Category Archives: Ocean Acidification

Ocean Acidification and its Effects on Corals III. Temperature

by James R. Barrante, Ph.D.


In OA I and OA II we considered the ocean chemistry of the carbonic acid system at constant temperature.  Under these circumstances, it is apparent that if the partial pressure of carbon dioxide in the atmosphere increases, the pH of a buffered ocean must drop.  We were able to show in OAII that increasing the partial pressure from 280 ppmv to 380 ppmv will decrease ocean pH from a values of approximately 8.2 to 8.1. pH units.  In OAIII we shall consider the effect of temperature on these equilibria.  Since we are working with activities rather than concentrations, it is not necessary to consider ocean salinity here.  A significant amount of research has been done concerning the temperature dependence of the equilibrium constants.  This data can be found online.  A typical set of equations are:

ln K1 =  – 1596.1/T  –  9.2597

ln K2 =  – 2174.5/T  – 16.467

ln kH =  – 2400/T  +  11.431

ln Ksp =  2388.9/T  – 27.213

where K1 is the first dissociation constant of H2CO3, K2 is the second dissociation constant of H2CO3, kH is the Henry’s Law constant, and Ksp is the average solubility constant of CaCO3.

The equation relating the pH of ocean water to the partial pressure of atmospheric CO2 at temperature  is


This equation was derived in OAII.  There are obviously a number of variables in this equation that could be changing at the same time.  It might be interesting to approach the problem as one does with PVT data and look at a surface graph.  First note that because the concentration of calcium ion in the oceans is so large, we can assume that the activity is constant at 0.00123.

It is well-known that pH is a sensitive function of temperature.  Consequently, to assume that the pH of our oceans depends only on the concentration of dissolved CO2 is a sophomoric definition of the boundaries of the system.  To express the data graphically, it is necessary to do so on a surface.  Slices of the three-dimensional graph are easily seen by following isotherms or CO2 isobars.  Note that the change in pH with temperature is not insignificant.  It has been noted that the pH of the oceans has dropped about 0.1 pH units in 150 years.  This normally is incorrectly attributed to the absorption of atmospheric CO2, and while atmospheric CO2 does come into play here, one should note that as little as a 2-degree C increase in ocean temperature can decrease ocean pH by as much as 0.05 pH units.  Moreover, assuming that the concentration of dissolved CO2 increases in a solution in which its temperature increases is not consistent with Henry’s Law.

Below is the P-pH-T representation of ocean pH.  Keep in mind that the system is highly buffered.  For clarity, the pH at various intersections of the curves is given.  Because of the three-dimensional nature of the graph, to find temperatures and pressures, be sure to follow the intersections along lines to their respective axes.  The temperature range was taken to represent global SST in zones from the equator at 303K to Antarctica at 273K.  Note the variation in ocean pH between these two temperatures on any isobar.  At today’s value of 400 ppmv, the pH changes from 8.30 to 8.00.  This would suggest that describing an average ocean pH has no physical meaning.  I would imagine that a similar effect occurs going from surface temperature to deep-water temperature.  It’s clear that using a secondary school chemistry course definition of pH in this complex system serves no useful purpose and leads one to the wrong conclusions about ocean acidification.


    P-pH-T Data for Ocean pH.


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Acid – Base Chemistry

by James R. Barrante, Ph.D.

There have been a lot of articles and blogs online covering the so-called “acidification of the oceans.”  (See OAI, OAII on this website).  Much of the information found in many of these articles and blogs, while very well written, is scientifically incorrect.  The primary reason is a complete misunderstanding of acid-base physical chemistry.  So this post hopefully will address some of these errors.

There are a number of ways to define an acid and a base.  In this post we will use what is referred to as the Arrhenius definition.  An aqueous solution is acidic if (H+) > (OH) and basic (alkaline) if (OH) < (H+), where () refers to molar concentration.  There is a notion out there that these are the only two states available, and the system is “dipolar,” like electrical charge.  That is, if a system is less basic, it must be more acidic.  This is not the case, because there is a third state that is neither acidic nor basic and this is the neutral state, (H+) = (OH).

Because hydrogen ion and hydroxide ion concentration can vary over a wide range of values (many powers of ten), a logarithmic scale, known as pH and pOH, has been designed to make concentrations more manageable.  The definition of pH and pOH are:

pH  = – log aH+     and     pH  = – log aOH-,

where aH+ and aOH- are the activities (effective concentrations) of the ions, respectively.  For example, the assumption is made that if the pH of an alkaline solution drops, it is becoming more acidic.  The problem with this idea has to do with the neutral state.  You see, you can lower the pH of an alkaline solution simply by adding water, a neutral substance.  The solution is simply becoming less basic approaching neutrality.  To be acidic, it would have to cross the pH 7 boundary, and it will never do that, no matter how much water you add.  It is akin to asking what is the pH of a 10-8 M HCl solution?  I know you want to say 8.  The pH of an acid solution can never be greater than 7.  It’s a problem we give our students in Analytical Chemistry to figure out.

So, having said all this, it is clear that with a pH around 8, our oceans are alkaline and dropping the pH toward 7 doesn’t make them more acidic, it simply makes them less basic.  A solution that is not acidic in the first place cannot become more acidic.  And it is scientifically dishonest to suggest that it could.  The question now centers around what happens to an aqueous solution when CO2 gas is bubbled through it.  We know that CO2 gas reacts with water to form carbonic acid H2CO3.  But carbonic acid is a very weak acid and that is important.  (By the way, the term weak and strong, when referring to acids and bases, has nothing to do with concentration.)  The acid dissociates according to the equation (we will consider only the first dissociation at this point):


The double arrow here means that the reaction is reversible.  At some the concentrations of these substances will reach thermodynamic equilibrium, at which point


where () designates molar concentration and K1 is the apparent equilibrium constant.  A true thermodynamic equilibrium constant would require the use of activities (effective concentrations) of the substances rather than the concentrations themselves.  In this case we will take K1  = 4.45 x 10-7.  Obviously, the excess of hydrogen ion in solution makes the solution acidic.  But look at the equilibrium constant.  It is telling us that most of the dissolved carbon dioxide is H2CO3.  We know that at a temperature of 298.2K, when the pressure of CO2(g) is 400 ppm (0.0004 atm), the concentration of dissolved CO2 is about 1.35 x 10-5  M.  Using Eq (1), we can find that the concentrations of H+ and HCO3  are both equal to 2.47 x 10-6 M,  giving a pH = 5.61, which is mildly acidic.

Wouldn’t it be nice if nature was so simple.  Unfortunately, bicarbonate ion also is a weak acid.  That is, it dissociates according to the equation



where K2 is the second dissociation constant of carbonic acid equal to 4.69 x 10-11 .  From the size of K2 you can see that very little hydrogen ion is produced by the dissociation of bicarbonate.  In fact, the pH of a saturated solution of sodium bicarbonate can be found by the equation

pH  =  1/2 (pK1 + pK2)

where pK1 = – log K1  and pK2 = – log K2.

pH  =  1/2 (6.35 + 10.33)  =  8.34

considerably alkaline.  Of course, this explains why bicarbonate of soda is a good antacid.  Moreover, it turns out that the solution of sodium bicarbonate does not have to be saturated.  Since a solution of NaHCO3 is the first equivalence point in the titration of carbonic acid, any solution of  NaHCO3 in water will have a pH of 8.34.

So let’s see what would happen to ocean water if we added a little Na2CO3 to it.  Not too much, just enough to make it equal the carbonic acid concentration.  Combining the two equilibrium constant expressions gives


Since  (CO3-2)  =  (H2CO3) ,  (H+)2  =  K1K2  and pH  =  ½ (pK1  +  pK2)  =  8.34.  Adding a small amount of carbonate ion to the system drastically increases the pH to make the system alkaline.  You will find that at this point also, it is very difficult to change the pH of the solution.  The solution here is said to be “buffered.”  In fact, our oceans are gigantic buffered systems.  It is important to note that since we are using concentrations here, we should not expect to get very good answers.  This is because seawater has a high ionic strength and as the ionic strength goes up, the difference between activities and concentrations increases.  Either we use activities here or we correct equilibrium constants for salinity.

Of all the gases, CO2 gas is one of the most soluble.  But that being said, gases in general are not very soluble in water.  Even at the low temperature 280K, the solubility of CO2 in water at a pressure of 4000 ppm or 0.004 atm, is only about 2.4 x 10-4 M.  The point is that it is not enough to simply look at the production of hydrogen ions to decide on the acidity or alkalinity of a solution.  When the source of the hydrogen ions is a weak acid, the presence of other ions will drastically effect the pH of the solution.

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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.


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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