Question

Explain how the determination of the rate law equation significantly differs from the determination of the equilibrium constant Keq expression.

Answer 1

Equilibrium Constant Expressions

Reactions don't stop when they come to equilibrium. But the forward and reverse reactions are in balance at equilibrium, so there is no net change in the concentrations of the reactants or products, and the reaction appears to stop on the macroscopic scale. Chemical equilibrium is an example of a dynamic balance between opposing forces the forward and reverse reactions not a static balance.

Let's look at the logical consequences of the assumption that the reaction between ClNO₂ and NO eventually reaches equilibrium.

ClNO2(g)

+

NO(g)

NO2(g)

+

ClNO(g)

The rates of the forward and reverse reactions are the same when this system is at equilibrium.

At equilibrium:

rateforward

=

ratereverse

Substituting the rate laws for the forward and reverse reactions into this equality gives the following result.

At equilibrium:

kf(ClNO2)(NO)

=

kr(NO2)(ClNO)

But this equation is only valid when the system is at equilibrium, so we should replace the (ClNO₂), (NO), (NO₂), and (ClNO) terms with symbols that indicate that the reaction is at equilibrium. By convention, we use square brackets for this purpose. The equation describing the balance between the forward and reverse reactions when the system is at equilibrium should therefore be written as follows.

At equilibrium:

kf[ClNO2][NO]

=

kr[NO2][ClNO]

Rearranging this equation gives the following result.

Since k_f and k_r are constants, the ratio of k_f divided by k_r must also be a constant. This ratio is the equilibrium constant for the reaction, K_c. The ratio of the concentrations of the reactants and products is known as the equilibrium constant expression.

No matter what combination of concentrations of reactants and products we start with, the reaction will reach equilibrium when the ratio of the concentrations defined by the equilibrium constant expression is equal to the equilibrium constant for the reaction. We can start with a lot of ClNO₂ and very little NO, or a lot of NO and very little ClNO₂. It doesn't matter. When the reaction reaches equilibrium, the relationship between the concentrations of the reactants and products described by the equilibrium constant expression will always be the same. At 25^oC, this reaction always reaches equilibrium when the ratio of these concentrations is 1.3 x 10⁴.

The procedure used in this section to derive the equilibrium constant expression only works with reactions that occur in a single step, such as the transfer of a chlorine atom from ClNO₂ to NO. Many reactions take a number of steps to convert reactants into products. But any reaction that reaches equilibrium, no matter how simple or complex, has an equilibrium constant expression that satisfies the rules in the following section.