Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

2.3 Kinetics of reversible first-order reactions (relaxation processes) 20
2.3 Kinetics of reversible first-order reactions (relaxation processes)
A
1 À
−1
B (2.46)
I
Rate equation:
[A]
= − 1 [A] + −1 [B] (2.47)
I
Equilibrium at t →∞:
[A]
y
= − [B]
= − 1 [A] + −1 [B] = 0 (2.48)
[B] ∞
[A] ∞
= 1
−1
= (2.49)
• Therateconstantforthereversereaction −1 can be calculated from 1 and .
• Or the equilibrium constant can be determined from measurements of the
forward and reverse rate constants. From ,wecanthendetermineimportant
thermochemical quantities, for example for reactive free radicals, via
= ( B ª )( C ª )
=exp
∙− ∆ ¸
ª
(2.50)
( A ª )
• Important note:
— In the frequently encountered case that the number of species on the reactant
and product side of a reaction differ, one has to be very careful with the
units of and .
Consider, for example, a gas phase reaction of the type
In this case, has the dimension of mol cm 3 :
B C
= 1 [B] [C]
= =
−1 [A]
0 has the dimension of bar:
A → B+C (2.51)
A
= 1 B C
A
= 0
(2.52)
0 = B C
(2.53)
A
But the thermodynamic equilibrium constant is dimensionless:
= ( ∙
B ª )( C ª )
= 0
( A ª ) =exp − ∆ ¸
ª
(2.54)
ª
— General relation between 0 ,and :
= 0 × ¡ ª¢ −Σ ( ) = × ¡ ª¢ Σ ( )
(2.55)