One of the assumptions made in chemical kinetics is that the
number of atoms is preserved, i.e. atoms are neither created
nor destroyed. For example, if there are 
atoms
of Oxygen, 
, present before the reaction begins, then there
will be the same number, , of atoms of Oxygen during all
stages of the reaction. This is illustrated by the following
stoichiometric equation describing the decomposition of
nitrous oxide (a gas) into nitrogen and oxygen gases (do not
confuse the nitrogen and oxygen gases, 
and 
, with the
elements Oxygen, , and Nitrogen, 
):
The following reactions take place inside certain types of automobile
catalytic converters, based on the oxidation reaction of 
,
hydrocarbons and 
(the purpose is to avoid pollution by carbon
monoxide):
Note the conservation of atoms of C, H and O. Another common reaction takes place whenever you take an ...:
Suppose 
moles of 
react with 
moles of 
to produce
moles of 
and 
moles of 
:
Let 
, 
, etc. represent the molar amounts of the
chemical species in the reaction (measured in kmol, for
example). Recall that the derivative of a quantity with respect
to time, 
, expresses the instantaneous rate of change of
that quantity (positive if it is increasing at that instant,
negative if it is decreasing) at that time.
Let V be the volume occupied
by the reaction mixture (measured in liters). Usually the rate
of reactions is expressed in terms of change of molar amount per
unit volume of the reaction mixture. Thus, the rate of reaction
of the species A is expressed as:
Let's denote the
concentration of each species (measured in kmoles per liter) by a
square bracket: [A] denotes the concentration of , [B]
denotes the concentration of , etc. Then
When the reaction volume does not vary (density remains constant),
are simply the rates of change of the concentrations of ,
.
Since the number of atoms is preserved, the rates at which
and are produced are directly related to the rates at
which and are depleted. Consider only species
and , for the moment. For every moles of that
react, moles of are produced. Thus, for each mole
of that reacts, 
moles of appear. It should
now be clear that the rate of change of [C] is times
the rate of change of [A]. We need only account for the
fact that the signs are reversed (as [A] decreases, [C]
increases). Mathematically this is expressed as
You can reason the same way with any pair of species to conclude that
and any of the (equal) numbers above can be taken to define the reaction rate. Indeed, it is a good measure of the speed of the reaction.
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