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chem ed compact/ Comment on the Equilibrium Assumption in Chemical Kinetics Alejandro C. Ollvleri Facultad de Farmacia y Biaquimica PRIBiOR-CONICET Junin 956
Buenos Aims. Rep(lb1ica Argentina The application of the steady state and equilibrium assumptions in chemical kinetics has been the object of many articles in this Journal. The conditions for applying either assumption and the principles involved are well known. However, there are still unclear points, even in a first-order reaction sequence as simple as
If the equilibrium approximation is applied, the rate law is (dC/dt),, = k*K,[A], a well-established result that does not seem to attract much attention. Students are often puzzled, however, when they consider the values of d[A]/dt and d[B]/ d t under this assumption. The question may he put in the following form: if [B]/[A] = Keg throughout the reaction, then the equilibrium requires that d[A]ldt = d[B]ldt = 0. How can the reaction proceed? There are two standard explanations: 1.
The equilibrium state has two interpretations. "Literally"applied, it means that d[A]ldt = kl[A]- k-,[B] = 0,an unreasonable result in the kinetic context, since d[A]ldt is zero only at infinite time. On the other hand, "operationally" applied, it definesthe concentrations to be used in the rate law, by virtue of [B] = K,.IA].
h.K,[A]. Thismcansthat rdlAl dll., knot z e r o althvughir rr small (due torhasmnllncssot kl)compared ~ i t h I : ~ l Howevh]. er, the equilibrium approximation is not a special case of the steady state assumption2.
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I suggest the following explanation. Assume that A and B are not exactly at equilibrium. Instead, kl[A] k-,[B], the rates d[A]ldt and d[B]ldt being small numbers different than zero. If this quasi-equilibrium is to be maintained, these rates should be related by
Hence, putting d[A]ldt = -r and d[B]ldt = r - h*[B], it follows that d[A]ldt -k2Keq[A]l(l K.,) and d[B]ldt -h*K,,[B]I(l+ K,,). Integration, although straightforward, deserves a comment. If A and B reach the equilibrium before any appreciable reaction through the second step beings, then [A],, = [Alo/(l K,,) is the "initial value" of the integrated rate law:
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This is in complete agreement with the equation obtained when the eX3CI ~ d ~ l i oisl simvlifird l undrr the ronditions of the general equilibrium assumption2, which includes the possibility of a high concentration of the intermediate B. Furthermore, it reduces to the steady state equation [A](t) = [A10 exp(-k2K,,t) if the condition K,,
