The Paradox of Carbonate Solution

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay

Ordinary Solution: Gypsum

The solubility constant of gypsum is 2.4 x 10-5. That means if you have solid gypsum in equilibrium with water, the concentration of Ca (in moles per liter) times the concentration of SO4 (in moles per liter) equals 2.4 x 10-5. Or:

(Ca+2)(SO4-2) = 2.4 x 10-5

If you add a lot of sulfate (say as sulfuric acid), there's a vastly increased chance of sulfate encountering a calcium ion, gypsum precipitates, and the concentration of calcium drops. If you add a lot of calcium (say adding calcium chloride), there's a vastly increased chance of calcium encountering a sulfate ion, gypsum precipitates, and the concentration of sulfate drops.

Bottom line: if you have a mineral in equilibrium with water, and you add one of its constituents to the water, you inhibit solution.

So how come carbon dioxide in water increases the solubility of carbonate rocks? That's exactly opposite to what we would expect from the case of gypsum.

Carbon Dioxide in Water

Let's look at the steps that take place when carbon dioxide dissolves in water:

  1. Most of the carbon dioxide stays in solution but about 0.4% of it combines with water to make carbonic acid, H2CO3. For purposes of carbonate chemistry, we can ignore the distinction and treat all the dissolved carbon dioxide as H2CO3.
  2. Carbonic acid is a weak acid and ionizes slightly to give H+ and HCO3- (bicarbonate ion).
  3. Bicarbonate ion ionizes a second time to give H+ and CO3-2 (carbonate ion).

That intermediate step makes a ton of difference. Add CO2 to the solution and you increase the amount of bicarbonate produced in Step 2, as well as the amount of hydrogen ion. That increases the acidity of the solution. Increase the amount of CO3-2  and you run reaction 3 in reverse and again create more bicarbonate ion.

Calcium Carbonate and Acid

Let's say you pour dilute hydrochloric acid on calcium carbonate. It fizzes. Why? We can pretty much ignore the roles of chloride ion and carbonic acid here. What happens?

  1. The calcite dissolves in the solution, liberating calcium and carbonate ions.
  2. Hydrogen ion combines with carbonate ions, creating bicarbonate ion.
  3. The reaction of a carbonate ion removes it from the solution, enabling another to take its place and also dissolving a calcium ion. This process will continue as long as there is a large excess of hydrogen ions.
  4. There's so much hydrogen ion that it combines with bicarbonate to make carbonic acid, which mostly breaks down to dissolved carbon dioxide and water.
  5. If there's a whole lot of hydrogen ion, it will create enough carbonic acid to exceed the solubility of carbon dioxide in water. The excess carbon dioxide forms bubbles. The dissolving calcium carbonate fizzes.

Calcium Carbonate and Surface Water

  1. Most of the carbon dioxide stays in solution but about 0.4% of it combines with water to make carbonic acid, H2CO3. For purposes of carbonate chemistry, we can ignore the distinction and treat all the dissolved carbon dioxide as H2CO3.
  2. Carbonic acid is a weak acid and ionizes slightly to give H+ and HCO3- (bicarbonate ion).
  3. Bicarbonate ion ionizes a second time to give H+ and CO3-2 (carbonate ion). Meanwhile ...
  4. Calcite dissolves in the water, liberating calcium and carbonate ions.
  5. Hydrogen ion combines with carbonate ions, creating bicarbonate ion. There is way more carbonate ion available than would normally be present due to reaction 3, so the equilibrium is pushed very much toward the direction of bicarbonate ion.
  6. The reaction of a carbonate ion removes it from the solution, enabling another to take its place and also dissolving a calcium ion. This process will continue as long as there is a supply of hydrogen ions, which there will be as long as carbon dioxide continues to dissolve in the water.
  7. Eventually equilibrium is reached The production of bicarbonate by ionization of carbonic acid is balanced by the amount reacting with hydrogen to make carbonic acid.

SC of CaCO3 = 4.8x10-9

SC of Gyps = 2.4 x 10-5

H * HCO3 - /h2CO3 = 4.3 x 10-7

H * CO3-- /hCO3 - = 4.7 x 10-11

CO2aq/cO2air = 0.034

Carbon Dioxide and Surface Water

In normal air, CO2 is 300 ppm or in other words exerts 3 x 10-4 atmospheres of partial pressure. Therefore we can expect the dissolved concentration of CO2 in water to be 0.034  x 3 x 10-4 = (10-5)

The term "carbonic acid" conventionally includes both dissolved CO2 and true H2CO3. Actually only 0.4% of the CO2 in solution goes into H2CO3; the rest is simply dissolved CO2. With that understood, we know

H * HCO3 - /(H2CO3) = 4.3 x 10-7

H * HCO3 - = 4.3 x 10-7 (H2CO3) = 4.3 x 10-7 (10-5) = 4.3 x 10-12

Since equal numbers of H and HCO3 ions form, we can write

H = HCO3 = sqrt(4.3 x 10-12) = 2.1 x 10-6

Note that in neutral water the concentration of H+ is 10-7, so this ionization results in 21 times as much hydrogen ion as is normally present. Thus we can safely ignore the original hydrogen ion concentration.

Log 2.1 x 10-6 = -5.7, or pH = 5.7

Therefore all water in equilibrium with the air is slightly acidic due to the presence of carbonic acid. This has nothing to do with acid rain.

The next breakdown is easy to calculate. We have

(H+)(CO3=) /(HCO3 -) = 4.7 x 10-11

Since (H+) = (HCO3 -), these two terms cancel out, leaving CO3-- = 4.7 x 10-11. Period. So regardless of whatever else is going on, in any solution containing carbonic acid, the CO3-- concentration is 4.7 x 10-11

Solution of Limestone on the Surface

We can't just take the solubility constant of calcite, the concentration of CO3, and calculate the concentration of dissolved Ca, because as we liberate CO3 from the limestone, some CO3 will react to form HCO3 and thence carbonic acid. Calcite will continue to dissolve until all three species are in equilibrium. The complete reaction, taking HCO3 into account, is

CaCO3 + H2O + CO2 (or H2CO3) <--> Ca++ + 2HCO3 -

We ignore excess CaCO3 and water in the calculation, and that leaves us with the need to determine (Ca++)(HCO3 -)2/(H2CO3)

We have

Putting them together to get Ca and HCO3 on top and H2CO3 on the bottom, we get

On the surface we can assume that whatever CO2 is consumed will be replaced from the air, so we have

Since each Ca combines with 2HCO3, obviously (HCO3) = 2(Ca), and we have

Thus a cubic meter of water (1000 kg = 1000 liters) could dissolve 0.48 moles of calcium (19 grams) or 48 grams of limestone.

In a warm rainy climate with 1 m of precipitation per year, we could dissolve 48 grams of limestone per square meter per year or about 18 cm3. That works out to .0018 cm of material removed from the surface per square meter, or 1.8 cm per 1000 years, or 18 meters per million years. That's actually slow compared to some observed weathering rates.

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Created 03 April 2006, Last Update