Energy and Human Ambitions on a Finite Planet, 2021a

B.2 Stoichiometry 377
hydrogen
atom
oxygen
atom
carbon
atom
oxygen
molecule
water
molecule
H O
C
O O
H O H
H 2
O
O 2
carbon dioxide
molecule
methane
molecule
ethanol
molecule
O
C
CO 2
O
H
H
C
H
CH 4
H
H H
H C C O H
H H
C 2
H 6
O or C 2
H 5
OH
Figure B.2: Representing atoms as colored
spheres for schematic purposes, we can depict
the general appearance of molecules as
bonded collections of atoms. Here, we have
three elements—hydrogen, oxygen, <strong>and</strong>
carbon—combined into familiar molecules.
Oxygen in the air we breathe is self-bonded
into a “diatomic” molecule. Two representations
appear below each molecule: a diagram
indicating bonds (including doublebonds
in some cases), <strong>and</strong> the chemical
formula.
electron to share), oxygen has two (wants to “borrow” two electrons to
feel good about itself), <strong>and</strong> carbon tends to have four (either donating
four in the case of CO 2 , or accepting four when bonding to hydrogen).
The chemical formula for each uses elemental symbols to denote the
participants <strong>and</strong> subscripts to count how many are present. 9
Now we come to a bedrock practice in chemistry called stoichiometry—
which boils down to counting atoms in a reaction to make sure no atoms
are missing or spontaneously appear. To get a sense of this, see Figure
B.3 for two examples. The graphical version captures the physical reality,
so that simply counting the number of spheres of each color on the
left <strong>and</strong> right had better match. Below each graphical reaction is the
associated chemical formula. Each formula contains an arrow indicating
the direction of the reaction (separating “before” <strong>and</strong> “after”). Numerical
factors (coefficients, or prefactors) in front of a molecule indicate how
many molecules are present in the reaction. To get the total number
of atoms represented, we must multiply the subscript for that atom
(implicitly 1 if not present) by the prefactor. 10
Example B.2.1 Let’s figure out a tougher formula, pertaining to the
combustion of ethanol (depicted in Figure B.2). In this situation, we
combine a C 2 H 6 O molecule with some number of oxygen molecules
(O 2 ), <strong>and</strong> the reaction products will be CO 2 <strong>and</strong> H 2 O (carbon dioxide
<strong>and</strong> water). Our job is to figure out how many molecules are needed
to balance the reaction:
9: Two variants are shown for ethanol. The
first is a no-nonsense census of the atoms,
while the second pulls one of the H symbols
to the end to call attention to the OH (hydroxyl)
tagged onto the end of the molecule.
In either case, the formula specifies 2 carbons,
6 hydrogens, <strong>and</strong> 1 oxygen, in total.
10: For example, 2H 2O has a total of 4 hydrogen
atoms <strong>and</strong> 2 oxygens.
C 2 H 6 O + ?O 2
→ ?CO 2 + ?H 2 O
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.