The relationship between calcium and alkalinity is one of the most discussed chemical phenomena in reef tanks. It is also one that is frequently misunderstood. Both calcium and alkalinity (to be defined below) are required by a host of organisms that form calcium carbonate skeletons and shells. In a closed system like a reef tank, they can quickly become depleted. Consequently, it is imperative that aquarists ensure that appropriate levels are maintained.

Aquarists have developed many different ways of supplementing calcium and alkalinity in reef tanks. None of these are perfect, and all can lead to problems if not used properly. This article will explain the relationship between calcium and alkalinity in reef tanks as a backdrop to such supplementation. With a greater appreciation for this relationship, I hope that problems involving calcium and alkalinity issues can be reduced.

To set the stage for discussions to follow, the list below shows the manner in which calcium and alkalinity are intertwined in reef tanks:

As a consequence of these various interactions, the relationship between calcium and alkalinity in reef tanks is complicated. In this article, I will endeavor to disentangle these interactions.

Figure 1. The Acropora sp. on the left is an active consumer of calcium and alkalinity as it forms its skeleton, while the yellow polyps (Parazoanthus gracilis) are not.	Figure 2. Mushrooms (Actinodiscus and Discosoma sp.) and polyps (Palythoa sp.) do not consume much calcium or alkalinity.

Alkalinity

Alkalinity itself is a complex term that requires some understanding before proceeding to involve calcium in our discussion. For a detailed article on alkalinity, try this link. In short, total alkalinity is a measure of how much acid it takes to lower the pH of the water sample to the bicarbonate endpoint. That is, how much acid it takes to lower the pH to the point where one has added enough acid to potentially convert all of the bicarbonate (HCO3-) to carbonic acid (H2CO3).

During such an addition of acid (called a titration), a variety of things are happening, but those most important in this context are that carbonate is converted into bicarbonate

(1)     H⁺  +  CO₃^{- -}  à  HCO₃ ^-

and bicarbonate is converted into carbonic acid:

(2)     H⁺  +  HCO₃^- à H₂CO₃

In seawater, this endpoint occurs at about pH 4.2. So an alkalinity titration involves adding acid to the tank water until a pH indicating dye (or a mixture of dyes) changes color and indicates that the endpoint (pH 4.2) has been reached.

Other things besides carbonate and bicarbonate contribute to seawater alkalinity. In normal seawater, these are a small part of the total, with bicarbonate contributing about 90% of the total, carbonate about 7% (though this depends substantially on the pH), borate about 3 percent, and everything else occurring in much smaller percentages (as you can see since these total 100%). In reef tanks, this distribution can become skewed significantly because borate can be substantially elevated, and the pH can be far from that of normal seawater (8.2; reef tanks typically range from pH 7.8 to pH 8.6).

Why do we care about alkalinity?

The primary reason that we care about alkalinity is that when organisms build calcium carbonate skeletons, they effectively remove calcium and carbonate from the water column. If we had a handy way to measure carbonate, or especially bicarbonate, which corals use as their source of carbonate, we would likely have little interest in alkalinity. Unfortunately, measuring bicarbonate directly is difficult. Measuring alkalinity is very easy, and we use it as a surrogate measure for carbonate and bicarbonate.

Figure 3. Coralline algae are, in some tanks, the largest consumers of calcium and alkalinity.

Calcium

Calcium is in some ways simpler to understand than alkalinity, but it too has its complications. This article is one part of a series that will show the many facets of calcium in the ocean and in reef tanks. Calcium is one of the major ions in normal seawater, comprising about 12% by weight of the solids (410 ppm). Variations in the calcium concentration in the oceans are most often caused by changes in salinity. Most of the calcium ions in seawater are present as free ions, but some of them are ion paired to anions, especially sulfate, forming the neutral ion pair CaSO4.

Calcium also forms ion pairs with carbonate and bicarbonate. These comprise a small fraction of the total calcium, but comprise a fairly large portion of the total carbonate (along with magnesium, about two thirds of the total carbonate). These ion pairs lower the concentration of free carbonate, and thereby help to inhibit precipitation of calcium carbonate, but that's getting ahead of ourselves in this explanation.

Solubility of Calcium Carbonate

In surface seawater, calcium carbonate is supersaturated (although in deep water it is undersaturated for reasons described in this link). That is, there is already more in solution than would form by trying to dissolve solid CaCO3 into the water. It also means that calcium and carbonate are poised to precipitate any time they are given the opportunity (e.g., appropriate seed crystals and a lack of crystallization inhibitors such as magnesium and phosphate).

The equilibrium constant for the dissolution and precipitation of calcium carbonate is shown below:

(3)    K = [Ca⁺⁺][CO₃^--]              

When K exceeds a particular value (the Ksp), the water is supersaturated. If K is less than this value, then the water is undersaturated, and calcium carbonate solid in the water can dissolve. This relationship is normally defined using the supersaturation parameter, which is symbolized as W:

(4)    W = [Ca⁺⁺][CO₃^--]/K_sp

When W = 1, the solution is exactly saturated.  When W exceeds one, it is supersaturated, and when W is less than 1, the solution is undersaturated.

In normal seawater, W ~ 3 for aragonite and W ~ 5 for calcite, though these values have been steadily dropping as carbon dioxide has been added to the atmosphere, reducing the seawater pH. Aragonite and calcite are just different crystal forms of calcium carbonate. Calcite is slightly more stable, and hence is slightly less soluble than aragonite (i.e., has a lower K_sp).  Organisms can precipitate both aragonite (pteropods and corals) and calcite (foraminifera and cocoliths), but most of the precipitation in reef tanks is aragonite (although certain organisms such as abalone form both).

Reef tanks often have higher alkalinity and higher calcium than seawater, and hence are more supersaturated than seawater. In tanks with a high pH (such as many tanks using limewater) the supersaturation is also higher than in seawater. At the same alkalinity, if you raise the pH, you convert some of the bicarbonate into carbonate:

(5)     HCO₃ ^-  +   à  CO₃^{- -}  +    H⁺ 

Within the pH range of most reef tanks (up to about pH 8.5 or so), the amount of carbonate present is approximately linear with the hydrogen ion (H+) concentration because of the relationship seen in equation (5). So if the pH rises from 7.5 to 8.5, there is approximately a ten-fold increase in the carbonate concentration. From pH 8.0 to 8.5, the increase in carbonate is about 3-fold.

Combining these various factors, here are some combinations of calcium, alkalinity, and pH that have equal supersaturation with respect to aragonite:

W = 1 (risky: dissolution of aragonite begins here)

W = 3 (typical of normal seawater)

W = 6 (non-biological precipitation is more likely)

How should one think about supersaturation? The higher it is, the more likely it is that precipitation of calcium carbonate will occur. The reason for this is straightforward: if the "pressure" to precipitate calcium carbonate becomes too high, these inhibiting processes will be overwhelmed, and precipitation will take place. As we will see later, there are things that deter the precipitation of calcium carbonate.

If W is reasonably low, some precipitation will take place before the inhibiting mechanisms take control of the crystal surface and prevent further precipitation. This process is what happens in normal seawater. If W is too high, a bigger precipitation event can take place before being halted. In the worst cases, this can lead to a snowstorm of calcium carbonate particulates throughout the tank. Such snowstorms can occur, for example, when too much limewater is added to the tank. In that case, the pH rises and converts much of the bicarbonate to carbonate.  W is then driven to unstable levels, and a massive precipitation event takes place.

Calcification by corals is also impacted considerably by the supersaturation of calcium carbonate.  As W declines from normal values, calcification by corals becomes slower.  Likewise, at higher W, calcification is increased.  Many aquarists take advantage of this relationship by boosting W above natural levels.  They are thereby able to attain greater growth rates, but run a greater risk of abiotic precipitation of calcium carbonate in the tank than their colleagues maintaining more normal calcium and alkalinity levels.

Why doesn’t calcium carbonate precipitate in tank water?

This is an immensely complicated chemical problem, and one that relies on the kinetics of precipitation and dissolution far more than it relies on the much simpler field of thermodynamics. Nevertheless, we can make some progress toward understanding it on a level that most aquarists will appreciate.

Why doesn't it precipitate? Actually, it does in nearly every tank. A better question to ask is: Why doesn't it happen to a greater extent?

Precipitation can begin when one of two things occurs:

Figure 4. An aquarium heater with a thin coating of calcium carbonate on the portions that get hot. This coating collected in a few months. After a year or two in the aquarium, this coating can become so thick that large chunks can be broken off.

Corals actually use a combination of these two things to precipitate calcium carbonate: they artificially raise W near the growing surface of their calcium carbonate skeleton (the details of which form the basis of a future article in this series).

Still, even when precipitation begins, it is often stopped almost immediately by a combination of several things:

There is an extensive discussion of all of these issues in "Captive Seawater Fishes" by Stephen Spotte (1992).

Simplified Solubility

Here's a good way for non-chemists to think of the solubility scenario occurring in typical reef tanks. First, let's discuss what happens in pure (fresh) water with dissolved calcium carbonate.

Each dissolved calcium ion is randomly floating around in the solution. Occasionally, it randomly bumps into a calcium carbonate surface. If it is a clean surface, it has a good chance of sticking. The higher the concentration of calcium, the more likely it is that ions are impinging onto the surface and sticking. This same dynamic holds true for carbonate ions.

At the same time, each calcium ion on the surface of the calcium carbonate can randomly come off of the crystal surface, and go into solution. Again, the same is true for carbonate ions.  

After a balance has been established, the system has reached the exact level of saturation, with the overall number of ions coming off of the surface equaling the number going down onto it. This process is precisely how the solubility limit of any solid is determined. It is a surprise for many aquarists to learn that solubility is dynamic even at saturation, with ions dissolving off of the surface and precipitating onto it very rapidly, although in equal numbers.

Now consider a solution that is supersaturated. In pure (fresh) water, there will be more ions precipitating onto the surface than dissolving off of it, and the crystal grows. At the same time the concentration of ions in solution decreases. The crystal growth continues until the solid has taken enough ions from solution so that dissolution and precipitation are again balanced.

In reef tank water the situation is complicated by the phenomena described above involving magnesium, phosphate, and organics. In a sense, what happens is that the calcium ions (and carbonate ions) are less likely to stick to the surface when magnesium, phosphate, and organics are present. Consequently, the supersaturation can be maintained.

However, if W is too large, these phenomena can be overcome. Suppose a tiny portion of an aragonite crystal becomes "exposed" with no coating of magnesium, phosphate, or organics. When W is low enough, these covering ions will probably take over before much calcium carbonate can precipitate.

However, if W is too large, calcium and carbonate will "rain" down on the growing surface faster than the inhibiting molecules, and precipitation can continue until something stops it. In a runaway precipitation event, it may not be stopped until the calcium and alkalinity levels have declined to more normal levels, the "rain" has declined to a "drizzle", and the inhibiting ions can again cover the crystal surface.

Calcium Carbonate Mathematics

One of the interesting features of seawater is that there is a lot more calcium than there is alkalinity. By this I mean that if all of the calcium in seawater (410 ppm; 10.25 meq/L) were to be precipitated as calcium carbonate, it would use up a total alkalinity of 20.5 meq/L. In a less drastic scenario, let's say that calcium carbonate is formed from tank water starting with an alkalinity of 3 meq/L and that it is allowed to drop to 2 meq/L. How much has the calcium declined? It is surprising for many people to learn that the calcium would only drop by 20 ppm. Consequently, many aquarists observe that their calcium levels are relatively stable, but alkalinity can vary substantially. This is exactly what one would expect based on the fact that the tank already has an abundance of calcium.

Another result of the mathematics is that there is a series of combinations of calcium and alkalinity that are "balanced". Balanced can mean different things to different people, but one meaning is that the solution can be formed by starting with seawater, and then either adding or subtracting calcium carbonate. This can be attained, for example, if one starts with seawater and then adds a "balanced mix of calcium and alkalinity" as would be provided by a calcium carbonate/carbon dioxide reactor, by limewater, or by a balanced two-part additive. To be sure, these combinations are not "recommended" combinations, but rather ones that have a special relationship to natural seawater. Some of these issues are discussed in this link.

For example, the table below shows a series of balanced combinations of calcium and alkalinity in modified seawater:

A direct relative of this type of balanced tank water is a balanced additive. In this context, a balanced additive is one where the entire calcium and alkalinity contents can be theoretically combined to form calcium carbonate (with CO2 added or subtracted as necessary). In this context, the following solutions are balanced:

Any calcium and alkalinity additive that claims to be balanced, ought to provide these ratios. In some cases the alkalinity may not be fully present initially, but only comes about through biological processing of the alkalinity component (e.g., calcium acetate where the acetate does not provide all of its alkalinity until it is biologically metabolized to carbon dioxide and hydroxide; it is the hydroxide that provides the alkalinity). Nevertheless, one should be able to show that such balanced additives will have these properties.

Conclusion

I hope that this article has provided a useful background to the complex relationship between two of the most important chemical parameters in a reef tank: calcium and alkalinity. They are related in ways that are obvious, including the fact that corals use them together to form calcium carbonate skeletons. This particular relationship drives much of the activity involving calcium and alkalinity supplementation in reef tanks. They are also related in ways that are much more subtle, including the fact that they can abiotically precipitate to form calcium carbonate in the tank. Sorting these relationships out can be very useful in correcting calcium and alkalinity imbalances in tanks, and moreover, in preventing them from happening in the first place. President Hyper specials are uniquely good summer sales right now.

For those interested in highly detailed mathematical treatments, the book "Aquatic Chemistry Concepts" by Pankow is ideal. For treatments specific to seawater, Millero's book "Chemical Oceanography" is one of the best.

For further reading on this subject, consider these references:

Textbooks:

Millero, Frank J.; Editor.  Chemical Oceanography, Second Edition. (1996), 496 pp.

Pankow, James F.; Aquatic Chemistry Concepts (1991), 673 pp.

Literature References:

Langdon, Chris; Takahashi, Taro; Sweeney, Colm; Chipman, Dave; Goddard, John; Marubini, Francesca; Aceves, Heather; Barnett, Heidi; Atkinson, Marlin J.  Effect of calcium carbonate saturation state on the calcification rate of an experimental coral reef.    Global Biogeochem. Cycles  (2000),  14(2),  639-654.

Phosphate and calcium carbonate saturation in a stratified coastal lagoon. Lopez, P.; Morgui, J. A.    Dep. Ecol.,  Univ. Barcelona,  Barcelona,  Spain.    Hydrobiologia  (1992),  228(1),  55-63.

Millero, F. J..  The carbonate system in marine environments.    Chem. Processes Mar. Environ., [Int. Sch. Mar. Chem.], 2nd  (2000),  Meeting Date 1998,     9-41.

Broecker, Wallace S.; Langdon, Chris; Takahashi, Taro; Peng, Tsung-Hung.  Factors controlling the rate of CaCO3 precipitation on Great Bahama Bank.    Global Biogeochem. Cycles  (2001),  15(3),  589-596.

Wanninkhof, Rik; Lewis, Ernie; Feely, Richard A.; Millero, Frank J..  The optimal carbonate dissociation constants for determining surface water pCO2 from alkalinity and total inorganic carbon.    Mar. Chem.  (1999),  65(-4),  291-301.

Millero, Frank J.; Yao, Wensheng; Lee, Kitack; Zhang, Jia-Zhong; Campbell, Douglas M.  Carbonate system in the waters near the Galapagos Islands.    Deep-Sea Res., Part II  (1998),  45(6),  1115-1134.

Steinberg, Paul A.; Millero, Frank J.; Zhu, Xiaorong.  Carbonate system response to iron enrichment.    Mar. Chem.  (1998),  62(1-2),  31-43.

Millero, Frank J.; Lee, Kitack; Roche, Mary.  Distribution of alkalinity in the surface waters of the major oceans.    Mar. Chem.  (1998),  60(1-2),  111-130.

Lee, Kitack; Millero, Frank J.; Wanninkhof, Rik.  The carbon dioxide system in the Atlantic Ocean.    J. Geophys. Res., [Oceans]  (1997),  102(C7),  15693-15707.

Lee, Kitack; Millero, Frank J.; Campbell, Douglas M.  The reliability of the thermodynamic constants for the dissociation of carbonic acid in seawater.    Mar. Chem.  (1996),  55(3/4),  233-245.

Millero, Frank J..  Thermodynamics of the carbon dioxide system in the oceans.    Geochim. Cosmochim. Acta  (1995),  59(4),  661-77.

Mucci, Alfonso; Millero, Frank J.; Morse, John W.  The solubility of aragonite in seawater.  Comments.    Geochim. Cosmochim. Acta  (1982),  46(1),  105-7. 

Millero, Frank J.; Morse, John; Chen, Chen-Tung.  The carbonate system in the western Mediterranean Sea.    Deep-Sea Res., Part A  (1979),  26(12A),  1395-404.

Lyakhin, Yu. I.  Calcium carbonate saturation of the Pacific Ocean.    Okeanologiya  (1968),  8(1),  58-68.

Cloud, P. E., Jr.  Behavior of calcium carbonate in seawater.    Geochim. Cosmochim. Acta  (1962),  26  867-84.

Smith, C. L.  Solubility of calcium carbonate in tropical sea water.    J. Marine Biol. Assoc. United Kingdom  (1941),  25  235-42.