We can get the formation reaction we are seeking by subtracting the first reaction from this one:
      2C(s) + 3H₂(g) + �O₂(g) � CH₃CH₂OH(g)
      DH = (+715.1) - (+771.7) = -56.6 kcal per mole of ethanol

Compare this with the value of -56.3 kcal mole-1 from the table of measured heats of formation given on Page 22. Accuracy to within one kilocalorie is considered quite good. We can see what is going on physically by means of the energy level diagram opposite.

The isolated C, H, and O atoms are in a state 715.1 kcal higher in energy than graphite crystals and H₂ and O₂ gases, because 715.1 kcal are required to produce the separated atoms. In turn, because the calculation from bond energies showed that 771.7 kcal are required to tear an ethanol molecule apart, the intact molecule must be 771.7 kcal lower in energy than the separated atoms. The observable heat of formation of ethanol molecules from elements (not atoms), unfortunately, is a small difference between two large numbers:

      DH = +715.1 - 771.7 = -56.6 kcal mole^-1

This is one reason for the relative inaccuracy of bond-energy calculations. A small percent error in a number the size of 700 means a much bigger percent error in the difference of 57.