M. Simonyi and I. Mayer. Central Research Institute for Chemistry of the Hungarian Academy of Sciences,. Budapest, Pf. 17. H-1525. Received September 11 ...
React. Kinet. Catal. Lett., Vol. 18, No. 3-4, 431-432 (1981) FORMAL SIMILARITY BETWEEN IRREVERSIBLE AND REVERSIBLE BIMOLECULAR KINETICS M. Simonyi and I. Mayer Central Research Institute for Chemistry of the Hungarian Academy of Sciences, Budapest, Pf. 17. H-1525 Received September 11, 1981 Accepted September 15, 1981
A simple kinetic solution for reversible bimolecular associations is presented. Kinetic
data of association alone often do not allow to distinguish between reversible and irreversible processes owing to the mathematical similarity of the two cases. Bbmo npe~o~reHo npoeroe KHHeTnqecKoe petueHae o6paTHMI~IX 6nMOJleKy.rl~pHblX
accottaattnll. Hcxo/lz
nnmb
Ha Knnernqec~:ax /~aHHrbix accottaarana, Hea~a~t pemrtr~
is a reaction o f fundamental importance in biochemistry. It is generally believed that the kinetic solution for this mechanism is simple only if the initial concentrations of A and B are identical ([A]o = [B]o) /1/. The correct general solution for the above scheme was given by Benson in 1 9 6 0 / 2 / , but its complicated form seems to discourage practical applications. The simple solution derived by Capellos and Bielski/1/ for [A]o = [B]o is Xe [A]2o - x2e 12"
In
Xe([A]o2 - XeX)
= k2 t
(2)
[A]2o (Xe - x) 431
SIMONYI, MAYER: BIMOLECULAR KINETICS where Xe is the value of x at equilibrium. The derivation applied /1] does not require, however, the limitation of the initial concentration ratio. For [A]o ~ [B]o the same treatment yields: Xe
in
[A]o [B]o - xe2
Xe([A]o [ B ] o - XeX)
= k2t;
(3)
[A]o [B]o ( x e - x )
or by defining [A]o [B]o
Q-
(4)
Xe
one obtains: 1
In
Q - Xe
xe(Q - x)
-
k2t
Q(xe - x)
(5)
The simple equation (5) is virtually unknown. Its form resembles strikingly the well-known kinetic solution 1 [B]o - [A]o
In
[A]o ([B]o - x)
= k2t
(6)
[B]o ([A]o - x)
of an irreversible bimolecular reaction. The formal identity of equations (5) and (6) results in the same character of x = x(t) curves irrespective of the reversible or irreversible nature of the process. If one does not know the initial concentration of one of the components - a practical case for many biochemical problems kinetic data of bimolecular association alone cannot check the reversibility of the reaction studied. For such a conclusion the dissociation process should be investigated separately. Acknowledgement. The authors thank Profs. G. Schay and T. Keleti for helpful discussions.
REFERENCES 1. C. CapeUos, B.HJ. Bielski: Kinetic Systems. Wiley-lnterscience, New York, 1972. 2. S.W. Benson: The Foundations of Chemical Kinetics. McGraw Hill, New York, 1960.
