Energy and Human Ambitions on a Finite Planet, 2021a

B.3 Chemical <strong>Energy</strong> 380
to ascertain a net energy value. We’re going to take a shortcut to all
that, by introducing the following approximate formula for combustion
energy.
The approximate energy available from the compound C c H h O o N n —
where the subscripts represent the number of each atom in the molecule
to be burned—is:
This empirical formula can serve as a general
guide, but should not be taken as a
literal truth from some profound derivation.
It captures the main energy features
<strong>and</strong> produces a useful, approximate result.
c + 0.3h − 0.5o
100
12c + h + 16o + 14n kcal/g.
(B.1)
For instance, sucrose has the formula C 12 H 22 O 11 ,sothatc 12, h 22,
o 11, <strong>and</strong> n 0. The denominator in the formula is just the molar
mass, 16 or 342 in this case. The numerator adds to 13.1, so that the result
is 3.8 kcal/g—very close to the expected value around 4 kcal/g for a
carbohydrate like sugar.
The numerator of Eq. B.1 tells us that we get the most energy from each
carbon atom, 30% as much from each hydrogen atom, <strong>and</strong> take a 50%
hit (deduction) for each oxygen atom. Nitrogen is energetically inert
<strong>and</strong> does not contribute to the numerator—while degrading the energy
density by adding mass in the denominator. The negative coefficient for
oxygen tells us something important. Since combustion is a process of
joining oxygen to atoms in the fuel, the presence of oxygen already in the
fuel means it is already partly “reacted” <strong>and</strong> has less to offer in the way
of new oxygen bonds.
We can explore the sensibility of Eq. B.1 by testing it on some known
boundary cases. 17 Since one ubiquitous end-product of combustion is
CO 2 , calculating for CO 2 should offer no energy to us, since it’s a “waste”
product at the end of the energy process. H 2 O, as another common
combustion product, is likewise effectively neutralized in the formula
(the result is at least made to be very small). Table B.1 provides some
examples of what Eq. B.1 delivers for familiar carbon-based substances.
Note that oxygen content (last column) drives energy down, while
hydrogen offers a boost.
substance formula Eq. B.1 kcal/g true kcal/g %C %H %O
glucose C 6 H 12 O 6 3.7 3.7 40 7 53
typ. protein C 5 H 10 O 3 N 2 4.4 ∼ 4 41 7 52
coal C 8.3 7.8 100 0 0
typ. fat C 58 H 112 O 6 9.8 ∼ 9 77 12 11
octane C 8 H 18 11.8 11.5 84 16 0
methane CH 4 13.8 13.3 75 25 0
16: The coefficients in the denominator reflect
the fact that carbon is 12 units of mass,
oxygen is 16, etc.
17: This is a generically useful practice: it
helps integrate new knowledge into your
brain by validating the behavior in known
contexts. Does it make sense? Can you accept
it, or does it seem wrong/suspect?
Experts often apply new tools first to familiar
situations whose answers are known to
build trust <strong>and</strong> competence using the new
tool before applying it more broadly.
Try it out, using c 1 <strong>and</strong> o 2.
Try this one, too, coming up with
your own values for h <strong>and</strong> o.
Table B.1: Example approximate chemical
energies. The results of the approximate
formula are compared to true values (favorably).
Fractional mass in carbon, hydrogen,
<strong>and</strong> oxygen also appear—emphasizing the
penalty for molecules already carrying oxygen.
The resulting calculated energies are definitely in the right (expected)
ranges. Notice that the “winners” have little or no oxygen as a percentage
of the total molecular mass. The lower-energy entries in Table B.1 are
more than half oxygen, by mass.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.