The Foundations of Chemistry

The results of these experiments are summarized in the following table and in Figure
17-2.

Initial Concentrations Equilibrium Concentrations

[SO 2 ][O 2 ] [SO 3 ] [SO 2 ][O 2 ] [SO 3 ]

Experiment 1 0.400 M 0.200 M 0 M 0.344 M 0.172 M 0.056 M
Experiment 2 0 M 0 M 0.500 M 0.424 M 0.212 M 0.076 M

THE EQUILIBRIUM CONSTANT

Suppose a reversible reaction occurs by a one-step mechanism.

2AB 34 A 2 B

The rate of the forward reaction is Ratefkf[A]^2 [B]; the rate of the reverse reaction is
Raterkr[A 2 B]. In these expressions, kfand krare the specific rate constantsof the forward
and reverse reactions, respectively. By definition, the two rates are equal at equilibrium
(RatefRater). So we write

kf[A]^2 [B]kr[A 2 B] (at equilibrium)

Dividing both sides of this equation by krand by [A]^2 [B] gives



At any specific temperature, both kfand krare constants, so kf/kris also a constant.
This ratio is given a special name and symbol, the equilibrium constant, Kcor simply K.

Kc (at equilibrium)

Even if the overall reaction occurs by a multistep mechanism, we can show that the
equilibrium constant is the product and ratio of the rate constants for each step of the
mechanism. Regardless of the mechanism by which this reaction occurs, the concentra-
tions of reaction intermediates cancel out and the equilibrium constant expression has the
same form. For a reaction in general terms, the equilibrium constant can always be written
as follows:

The equilibrium constant Kc, is defined as the product of the equilibrium concentra-

tions(moles per liter) of the products, each raised to the power that corresponds to

its coefficient in the balanced equation, divided by the product of the equilibrium

concentrationsof reactants, each raised to the power that corresponds to its coeffi-

cient in the balanced equation.

For aA  bB cC  dD,

reactants products reactants

products

Kc 

[C]eqc[D]eqd

[A]eqa[B]eqb

[A 2 B]



[A]^2 [B]

[A 2 B]



[A]^2 [B]

kf



kr

17-2

The subscript c refers to

concentrations. The brackets, [ ], in

this expression indicate equilibrium

concentrations in moles per liter.

17-2 The Equilibrium Constant 711

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 16.4, The Equilibrium Constant.