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# How to get an enthalpy of formation from ab initio calculations

## Conversion from 0 K to 298 K

To convert from 0 K to some other temperature we again need to define a reaction. This time the reaction involves the elements in their standard states. For C2H4 we have the reaction:
C2H4 = 2 C(s) + 2 H2(g) We have the enthaply of formation at 0 K of 61.1 kJ/mol for C2H4. (From the HF/6-31G* calculation on the previous page.) Because the products of this reaction are standard states their enthalpy of formation is defined as 0 kJ/mol. We use the integrated heat capacities to convert the reaction energy to 298 K. The integrated heat capacities we obtain from the calculation using standard statistical thermodynamics. (See section I.D. A brief description of the thermochemical quantities and methods.) Section III.A.3 lists entropies and integrated heat capacities for the species and calculations in the CCCBDB and the experimental values for the elements in their standard states are listed in section II.B.

reactant products reaction total
Species C2H4 2 C(s) 2 H2(g)
Enthalpy of formation at 0 K (kJ/mol) 61.1 0 0 -61.1
Integrated Heat Capacity 0 K to 298 K (kJ/mol) 10.502 2 × 1.050 2 × 8.468 8.534
Enthalpy of formation at 298 K (kJ/mol) 52.6 0 0 -52.6