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OA not OK part 2: Thermodynamic duo

Posted on 5 July 2011 by Doug Mackie

This post is number 2 in a series about ocean acidification. Other posts: Introduction , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, Summary 1 of 2, Summary 2 of 2.

Welcome to the second post in our series about ocean acidification. In the first post we introduced Equation 1 (shown again below) for the formation of calcium carbonate and showed that the formation of calcium carbonate shells is a source of CO2, not a sink for CO2.

Equation 1

We noted that most chemical reactions can go both forward or backwards and that we could use thermodynamics to predict the direction.

In fact, most reactions go in both directions at once but there is usually a more favoured direction. Consider a dinner party with 6 people. There are 5 people on one side of the table and 1 person on the other. Each side starts with a bowl of peanuts and they begin to throw them at each other. At any one time a few peanuts will be in flight, most of them coming from the side with 5 people. However, it is plain that very quickly almost all of the peanuts will end up on the side with 1 person. At this point, the side with 5 people can only throw peanuts as quickly as the lone peanut pitcher sends them over. An equilibrium has been reached. The number of peanuts on either side does not change even though a few individual peanuts swap sides.

Chemical reactions also proceed until equilibrium is reached. That is, the reaction proceeds until the forward reaction (the reaction on the left side of the equation) and the backwards reaction (the reaction on the right side of the equation) occur at the same rate. For most reactions, one side of an equation is vastly (by a factor of thousands or millions) more favoured than the other and for convenience chemists often write a single arrow to show the favoured direction.

Thermodynamics is based on energy differences and tells us if a reaction occurs under the given conditions. Chemists use the word spontaneous to describe a reaction that occurs without outside intervention. For example, ice melting at room temperature is spontaneous, while liquid water freezing at room temperature is not spontaneous.

Millions of experiments - like ice melting - have been done and the data has allowed chemists to calculate a change in energy content for every type of chemical reaction. It is, of course, complex and there are many considerations. Nevertheless these energy calculations show – and experiments confirm – that calcium and bicarbonate ions react according to Equation 1 (shown above).

Thermodynamics also tells us that the reaction in equation 1 is spontaneous under the conditions in the surface oceans. That is, marine organisms like corals and shellfish are able to extract bicarbonate ions from seawater to make their shells or skeletons. However, as we will see in a later post, those conditions can be changed so that the reverse reaction happens, causing the calcium carbonate to dissolve:

Equation 4

Equation 4 is just Equation 1 running in the reverse direction. This is what takes place when limestone rocks are weathered by the action of rain and air. It is no surprise, therefore, that the most abundant ions in most river waters, calcium (Ca2+) and bicarbonate (HCO3), are derived from weathering. (Post 6 discusses weathering in detail).

Thus equations 1 and 4, gentle readers, explain the formation of carbonates and rock weathering. They also explain the time scales on which these reactions occur, oceanic control of atmospheric CO2, and why acidification is happening in our ocean. We will cover each of these in the coming series of posts. In the next post we cover why it is easy to use Equation 1 to make shells.

Written by Doug Mackie, Christina McGraw , and Keith Hunter . This post is number 2 in a series about ocean acidification. Other posts: Introduction , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, Summary 1 of 2, Summary 2 of 2.

 

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Comments

Comments 1 to 15:

  1. Thanks Doug,

    I liked the memorable illustration of the peanuts.
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  2. This stuff is mind-blowingly confusing, thanks for making it sound so clear! I've always been completely flummoxed trying to understand how chemical energy and mechanical / kinetic energy can go back and forth and still keep within thermodynamic limits.
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  3. The peanut-tossing analogy is a doozy!
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  4. @Doug Mackie, I appreciate the topic very much, but I hope you go more in depth later on.
    What is the value of the dissociation constant (pK) of this calcification reaction ? Is there a difference in pK for the two main forms of calcium carbonate, aragonite and calcite ?
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  5. @4JosHag:
    1) No simple K for this reaction as calcification is biological and multistep. 2) Yes, calcite and aragonite are different. We cover both of these later. Right now we are just getting a few basics straight.
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  6. Doug,

    Are you going to use Rustum Roy's work as examples in this for the biological side of things?

    Anyhow good with the peanuts, but it may not carry the speed or extent to which individual atoms and molecules can move from one side to the other, while the numbers remain constant on each side at equilibrium.
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  7. 3 - Rob Painting

    of course food is going to come into the argument sooner or later. It's what all 'real' scientists know; chemistry is just cooking.
    "thermodynamics" == oven temperature
    "equation" == recipe
    etc.
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  8. Equation 1 is not sufficient. The correct approach depends upon the model system. Taking a solution of dissolved carbon dioxide, bicarbonate, carbonate, calcium ion and water (containing as always hydrogen ion and hydroxide ion) to be in equilibrium with solid calcium carbonate and gaseous carbon dioxide we can ask what happens when the partial pressure of caron dioxide increases? First the equiulibrium between gaseous and dissolved molecular carbon dioxide is determined by the Henry's Law constant and the concentration of dissolved cabon dioxide increases independent of what happens to the other chemical species. Secondly the product of the carbonate ion and calcium ion concentrations is a constant (the solubility product) and since in this model calcium ion is fixed the concentration of carbonate remains fixed. That leaves the bicarbonate ion concentration to be considered. This concentration will increase and, by electrical neutrality, the hydrogen ion concentration will increase as well (unless it is determined by other reactions not involving carbon dioxide species). The hydroxide concentration will decrease according to the ion dissociation constant for water. When all of these constraints are considered the net result of increasing the carbon dioxide pressure (say according to the Keeling curve): 1. dissolved mo;ecular carbon dioxide concentration increases, 2. dissolved bicarbonate ion concentration increases, 3. pH decreases, 4. carbonate ion concentration remains fixed, 5. calcium carbonate precipitates. This discussion can be modified for the case of "buffering". i.e. nearly fixed hydrogen ion concentration in which case the molecular carbon dioxide concentration increases (Henry's Law), carbonate is fixed by the calcium carbonate solubility product, bicarbonate is fixed by electroneutrality and calcium carbonate precipitates.
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  9. Thanks Hugo, we appreciate your interest, but please be patient. This is post 2 of 18. We will get there.

    It would be fair to say that one of the many motivations to write this series was what we see as misconceptions in your seawater equilibria post at Skeptical Science.

    Most of the responses to your thoughts, here and in that post, can be addressed by responding to a single point. You said:
    Taking a solution of dissolved carbon dioxide, bicarbonate, carbonate, calcium ion and water ... to be in equilibrium with solid calcium carbonate and gaseous carbon dioxide...
    While equilibrium chemistry is indeed quite simple, it is an inconvenient fact that the ocean is not in such an equilibrium. It is very important to remember that non-equilibrium systems behave quite differently to equilibrium systems. This fact changes much of what you have said here and in your previous posts.
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  10. What I meant to say above is: Please know that I understand thoroughly that the ocean is not at equilibrium. I also know that all spontaneous processes proceed in the direction of equilibrium. Therefore as a starting point for considering the direction of chemical processes it is useful to start with a determination of the equilibrium of a model system. That is what I thought you were doing. My point is that the correct approach to considering the equilibrium state of a model system is to list the chemical species present,find all constarints on the system (one equilibrium constant for each independent net reaction and charge balance) and then solve the resultant equations for the equilibrium concentrations of the species. To say, as you do, that thermodynamics tells us the reaction 1 is spontaneous in the surface oceans is incorrect. What is correct is to say that on average the surface oceans are, so long as the partial pressure of carbon dioxide increases, continously perturbed by the addition of carbon dioxide from the vapor phase and that this pertubation results in an increase in the concentration of dissolved carbon dioxide, dissolved bicarbonate ion, dissolved hydrogen ion and, unless the ion product equals the solubity product, carbonate ion. If the local ion product equals or exceeds the solubity product of calcium carbonate then solid calcium carbonate sponateously precipitates. Your equation 1 implies a spontaneity without providing the perturbation driving it. Eq.1, in fact, implies that the precipitation of calcium carbonate drives an increase in the amount of carbon dioxide in the vapor hase whereas the opposite is the case.
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  11. Fritz, I am sorry to say that you are wrong. We have mostly written a detailed discussion of you 'seawater equilibria' post and the 'cb with buffering' document. I expect to send it to you early in the week.
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  12. Fritz: I have to say I agree with Doug. As a fellow author of this series of posts, I've sent him some comments. However, I'll add this:

    You say that if the local ion product equals or exceeds the solubility product of CaCO3 then solid CaCO3 spontaneously precipitates. Like you, I am a professor of physical chemistry, and both of us know that this statement, while true in a strict sense, does not mean what lay people think it means. What it actually means is that provided there is a facile mechanism for the reaction, there is no thermodynamic reason for the reaction to not proceed spontaneously. In fact, all marine chemists (and I am one) know that CaCO3 almost never spontaneously precipitates in the surface ocean because the mechanism is blocked, for kinetic reasons, by magnesium ions. Thus almost all surface waters in the ocean are supersaturated, i.e. NOT at equilibrium.

    For this reason, an equilibrium analysis of CaCO3 formation in the ocean is of purely academic interest and bears no relationship with reality. I respectfully suggest you consult any textbook on the thermodynamics of natural waters, of which there are many. I particularly recommen the fine book by Werner Stumm and James Morgan. I am sure you will find it an edifying read.
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  13. Please understand that I am not claiming to provide anything more than a correct analysis of a model system. The actual behavior of the real seawater system I gladly leave to others such as yourself and greatly appreciate your efforts. On the other hand, the point under discussion is the use of thermodyanmics and eq, 1 of the post. In that area I am an expert I assert that it is necessary when considering the thermodynamics of a complex system to consider the independent net reactions (any set will do - all yield the same result - but the set must be complete!) From this set of net reactions one finds the indepndent equilibrium constants and then combines these with other constraints to obtain as many equations as unknowns. It is not only incorrect but extremely misleading to select one equation (eq, 1) and then assert spontaneity of that reaction without specifying the source of the spontaneity. I have thought a great deal about this subject in general, published several times on it in J. Chem Ed. and have had some impact on the way the subject is taught. But my contribution here is simply to ask that the thermodyanmaics of ideal systems be correctly considered - not that I can proovide the final (or even a partial) answer to the description of sea water chemistry. Believe me I feel better knowing that folks such as yourself are considering the details of seawater chemistry and you will feel much more secure in your considerstion if your treatment of the basic P. Chem. of model systems is done correctly. And this is more than a pedantic point. To choose a single independent net reaction (eq.1) and assert that the precipitaion of carbonate is accompnaied by the liberation of CO2 as was done in the post is just not correct.
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  14. The utility of a model like yours which does not represent reality escapes us.

    The crux of your argument appears to be that the ocean is permanently in equilibrium with both atmospheric CO2 and oceanic CaCO3. Neither of these is true. This has been very well researched; in a comment to your original 'seawater equilibria' post you mentioned you got some values from one of Frank Millero's papers. I take it that his values differed from the ones you calculated? What do you think accounts for the difference?

    We strongly suggest you read a few of Millero's books.

    Also, Chapter 5 of the CDIAC (Carbon Dioxide Information Analysis Centre – a part of the DOE) book The Analysis of Carbon Dioxide Parameters in Seawater provides a comprehensive view. Available here
    (The book has been updated since 1994, I think the new 2007 version is at the EPOCA site (European Project on OCean Acidification).

    More recently, the SCOR (International Council for Science: Scientific Committee on Ocean Research) publication 127: Thermodynamics and Equation of Seawater, available here may also be useful. This page in turn links to the home page of the Thermodynamic Equation of Seawater v10 (TEOS) at here.

    As you can see, the issue has been very well studied for many years by many physical chemists. Their conclusions differ from yours.

    Here are a few points to consider:

    1.
    You calculate the total molality of CO2 in seawater at pH 8 and at 15oC as 1650 umol/kg. Why not take 5 minutes to google up what the measured values are? (KH's research group has been collecting such data for 15 years).

    2.
    The spontaneity of eq. 1 or its reverse depends on the chemical conditions. To suggest that when eq. 1 is spontaneous it leads to a decrease in atmospheric CO2 is the same as saying that the reverse, when spontaneous, (weathering of limestone by CO2) causes an increase. Both are obviously wrong as either would make these supposed equilibria unstable. Equilibria are not unstable, by definition.

    3.
    CaCO3 is a base. If it precipitates spontaneously from seawater, then the latter must become more acidic, just as it gets more alkaline when a base dissolves. If you make seawater more acidic, bicarbonate converts to carbonic acid, which will increase the CO2 of an atmosphere previously in equilibrium (exactly as eq. 1 describes).

    4.
    It is not possible to write a balanced chemical equation that converts CO2 to CaCO3 that does not generate unreacted H+ or its chemical equivalent on the RHS of the equation. Reason: you have to put the 2+ charge of the Ca2+ ion somewhere to maintain charge balance.


    2, 3, and 4 are essentially equivalent arguments. No thermodynamics is needed. It is elementary stoichiometry (Daltons laws) and acid-base chemistry (Lowry-Bronsted & Lewis).


    5.
    In the document CB with buffering you have used a Henry's law constant at 15oC of 22.1. However, this is the value for the transfer of CO2 in air into freshwater. In seawater at 15oC KH = 26.7. (See: Weiss 1974, Carbon dioxide in water and seawater: the solubility of a non-ideal gas. Marine Chemistry 2, 203-215).

    We suggest that once a simple model like yours diverges from reality by as much as 20% then the utility of the simple model should be questioned. Similarly, some of your other calculated values differ from reality.
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  15. second summary post

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