To show on the basis of results from NO2-dimerization
that, for a specific reaction at a particular temperature, an equilibrium
constant governs the equilibrium regardless of the initial concentrations.
To derive the equilibrium constant.
E06 gives the initial ([ ]i) and equilibrium
([ ]e) concentrations of NO2 and N2O4
at 25 °C for five different NO2-dimerization experiments :
A, B, C, D and E.
The results for experiments A, B and C have already been shown in illustration
E01. The initial
NO2-concentrations in experiments A, B and C are very similar, whereas
those in experiments D and E are much lower.
of conversion, a, of NO2 for these
five experiments vary with NO2-concentration. How is it that
the degree of conversion can vary significantly for a particular equilibrium
It is true that these equilibrium mixtures are reached from different
initial concentrations, but the final equilibrium temperature is the same
in all five cases.
Taking account of the different initial NO2-concentrations,
can a fundamental relationship be found which governs the NO2-dimerization
equilibrium reaction at 25 °C?
Scientists are, in general, always looking for underlying relationships
with which to explain such observations.so that fundamental relationships
can be derived with a more general applicability. One only has to think
of the search for a fundamental law governing gravitational forces, coulombic
forces, nuclear forces and cosmic forces, thereby producing a law underlying
these different forces.
So it was, that in the second half of the nineteenth century eminent scientists,
such as van 't Hoff, Guldberg and Waage, were pondering the possibility
of a fundamental relationship underlying the phenomenon of chemical equilibrium,
which could be used to predict the equilibrium concentrations and degree
of conversion for particular initial reactant concentrations under particular
Their experimental and theoretical work was eventually, after much trial
and error, rewarded with the discovery of an underlying fundamental law
with numerous practical applications.
of the relationship
Is there a
fundamental quantity, which characterizes all ossible equilibrium mixtures
for a specific equilibrium reaction under particular conditions? This
is not the degree of conversion as it varies with initial NO2-concentrations,
but perhaps a related expression.
In illustration E08, five possible expressions are tested:
None of them
produce a constant value for all five experiments.
Eventually, by trial and error and perseverance, an expression can be
found which produces values which vary round a value of 222
This is shown
in illustration E07, which can be used as an overlay with illustration
It is possible
that another relationship can be found, or a variant thereof (e.g. the
reciprocal or the square root), but a relationship does exist.
Thus for the specific case of a homogeneous equilibrium reaction one or
more relationships have been found which produce a constant value for
any variant of this equilibrium reaction at a particular temperature,
regardless the initial concentrations of the reactants and products.
The form of the relationship agreedly international convention is :
to put the product equilibrium concentrations in the
to put the reactant equilibrium concentrations in the
Fe(III)-ions and iodide-ions on the one hand and Fe(II)- ions and iodine
on the other hand can set up different equilibria in water. Two are shown
in illustration E03, one from the reactants and the other from the reaction
products. The corresponding expression for the equilibrium constant is
In practice, solid iron(III) chloride and potassium iodide or iron(II)
chloride and iodine can be added to water to realize equilibrium mixtures.
The general equilibrium law or equilibrium
For any equilibrium reaction, the equilibrium concentrations inserted
in the appropriate Kc-expression always give the same
value. This holds, regardless of the initial composition of the mixture,
when equilibria are compared at the same reaction temperature.
Conversely, whether or not a reaction mixture is at equilibrium can be
established by inserting the concentrations of reactants and products
into the appropriate expression for Kc and comparing the value obtained
with the known value of Kc for that reaction at that particular temperature.
The equilibrium law or the equilibrium constant are in thefirst instance
derived from the thermodynamics of the reaction, the value of the equilibrium
constant Kc depending entirely upon the characteristics
of the reactants and these of the reaction products (see illustration
Rate of reaction and reaction mechanism are kinetic aspects of the reaction.
They have nothing to do with the expression for Kc
or with the value of Kc. It would be simplistic and
imprudent to assume all sorts of unrealistic reaction equations to obtain
an expression for Kc.