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In any chemical reaction, the coefficients of the reactants and products are
always multiples of some positive integer coefficients, which are called stoi-
chiometric coefficients .
This principle is a consequence of the fact that molecules are multisets of atoms
and the atoms in each molecule occur with an integer positive multiplicity, therefore,
for the conservation principle, the multisets of atoms corresponding to molecules
have to occur with positive integer multiplicities. The Italian scientist Avogadro
introduced a number as a standard value for indicating a population of molecules.
Its value corresponds to the number of hydrogen molecules contained in one gram
of this substance, its value was estimated as (the two digits between parentheses are
the standard deviation of the last two digits):
10 23
6
.
02214179
(
30
) ×
.
A concrete example of stoichiometric coefficients, for balancing a chemical reac-
tion, is given by one of the most important reactions for life. The sugar glucose
C 6 (
) 6 and oxygen O 2 are formed from water H 2 O and carbon dioxide CO 2 ,by
means of chlorophyll synthesis. In this case, the stoichiometric coefficients which
provide the chemical balance are the following (the light energy is converted into
the chemical energy of glucose, which, burning in presence of oxygen, reverts the
process by producing energy):
H 2 O
+
(
)
+
.
6 CO 2
6 H 2 O
C 6
H 2 O
6 O 2
6
1.5
Liposome Membranes
If we need to put together a number of molecules of some types, we need to collect
them in a space containing them. A realization of this compartmentalization is bio-
logically provided by liposomes . They are membranes realized in a very simple and
efficient manner, by using a special kind of organic molecules, called p hospholipids,
which, put in the water, are subjected to two opposite forces. In fact, they are asym-
metric, with one head and one tail. The head part is hydrophilic, while the tail part is
hydrophobic. In the water, they can solve the hydrophilicity versus hydrophobicity
contradiction by aggregating each one, side by side, in such a way that all heads re-
main externally in contact with water, while the tail of any phospholipid is opposite
to the tail of another phospholipid (see Fig. 1.1). In this way, a “bilayer” structure is
realized, where tails remain dry, while heads are wet.
The emergence of life requires that a number of reactions may work, and persist
for some time. Reactions need membranes where reactants are collected as multisets
 
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