9.21 Biochemical Reactions
393
More generally, given the reaction
J
ν J {M J } = {0} ,
(9.194)
where M J is the molecule symbol, then each of the additive conservation laws can
be expressed symbolically as
J
ν J {m J } = − {q} ,
(9.195)
with {m J } as an ordered set of numbers giving the amount of the conserved quantity
in the molecule, ion, or electron of component type J . The quantity q is the amount
of the conserved quantity released into the environment. If the conserved quantity
is expressed in terms of basic units, the size of those units is not made explicit, as
each side of the equation can be divided by that basic unit. For quantities that are
quantized by integers times a basic unit, one can use just the integers in the balance
equation.
One conserved and quantized count is the number each particular atom in the
molecule. The number of each kind of atom is conserved during a reaction because
of baryon number conservation and the fact that atomic nuclei are not transformed
by a chemical reaction. Because chemical energies are much less than the binding
energies stored in atomic nuclei, balancing of atomic kind in a chemical reaction
also ensures that mass will be practically unchanged. Energy as an additively
conserved quantity can then be applied to the chemical energy stored in each type of
molecule and to the energy released or absorbed in the reaction. Electric charge too
must additively balance. (For chemical reactions, charge conservation and baryon
number conservation will automatically account for lepton number conservation.)
Total charge conservation reads:
J
ν J Q J + ν e (−1) = 0 ,
(9.196)
where Q J is the number of charges on molecule of type J , including sign (if Q J is
non-zero, the molecule type would be called ionic), and ν e is the number of electrons
in the balanced reaction, with negative numbers for the electrons on the reactant
side, and positive for those on the product side (in conformity with the convention
on the stoichiometric numbers).
For example, in the oxidation of water,
2 H 2 + O 2 → 2 H 2 O ,
(9.197)
we have ν 1 = −2, ν 2 = −1, and ν 3 = 2. The conservation of atoms for each species
in this reaction can be expressed as
393
More generally, given the reaction
J
ν J {M J } = {0} ,
(9.194)
where M J is the molecule symbol, then each of the additive conservation laws can
be expressed symbolically as
J
ν J {m J } = − {q} ,
(9.195)
with {m J } as an ordered set of numbers giving the amount of the conserved quantity
in the molecule, ion, or electron of component type J . The quantity q is the amount
of the conserved quantity released into the environment. If the conserved quantity
is expressed in terms of basic units, the size of those units is not made explicit, as
each side of the equation can be divided by that basic unit. For quantities that are
quantized by integers times a basic unit, one can use just the integers in the balance
equation.
One conserved and quantized count is the number each particular atom in the
molecule. The number of each kind of atom is conserved during a reaction because
of baryon number conservation and the fact that atomic nuclei are not transformed
by a chemical reaction. Because chemical energies are much less than the binding
energies stored in atomic nuclei, balancing of atomic kind in a chemical reaction
also ensures that mass will be practically unchanged. Energy as an additively
conserved quantity can then be applied to the chemical energy stored in each type of
molecule and to the energy released or absorbed in the reaction. Electric charge too
must additively balance. (For chemical reactions, charge conservation and baryon
number conservation will automatically account for lepton number conservation.)
Total charge conservation reads:
J
ν J Q J + ν e (−1) = 0 ,
(9.196)
where Q J is the number of charges on molecule of type J , including sign (if Q J is
non-zero, the molecule type would be called ionic), and ν e is the number of electrons
in the balanced reaction, with negative numbers for the electrons on the reactant
side, and positive for those on the product side (in conformity with the convention
on the stoichiometric numbers).
For example, in the oxidation of water,
2 H 2 + O 2 → 2 H 2 O ,
(9.197)
we have ν 1 = −2, ν 2 = −1, and ν 3 = 2. The conservation of atoms for each species
in this reaction can be expressed as