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The Thermodynamic Sinks of this World

What would an elemental soup cook up to?

Roald Hoffmann

Thermodynamic Sinks

Let’s use some simple chemistry to get a feeling for the thermodynamic sinks of this world. We are looking for compounds with the most negative heats of formation. A heat of formation is defined as the enthalpy change (under standard terrestrial conditions, P = 1 atmosphere, T = 298 kelvin) for the process

A + B + C ↔ ABnCm,

where A, B and C are the elements and ABnCm a compound. Here it is a ternary, but the generalization is obvious.

Let’s start with carbon and oxygen. The well-known oxides of carbon are CO, CO2, and carbon suboxide, C3O2. Other oxides, CnO2, n = 2–7; CnO, n > 2; and CnOn, n = 2–6, are also experimentally known in small amounts, trapped in an inert matrix at low temperatures. The heats of formation of the oxides available in quantity are –110 (CO, [g]), –394 (CO2, [g]), –122 (C3O2, [l]) kJ/mol, respectively. Note the negative heats of formation, indicating stability with respect to the elements. Here is the first principle of stability, one we have already seen in the reaction forming water: Form oxides. This is confirmed for every element, except the noble gases. And gold. Incidentally, quartz, SiO2, is “better” than CO2, for the heat of formation of the former is a whopping –911 kJ/mol.

One oxide of carbon, CO2 , is much more stable than the others. This can be checked by calculating from the above heats of formation the energetics of all possible interconversion reactions, for example, CO2 ↔ CO + ½ O2, 3CO2 ↔ C3O2 + 2 O2 and so forth, and finding them all positive, endothermic.

But … if one introduced a lot of Ca in the environment, the Ca would react with CO2 (enough heat supplied to overcome all barriers) to give CaCO3, calcium carbonate, limestone, a real thermodynamic sink:

Ca (s) + ½ O2 (g) + CO2 (g) ↔ CaCO3 (s) ΔH = –813 kJ/mol

Is this going to go on? That is, are we going to get in a mix of 100 or so elements (let’s not worry about the late actinides) a most stable compound of “multinary” composition, AxByCzDw…? I don’t think so. Metastable molecules with more than 10 elements are known, and solid state compounds of 9 elements at least. But I think both experience and intuition indicate that such multielement compounds are likely to be unstable with respect to disproportionation or reaction with oxygen.

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