E06 - E07 - E08 The equilibrium law

Aim: 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.

Illustration 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.

The degrees 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 reaction?
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 reaction conditions.

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.

Derivation 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 E06.

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 :
ð to put the product equilibrium concentrations in the
    numerator
ð to put the reactant equilibrium concentrations in the
    denominator

 

  
Each of these concentrations is raised to a power determined by the stoichiometric number of the particular reactant or the particular product in the reaction equation.

REMARKS
ð
 It is clear that this constant can not be regarded an absolute value, it being only constant within experimental error (statistical average).
ð
 The value of this constant is mostly dependent upon the units used for concentration. According to convention the concentrations are expressed in mol/L, so that from a thermodynamic point of view, the equilibrium constant is dimensionless  


This expression is represented by the equilibrium constant Kc. For the NO2-dimerization reaction:

Extensive research of a wide range of equilibrium reactions has established that for homogeneous equilibrium reactions according to the general equation :

The following general expression holds :

This is a simple expression easily derived from the full equation describing the reaction.
ð
 This expression is independent of the way in which the equilibrium of a specific reaction is achieved. The equilibrium constant is a quantity, which describes the concentration of reactants and products at the final stage in the equilibration process, but not therate at which equilibrium is achieved.
ð
 For homogeneous reactions in a solvent, international convention dictates that the almost constant concentration of any solvent present, e.g. water, is not included in the Kc-expression.

A second example

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 conditions

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.

BEWARE:

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 E27).
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.