The element carbon is found in various forms that concern OpenAir. It is elemental carbon in coal and biochar. It is “reduced” in some organic molecules, represented in this article by methane and partially oxidized in others, such as alcohols. It is further oxidized in carbon dioxide and carbonate minerals. These different occurrences of carbon are separated by differences in chemical energy. Processes that lead to the chemical transformation of carbon from one condition to another are described by thermodynamics as “path independent” - that is, if you start with elemental carbon at some condition and end with carbon dioxide at some new condition, it does not matter HOW you do that - what path you take - the overall energy change in the chemical itself is the same. The overall process efficiency may not be the same, some paths in the real world could consume more energy than others to acheive the same endpoint.
CO2 - 44.0 g/mol; 1.977 kg/m3 gas density at 0C, 1atm; specific heat 37.135 J/mol*K (CRC Handbook and Lange’s Handbook of Chemistry via Wikipedia)
| chemical | formula | physical state | carbon oxidation | enthalpy of formation at 25C (kJ/mol) | Source |
|---|---|---|---|---|---|
| methane | CH4 | gas | - 4 | -74.6 | CRC Handbook, ISBN 9781498754293 |
| ethane | C2H6 | gas | -3 | -83.85 | Standard_enthalpy_change_of_formation_(data_table) |
| coal | C | solid | 0 | 0 | |
| formal-dehyde | CH2O | gas | 0 | -109.15 | Formaldehyde Enthalpy of Formation |
| glucose | C6H12O6 | solid | 0 | -1172.4 | Glucose (CAS 50-99-7) - Chemical & Physical Properties by Cheméo |
| methanol | CH3OH | liquid | +2 | -238.42 | Methanol Enthalpy of Formation |
| methanol | CH3OH | gas | +2 | -201.08 | |
| formic acid | HCOOH | liquid | +2 | -424.82 | Formic Acid Enthalpy of Formation |
| carbon dioxide | CO2 | gas | +4 | -393.5 | CRC Handbook and Lange’s Handbook of Chemistry via Wikipedia |
| calcium carbonate | CaCO3 | solid | +4 | -1207.6 | Calcium carbonate standard enthalpy - Big Chemical Encyclopedia |
| water | H2O | liquid | -292.74 | Water Enthalpy of Formation | |
| water | H2O | gas | -24.75 | ||
| calcium oxide | CaO | solid | -635.09 | ||
| calcium hydroxide | Ca(OH)2 | solid | -987 | Chemical Principles, Zumdahl, ISBN 9780618946907 |
Enthalpy of formation can give a basic idea of the energy requirements for a chemical reaction. Elements in their “standard state” - the phase in which they would be found at room temperature most commonly - have enthalpies of formation (Hf) of zero. So reactions that are “downhill” or negative, are reactions that are energetically favorable. This does NOT mean the reactions will actually occur. But if one knows the product can be synthesized, then determining the reaction energy from adding up other known reactions is valid. For example, formaldehyde is CH2O, and it looks like that might be a substance that could be formed from carbon and water. Carbon is an element so it has Hf = 0, liquid water has Hf = -293, and formaldehyde has Hf = -109. The reaction C + H2O = CH2O would therefore have a net reaction enthalpy found by the sum of products Hf minus the sum of reactants Hf: -109 - ( 0 + -293) = +184
This tells us that the reaction we proposed for making formaldehyde from carbon and water would also require the addition of some energy and would therefore be unlikely to occur spontaneously (although there are a few “endothermic” reactions - enthalpy of reaction is not the whole picture). A closer look at the Hf table reveals that water has two entries, one for liquid and one for gas. The difference between these two values represents the “enthalpy of vaporization” for water - some energy must be added to liquid water to make it enter the gas state. More importantly for our analysis though, it suggests that our proposed reaction for making formaldehyde would be more favorable if water were in the gas phase for the reaction. The net reaction enthalpy would be: -109 - ( 0 + -25) = -84
In reality, water vapor does not react spontaneously with carbon to form formaldehyde. Despite that the product has lower energy than the reactants, there exist one or more intermediate conditions or structures that are too unlikely to form, or require too much energy to create using processes currently known (albeit the energy barriers, once surpassed, return that excess energy). But based on the Hf values, the reaction is at least favorable from an energy standpoint.
If we consider the Hf for carbon dioxide, it is a relatively larger negative number than the various organic forms of carbon in the table. This comports with our experience that these organic substances will readily burn in the presence of oxygen to produce carbon dioxide. The reactions proceed spontaneously. We can use the Hf values to determine the minimum theoretical energy inputs we would expect to synthesize these organic compounds from carbon dioxide. As in the case of the fictitious formaldehyde reaction above, the minimum theoretical energy might still not gain us an actual synthesis reaction. There might be additional barriers to overcome.
Enthalpy of reaction calculation is one basic tool for assessing the possibilities when exploring chemical synthesis routes.