Vlad Marcel O, Popa Vlad T, Segal E, Ross John
Department of Chemistry, Stanford University, Stanford, California 94305-5080, USA.
J Phys Chem B. 2005 Feb 17;109(6):2455-60. doi: 10.1021/jp048426d.
We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.
我们表明，反应机理中单一速率决定步骤的动力学模型可以扩展到具有多个总反应的系统，其中基元反应服从非理想或分形动力学。需要以下假设：(1) 所研究的系统是封闭的或开放的，但不存在阻止向平衡演化的限制。(2) 基元反应以正向和反向步骤对的形式发生。(3) 基元步骤的动力学是非理想的或分形的，并且与平衡热力学兼容。(4) 反应路径的数量与速率决定步骤的数量相同。如果这些假设成立，那么总反应速率可以明确评估：它们具有与基元反应动力学方程相似的形式，并且表观反应级数和分形系数可以根据基元反应的动力学参数进行解析表达。我们推导了一组关系，这些关系将反应路径的平衡常数、相应的总速率系数以及速率决定步骤的化学计量数联系起来。我们还推导了一组广义的博列斯科夫关系，这些关系涉及正向和反向总过程的表观活化能、相应的反应焓以及速率决定步骤的化学计量系数。如果基元反应服从分形动力学，那么速率决定步骤也是如此。正向和反向总反应的分形指数是分形基元反应分形指数的线性组合。与单一速率决定步骤的理论类似，我们的方法可用于从实验数据中选择合适的反应机理。
