PHYSICAL CHEMISTRY IN BRIEF

CHAP. 8: CHEMICAL EQUILIBRIUM [CONTENTS] 246

8.3 Dependence of the equilibrium constant on state variables

8.3.1 Dependence on temperature

It holds that (
∂lnK
∂T

)

p

=

∆rH◦

RT^2

, (8.18)

where ∆rH◦is a change in the standard enthalpy of a given reaction at one mole of reaction.
Equation (8.18) is called thevan’t Hoff isobar.

Note: Note that in exothermic reactions (∆rH◦<0) the equilibrium constant decreases

with increasing temperature while in endothermic reactions it increases.

8.3.1.1 Integrated form.

lnK(T 2 ) = lnK(T 1 ) +

∫T 2

T 1

∆rH◦

RT^2

dT. (8.19)

To calculate the integral on the right side of equation (8.19) it is necessary to know the
temperature dependence of ∆rH◦[see5.3].

• For the simplest case when ∆rH◦can be assumed to be independent of temperature, we
  have
  lnK(T 2 ) = lnK(T 1 )−

∆rH◦

R

(

1

T 2

−

1

T 1

)

, (8.20)

• In general we write (5.16)

∆rH◦(T) = ∆rH◦(To) +

∫T

To

∆Cp◦dT.

If the temperature dependence of the isobaric molar heat capacities of individual components
are expressed in the form
Cpm,i◦ =ai+biT+ciT^2 +diT−^2 ,