Introduction to Equilibrium 
Reverse Reactions and Chemical Equilibrium 
In all the preceding work on chemical kinetics, reaction rates
and mechanisms, attention has been focused upon chemical reactions which are
proceeding in one direction only (forward). You should realize, however that
many reactions are reversible, i.e. they can occur in either direction. In
particular, for a given forward reaction 

one can conceive of the reverse process 

Now if no product molecules L & M are present at the beginning
of a reaction, the reverse reaction may well be forgotten about until an appreciable
concentration of products builds up, since the rate of the reverse reaction
will be proportional to some product of the concentrations of L and M. In
general, however, the reverse reaction becomes important eventually, since
the forward reaction slows down with time (reactant concentrations being
reduced by conversion to products) whereas the reverse reaction rate increases
with time (as product concentrations build up). Eventually a point in time
is reached when the 

At this point CHEMICAL EQUILIBRIUM is achieved; unless the system
is disturbed by a temperature change or by adding excess reactant or product
molecules, the equality of rates is maintained as are the "equilibrium" concentrations
of all chemical species. The variation of reaction rates with time is illustrated
graphically as follows: 

In any chemical system, which a state of equilibrium is reached
the reaction seems to be stopped. The macroscopic visible properties that
we can see are constant. In reality the reactions are still taking place.

H_{2}(g) + I_{2}(g) <====>
2 HI(g) 
Both the forward and reverse reactions are proceeding at the
same rate when a reaction is in a state of equilibrium. 
The observable properties and concentrations of all participants
(species) become constant when a chemical system reaches a states of equilibrium.

A chemical system is said to be in a state of equilibrium if
it meets the following criteria: 
1. The system is closed. 2. The observable macroscopic properties are constant. 3. The reaction is sufficiently reversible so that observable properties change and then return to the original rate when a factor that affects the rate of the reaction is varied and then restored to it's original value. 
Let's consider in detail the forward and reverse processes for
some general "atom exchange" reaction 
AB + CD > AC + BD 
Assuming that the forward reaction occurs by a onestep bimolecular
mechanism, then 
Rate Forward Reaction = R_{f }= k_{f }[AB][CD]

Similarly, assuming that the reverse reaction also occurs by
a onestep mechanism 
Rate Reverse Reaction = R_{r }= k_{r }[AC][BD]

Now according to the "Principle of Microscopic reversibility",
the activated complex which must be achieved in the reverse reaction is
identical with activated complex for the forward reaction;
thus the energy profile for the forward and revers reactions can be illustrated
by the same plot: 

In the graph above, E_{f }represents the activation
energy for the forward reaction and E_{r }that for the reverse;
since the activated complex is identical for both directions it follows that

H = E_{r } E_{r} 
Thus, if the reaction is exothermic (as shown), the activation
energy for the reverse reaction must be greater that for the forward
reaction. If the reaction is endothermic, the converse is true.
If H = 0 then E_{f }= E_{r}. 
Returning to the rate law constant expression, we know that
at equilibrium 
R_{f }= R_{r} 
therefore k_{f}[AB]_{e}[CD]_{e} = k_{r}[AD]_{e}[CB]_{e}

where the subscript e denotes equilibrium concentrations. By
rearrangement we can obtain the expression 
[AD]_{e}[CB]_{e}_{ }=
K_{f}= a constant Keq, the Equilbrium Constant
[AB]_{e}[CD]_{e} K_{r} 
The relationships derived above for a particular reaction type
are, in fact, completely general for any reaction regardless of its
complexity or mechanism. That is, for any reaction in which the forward and
reverse reaction rates have achieved equality (equilibrium as denoted by
a double arrow), 
aA + bB <> lL + mM 
then the product of the equilibrium concentration of the products,
each raised to its coefficients in the balanced equation, divided by the product
of the equilibrium concentrations of the reactants, each raised to its coefficients
in the balanced equation, is a characteristic constant for the system.


Before leaving this topic, one paradox" should be cleared up
 that is, the appearance of coefficients in the balanced equation as the
concentration exponents in K, whereas as I have emphasized earlier in the
rate unit, the exponents in the rate laws for the forward and reverse reactions
need not equal these coefficients unless the reaction proceeds by a singlestep
mechanism. The paradox is resolved by considering the particular reaction

AB + C > AC + B 
Where the reaction mechanism is deduced from the initial rate
data is 
AB > A + B (slow) 
A + C > AC (fast) 
to yield a rate law for the forward direction R_{f }=
k[AB] 
Now if true chemical equilibrium has been achieved in the system,
it must follow that EQUILIBRIUM HAS ALSO BEEN ESTABLISHED IN EVERY STEP OF
THE REACTION. That is, at equilibrium the reverse of each step is also important,
so the mechanism is 
step 1 AB >
A + B R_{1 }= k_{1}[AB] 
step 2 A + B > AB R_{2 }= k_{2}[A][B]

step 3 A + C > AC R_{3 }= k_{3}[A][C]

step 4 AC >
A + C R_{4 }= k_{4}[AC] 
Now since R_{1 }= R_{2} at equilibrium,

k_{1}[AB] = k_{2}[A][B] 
and since R_{4 }= R_{3 }at equilibrium,

k_{4}[AC] = k_{3}[A][C] 
By equating the ratio of the lefthand sides of the two equations
to the ratio of the righthand sides, we obtain 

or upon rearrangement 

(Note that the concentrations of the intermediate species cancel
out.) 
Therefore, even though the reaction proceeds by a multistep
mechanism, we have proved in this case (and can prove it for any other
particular case) that the ratio of product to reactant concentrations,
each raised to the corresponding coefficient in the balanced overall equation,
is still a constant K_{eq} characteristic of the reaction if
complete equilibrium has been established. Thus there is no "conflict"
between the use of reaction orders which are not equal to balanced equation
coefficients and the rule that in the equilibrium constant one always obtains
exponents which equal the coefficients. 
The properties and concentrations of an equilibrium system are constant because the rates of the forward and reverse reactions are equal so that it appears that no reactions are occurring. 