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The Thermodynamic Sinks of this World

What would an elemental soup cook up to?

Roald Hoffmann


2013-07MargHoffmannFC.jpgClick to Enlarge ImageSo what are the real thermodynamic sinks of this world? The place to look is with simple compounds with highly negative heats of formation. We have already met four such: NaCl, H2O, CO2, CaCO3. Their heats of formation are –411, –286, –394, –1,207 kJ/mol. The prescription is obvious: Form oxides, form solid state, ionic compounds. The elements don’t stand a chance, except for the early noble gases (the heats of formation of the xenon fluorides are not large, but negative).

Following up the clue from the low heat of formation of calcite, one finds that all carbonates are very stable, as are most salts containing nitrate (NO3-), sulfate (SO42-), phosphate (PO43-) and silicate ions. For instance the heat of formation of calcium phosphate (Ca3(PO4)2) is –4,132 kJ/mol, that of Fe2(SO4)3 –2,583 kJ/mol. After a while one realizes that what matters is the heat of formation increment per atom, so these values become somewhat less spectacular than they seem. But they are large and negative, for sure.

The stuff of this Earth, minerals such as silicates, also have very highly negative heats of formation. Their presence in planetary bodies, including ours, is evidence to their stability. Much more needs to be said about the silicates, which constitute up to 90 percent of the Earth’s crust. These occur in a remarkable variety, with cations of every kind coordinating to [SiO4]4- (olivine, for example), [Si2O7]6- (epidote), [SinO3n]2n- (tourmaline), [Si4nO11n]6n- (hornblende), [Si2nO5n]2n- (clays and mica), [AlxSiyO2(x+y)]x- (zeolites; x = 0, y = 1 is quartz). Along this series, the degree of cross-linking or O-coordination increases. Thus olivine has isolated SiO4 tetrahedra, whereas the various forms of quartz feature an interlinked three-dimensional network of the same. This is the Bowen reaction series, and as one progresses along it, one gets silicates that crystallize at lower temperatures from a magma—are more stable.

There is a pattern emerging in the nature of the more stable compounds: It’s not simply ionic bonding (Na+Cl-, Li+H-), but ionic bonding between an alkali or alkaline earth cation and a molecular anion (CO32-, SiO44-). Of course, within each molecular ion there lurks ionicity—the bonds that connect the centering N or C or Si or S atoms to oxygen in these anions are polar. Ions within ions!

But there are compounds more stable than oxides, and these are fluorides—for example, CaF2, fluorite, or Na3AlF3, cryolite. In these even more ionicity is provided than in oxides. The thermodynamic stability of all ionic fluorides, the magnitude of their negative heats of formation per atom, is astonishingly high. This can be understood in a qualitative way: The energy required to break apart the element, F2 molecules, is small. The electron affinity the resulting F atoms is as large as they get. And the size of the F- anion is relatively small, so that one gets a lot of electrostatic stabilization in inorganic fluoride crystals (the so-called Madelung energy).

Also, in the temperature range where water is a liquid, a good number of salts, hardly all, dissolve in water with a negative Gibbs energy of solution. The entropy contribution to this Gibbs energy change is often large, if not dominant, for obvious reasons. I don’t think other polar solvent liquids (each with their own temperature range of stability), such as ammonia, SO2, HF or supercritical CO2, will provide as much stabilization as water does.

So my tentative answer to the question posed at the beginning is not romantic. The final product (at P = 1 atmosphere and 298 kelvin) will be a messy soup of cations of the less electronegative elements (including the transition metals) with molecular anions, in water. Some pretty insoluble salts of similar composition (minerals!) will be there. And the first few noble gases standing by, if they are not allowed to escape.

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