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

3.3 Microscopic reversibility and detailed balancing 47
3.3 Microscopic reversibility and detailed balancing
The principle of microscopic reversibility is a consequence of the time reversal
symmetry of classical and quantum mechanics: If all atomic momenta of a molecule
that has reached some product state from an initial state are reversed, the molecule will
return to its initial state via thesamepath.
A macroscopic manifestation of the principle of microscopic reversibility is detailed
balancing which states that
(1) in equilibrium, the forward and reverse rates of a process are equal, i.e., for a
1
reaction A 1 À A 2 ,
−1
and
1 [A 1 ]= −1 [A 2 ] (3.44)
(2) if molecules A 1 and A 2 are in equilibrium and A 2 and A 3 are in equilibrium, both
with respect to each other, there is also equilibrium between A 1 and A 3 :
A 1
1
À
−1
A 2
2
À
−2
A 3 (3.45)
y
A 1
3
À
−3
A 3 (3.46)
Thus, we can write
[A 2 ]
= 1
= 12
[A 1 ]
−1
(3.47)
[A 3 ]
= 2
= 23
[A 2 ]
−2
(3.48)
[A 3 ]
= 3
= 13
[A 1 ]
−3
(3.49)
= 12 23 = 1 2
−1 −2
(3.50)
Detailed balancing allows us to simplify complex reaction systems by eliminating − 1
out of a sequence of reversible reactions that are in equilibrium.