273.15$$

Knowing the $$Delta G$$ of a reaction can tell us which microbes are likely to be active under different environmental conditions. This is because microbes can use a variety of compounds as so-called “final electron acceptors.” Depending on the final electron acceptor used by microbes the metabolism of energy bearing compounds like sugar or acetic acid will generate different amounts of energy. The microbes using the most energy-efficient pathway (i.e. the most negative $$Delta G$$) will “win” and likely that reaction will be dominant in those environmental conditions. The most efficient final electron acceptor is oxygen, but there are a large variety of other final electron acceptors with varying energy yields. To capture these complex ideas of energy yield, biogeochemists use a term called the “redox ladder.” This term indicates the declining energy yield as microbial communities switch final electron acceptors.

The above image is from this very thorough website at ESF which you can use for additional review.

As microbial communities descend down the redox ladder, there is increasingly less free energy produced. The order of electron acceptors from most energy to least energy is: oxygen, then nitrate, then manganese (not shown above), then iron, then sulfate, and finally, carbon dioxide. The redox ladder is mostly a conceptual idea of how microbial communities are organized by redox reactions and energy yields, but frequently the redox ladder is mapped directly onto physical space. For example, near the sediment surface of a shallow pond, there is oxygen exchange with the water column and oxygen is available as the most efficient final elecron acceptor. But as you go deeper into the sediment, the oxygen is consumed by microbes closer to the surface, and thre is eventually so little that it is more efficient to use nitrate ($$NO_3^-$$) as a final electron acceptor. Going even deeper the microbes run out of nitrate and switch to iron reduction, and so on. A good example of how the redox ladder maps to physical space is called a Winogradsky column

## 9.4 Redox potential

The redox ladder is one way of capturing the reactions that are likely to occur, but there are two other ways. First is to simpley describe the environment as oxygen-rich or not. An oxic environment is likely to have oxygen as the final electron acceptor, suboxic environments can have a mix of oxygen and other final electron acceptors, while microbes in anoxic (no oxygen) environments will rely on non-oxygen electron acceptors (like $$NO_3^-$$).

Another, more quantitative way to describe the redox environment of natural waters (like lakes or ponds) sediments, or aquifers is to directly measure the reduction potential in the environment. This $$E_h$$ scale goes from -1 to 1 with 1 representing oxic environments where reduction is likely to occur and -1 representing reduced environments with limited potential for reduction. This excellent paper (by a CSU professor, Thomas Borch) provides a clear explanation of how reduction potential and redox more generally control reactions that govern water quality, with a key figure below:

It’s beyond the scope of this course (at present) to deeply define the reduction potential scale but wikipedia does a pretty good job if you are curious.

## 9.5 Redox and nutrients

The paper above by Borch and others outlines a variety of ways that redox conditions control water quality, but I wanted to highlight specifically two ways that redox conditions control nutrient concentrations in inland waters.

### 9.5.1 Nitrogen cycling and redox

First, as highlighted previously the nitrogen cycle includes a critical step where biologically-available nitrogen in the form of $$NO_3^-$$ or $$NH_3$$ is eventually converted to biologically inert $$N_2$$. This removal of nitrogen from inland waters is a critical way that we can reduce nutrient pollution in lakes, rivers, and the near-coastal environment. For the denitrification to occur, microbes need anoxic conditions so that $$NO_3^-$$ reduction (denitrification) is the most efficient final electron acceptor. But, in order to remove all of the $$NH_3$$ from the system as well, a nitrification step must first occur where $$NH_3$$ is converted to $$NO_3^-$$. This process where $$NH_3$$ is used as electron donor (energy source) requires oxygen, so full removal of nitrogen from inland waters requires both oxic and anoxic conditions. These processes (with a more advanced picture of the redox reactions involved) are captured in the figure below from this very helpful explaner on the Nitrogen cycle.

### 9.5.2 Phosphorus

Unlike the nitrogen cycle, Phosphorus has no gaseous phase on earth, so removing it from inland waters either requires it to be taken up by plants or other lifeforms or for it to be bound up by other minerals. In many lakes, the most common form of P binding is when $$PO_4^{3-}$$ with it’s charge of -3 binds up with aqueous iron ($$Fe^{3+}$$). This effectively removes the Phosphorus from the water column and makes it inaccessible to algae. However, once the $$FePO_4$$ sinks to the bottom of a lake or wetland, the iron can be reduced to $$Fe^{2+}$$ and the phosphate will then desorb from the iron, being released into the environment as bioavailable P. As a result, Phosphorus dynamics in inland waters are deeply dependent on redox reactions and conditions.

Redox conditions are some of the ultimate controls on nutrient cycling, but what happens when excess nutrients reach the coast or lakes? Frequently, it causes harmful algal blooms.