Solubility Constants

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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Gypsum, Cops and Robbers

A good simple geological example of mineral solution is calcium sulfate. Technically, pure calcium sulfate is anhydrite and the more familiar gypsum is hydrated calcium sulfate. Since we're talking about what happens in water, we can safely call the resulting product gypsum. We can picture what happens with the following analogy.

Let's imagine the Ca ions are cops and the SO4 ions are robbers. When a cop and robber meet, they get handcuffed together. However, occasionally a robber breaks free of the cuffs. The Ca+2 and SO4-2 combine to make [relatively] insoluble calcium sulfate, but some of the Ca and SO4 ions return to the solution. This little thought experiment reveals several points.

In the sketch above, some of the cops are distracted and robbers are hiding behind civilians. The interactions of the cops and robbers won't be the same as if there were only cops and robbers around.

If the cops and robbers are widely spread out, they'll rarely meet. Similarly, if the calcium and sulfate are both exceedingly dilute, they won't form a precipitate. If you put Ca and  SO4 in water in such small amounts that their concentrations don't multiply out to 2.4 x 10-5 or greater, gypsum won't form.

We can expect the number of arrests per unit time will be (cops/square mile)(robbers/square mile) = constant. The same thing is true of chemical reactions.

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. If it's less, the gypsum will dissolve.

 

If there are far more cops than robbers, pretty soon almost all the robbers will be arrested, even if there are very few of them. If the sulfate concentration is extremely dilute, but the calcium is extremely concentrated, a precipitate will still form.

If there are far more robbers than cops, pretty soon almost all the cops will have arrested a robber, even if there are very few cops. If the calcium concentration is extremely dilute, but the sulfate is extremely concentrated, a precipitate will still form.

 

At equilibrium, we'll have cops booking robbers until the number of cops and robbers on the loose drops low enough for meetings to be infrequent. We'll still have occasional cops bringing in robbers, but we'll also have robbers escaping (or being sprung by lawyers, or serving their time). On the whole we'll have about the same rate of arrests as releases or escapes. The number of cops and robbers per square mile will stay about constant.

Similarly, if we put a chunk of gypsum in a liter of water, it will dissolve until (Ca)(SO4) = 2.4 x 10-5. If there's nothing else in the water, the concentrations of Ca and SO4 will be equal and we'll have (Ca) = (SO4) = 2.4 x 10-5 = .005. There will be .005 moles of Ca (.005 x 40 = 0.2 grams) and .005 moles of SO4 (.005 x (32 + 4*16) = 0.48 grams). As rocks go, this is very soluble. A cubic meter of water (1000 liters = 1000 kg) will dissolve 680 grams of gypsum.

If you're in a temperate rainy climate where it rains a meter per year, you'll dissolve away 680 grams or about 300 cubic centimeters per square meter per year. That will remove 0.03 cm/year from the surface, or 30 cm/1000 years, or 300 meters per million years. In geologic terms, that's carving with a chain saw.

A gypsum pavement block from the Minoan site of Knossos, on Crete. In the century plus since the site was excavated it has undergone several centimeters of sulution.

Sizes of Solubility Constants

Generally, the larger the solubility constant, the more soluble the material is. The smaller the solubility constant, the less soluble it is. For example, the solubility constant of NaCl is 3.6. For extremely insoluble galena (PbS) it's 10-29.


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Created 03 April 2006, Last Update 14 December 2009

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