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
 
 aA + bB ---> lL + mM
one can conceive of the reverse process
 
lL + mM ---> aA + bB
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
 
Rate Forward Reaction = Rate Reverse Reaction

 
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.
 
H2(g) + I2(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 one-step bimolecular mechanism, then
 
Rate Forward Reaction = Rf = kf [AB][CD]
 
Similarly, assuming that the reverse reaction also occurs by a one-step mechanism
 
Rate Reverse Reaction = Rr = kr [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, Erepresents the activation energy for the forward reaction and Ethat for the reverse; since the activated complex is identical for both directions it follows that
 
H = Er - Er
 
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 Ef = Er.
 
Returning to the rate law constant expression, we know that at equilibrium
 
Rf = Rr
 
therefore kf[AB]e[CD]e = kr[AD]e[CB]e
 
where the subscript e denotes equilibrium concentrations. By rearrangement we can obtain the expression
 
[AD]e[CB]e  = Kf= a constant Keq,  the Equilbrium Constant
[AB]e[CD]e    Kr
 
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 single-step 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 Rf = 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 R1 = k1[AB]
 
step 2    A + B ---> AB R2 = k2[A][B]
 
step 3    A + C ---> AC R3 = k3[A][C]
 
step 4        AC ---> A + C R4 = k4[AC]
 
Now since R1 = R2 at equilibrium,
 
                 k1[AB] = k2[A][B]
 
and since R4 = R3 at equilibrium,
 
                k4[AC] = k3[A][C]
 
By equating the ratio of the left-hand sides of the two equations to the ratio of the right-hand sides, we obtain
 

 
or upon rearrangement
 

 
(Note that the concentrations of the intermediate species cancel out.)
 
Therefore, even though the reaction proceeds by a multi-step 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 Keq 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.