Tag Archives: Ocean Acidification

Ocean Acidification and Its Effect on Corals II

by James R. Barrante, Ph.D.

In OAI we showed the effect of increasing dissolved CO2 in seawater on ocean pH, and the carbonic acid buffer system including insoluble carbonate salts.  The calculations performed in the study involved using thermodynamic equilibrium constants found in the literature at 298.2K.  It is important to understand that a true thermodynamic equilibrium constant depends only on temperature and requires that activities (effective concentrations) be used in the calculations.  If concentrations are used, then either activity coefficients must be known in order to substitute concentrations for activities, or apparent equilibrium constants must be used, found by correcting thermodynamic equilibrium constants for the ionic strength of the solutions.

Unfortunately, while the data presented in OAI is consistent with data presented by others performing similar calculations, it’s not consistent with reality.  For example, the calculated ocean pH at a CO2 pressure of 276 ppm is found to be 8.41.  According to published values for ocean pH experimentally determined in the mid-1800s at CO2 pressures of 280 ppm, the value was closer to 8.20.  Today, at atmospheric pressures of CO2 close to 380 ppm, experimental values for ocean pH are approximately 8.13.  The calculated value using numbers found in OAI is 8.29.  It is apparent that the model used in OAI is not correct.  One might think that perhaps the temperature is the problem.  The temperature of the oceans is not 25˚C, but closer to 15˚C and even colder as depth is increased.  Unfortunately, using values for the equilibrium constants at lower temperatures only make the discrepancies larger.  As temperature goes down, calculated pH values go up.

We find that if we assume that the pH of our oceans is behaving more like a system where the calcium ion concentration is constant,  we get calculated results that are closer to experimentally determined values.  Consider another approach to the  calculations performed in OAI.  First, let us combine the two dissociation equations for carbonic acid.  This  gives

Rearranging and taking the logarithm (base 10),

which is a modified form of the Henderson-Hasselbalch equation.  The activity of the dissolved carbon dioxide can be replaced with Henry’s Law and the activity of the carbonate ion can be replaced with the Ksp equation for CaCO3.

CodeCogsEqn-38

There are studies that show that the bulk calcium ion concentration in the surface layers of the ocean are relatively constant at approximately 0.0104M . The relationship between the activity of Ca++ and its concentration is

where γ+ is the activity coefficient of   Ca++ .  While it is impossible to measure the activity coefficient of an individual ion, we can approximate it using a modified form of the Debye-Hückel equation

where zi  is the charge number on the ion and I is the ionic strength of the solution.  The ionic strength of the oceans is approximately 0.7.  Therefore, we have

                  =   – 0.9274

γ+  =  0.1182

Substituting physical constants used in OAI for K1, K2, Ksp, and kinto the pH equation, we have

 

In the mid-1800s the partial pressure of CO2 in the atmosphere was approximately 0.000280 atm (280 ppm).  Substituting this into the pH equation gives

pH = 6.418 – 0.5 log (0.000280)  =  8.194

which is very close to the reported value.  Today, atmospheric CO2 level is close to 0.000380 atm (380 ppm).  Using this value in the equation gives pH = 8.128, again very close to the measured value.  Using this equation to find the pH, we can calculate the data found in the following graph:

The most difficult part of this model to come to terms with is assuming that  Ca+2 and CO3-2 concentrations are constant with changing pH.  A possible explanation is that while it is assumed that atmospheric CO2 is in equilibrium with CaCO3 in our oceans, it is apparent that the calcium ion concentration far exceeds the total concentration of all carbonate components.  That would indicate that the calcium ion concentration is so overwhelmingly large that the equilibrium between dissolved CO2 and CaCO3 is destroyed.  This is the only way the acceptable values for ocean pH can be found.  In OAIII we will look at the effect of temperature on the system.

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Ocean Acidification and Its Effect on Corals I

by James R. Barrante, Ph.D.

Ocean chemistry essentially involves the chemistry of the carbonic acid buffer system to which is added the chemistry of insoluble carbonates such as calcite and aragonite, CaCO3.  When the Earth formed, the atmosphere was approximately 95% carbon dioxide and water vapor.  No free oxygen or nitrogen gas was present.  As the planet cooled, however, the temperature dropped to below the boiling point of water, and the majority of the water vapor in the atmosphere along with outgassing vapors formed our oceans.  Because of its high solubility in water, the CO2 in the atmosphere began to dissolve into the oceans.  The high solubility of CO2 in water is mainly because CO2 reacts with water to form a weak acid, known as carbonic acid, H2CO3.  Carbonic acid in turn slightly dissociates in water giving:

Here the K‘s are the dissociation constants for carbonic acid and the a‘s represent the activities (effective concentrations) of the subscripted ions.

If we multiply the two dissociation constant equations together, we obtain an expression for the activity of CO3= .

As the concentration of CO3= increased in the oceans, it began to react with soluble salts of magnesium and calcium that found its way into the ocean to form insoluble carbonates.  These carbonates settled to the bottom of the oceans and became rock.  For example, marble is calcium carbonate.  The removal the carbonate ion from the ocean, allowed more CO2 to dissolve.  Eventually, the level of CO2 dropped to parts per million range and has remained there for millions of years.

The solubility of calcium carbonate (calcite and aragonite are two crystalline forms) can be described by the equation

where Ksp is the solubility product for CaCO3.  As a true equilibrium constant, it value is only a function of temperature.  To obtain concentrations from activities, however, require a knowledge of activity coefficients, and these are a function of the ionic strength of the solution.  In terms of concentrations, the above expression becomes

Here, γ ±2  represents the mean activity coefficient of calcium carbonate and () represent molar concentrations of the ions in solution.

Any solution of calcium carbonate in the presence of the carbonic acid buffer system must be electrically neutral.

Substituting the above equilibrium equations into this equation gives

The activity of dissolved CO2 (H2CO3) depends on the partial pressure of CO2 over the solution.  This is known as Henry’s Law

Here, kH  is the Henry’s Law constant and P is the partial pressure of CO2 in atmospheres.  Multiplying the above equation by  aH+2  and substituting Henry’s Law into the equation gives

We see this to be a quadric equation that can be solved numerically for pH as a function of CO2 pressure.  Once the pH is known, values of the other species can be determined.  The graph and Table below give values for pH, partial pressure of CO2, and activities of ionic species.  To get the concentrations from the activities, the high ionic strength of the sea water must be taken into account.  Concentrations could be significantly different from activities.  Other values at 298.2 K are:  K1  =  4.45 x 10-7, K2  =  4.69 x 10-11, kH  = 29.41 atm/M, Ksp = 6 x 10-9 (an average for the minerals marble and aragonite), and pH = – log aH+ .

It appears, looking at the activities of  Ca++ and CO3=, that as the partial pressure of CO2 in the atmosphere goes up, the activity of the Ca++  goes up, thus causing the activity of the CO3= to decrease.  The activity of the calcium ion represents the solubility of the CaCO3.  It is clear that the solubility of CaCO3 increases as the pH decreases.  What is not intuitively obvious is that the process is not linear.  Note that as the partial pressure of CO2 approaches 3000 ppm the concentrations of calcium and carbonate level off.  This would explain how the coral reefs could have formed in the first place at CO2 levels of 3000 to 4000 ppm.  The calculations producing the data in the graph were at 298.2K.

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