Chemistry, Third edition

MEANING OF EQUILIBRIUM CONSTANTS

The experimental rate expression for the back reaction(equation (15.2)) turns out

to be equally straightforward:

rate of reaction= kb[HI(g)]^2

As the concentration of HI builds up, the rate of the back reaction increases. At equi-

librium, the rates of the forward and back reactions are equal:

kb[HI(g)]^2 =kf[H 2 (g)] [I 2 (g)]

Comparing this with equation (15.4) shows that

Kc(T)

kf

kb

●This equation applies to all equilibrium reactions (and may be used whether or

not the reaction occurs in a single stage).

●Remember that a rate constant is the rate of reaction when the substances in the

rate expression are at unit concentration, i.e. 1 mol dm^3 (see page 251). The

above equation shows that the size of the equilibrium constant depends simply

upon how much faster the forward reaction is (at unit concentrations) than the

back reaction (at unit concentrations) at that temperature. We need only to know

the equilibrium constant and one of the rate constants in order to calculate the

remaining rate constant. For example, for the reaction

H 2 (g)I 2 (g)\===\2HI(g)

●kf= 1.66 mol^1 dm^3 s^1 andKc(T)= 45.6 at 764 K. Therefore,

kb(764 K) 

1.66 mol^1 dm^3 s^1

0.0364 mol^1 dm^3 s^1

45.6

The importance of stating the chemical equation to which

the equilibrium constant applies

An equilibrium constant applies to a particular chemical equation. For example,

whereas

[SO 3 (g)]^2

Kc(T)

[SO 2 (g)]^2 [O 2 (g)]

for 2SO 2 (g)O 2 (g)\===\2SO 3 (g)

we also write

[SO 3 (g)]

Kc(T)

[SO 2 (g)][O 2 (g)]^1 ⁄^2

for SO 2 (g)^1 ⁄ 2 O 2 (g)\===\SO 3 (g)

The equilibrium constants for these expressions will have different numerical values.

The moral is simple – never quote equilibrium constants unless you write down the

chemical equation (or equilibrium expression) to which that value of Kc(T)applies.

Meaning of equilibrium constants

Look back at Fig. 15.3(b). At equilibrium, the reaction mixture consisted of 12

molecules of A and 4 of B. Since, for a fixed volume, the molar concentration is pro-

portional to the number of molecules, we can write

Kc(T)

[B]



4

0.33

[A] 12

15.3

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