Kinetics of chemical reactions: overview Kinetic experiments study the rate at which reactions occur, that is how the concentration of some molecular species changes as a function of time. In a plot of concentration vs. time, the rate of the reaction at a certain time t is simply the slope of the curve at that time. In the kinetic experiment shown below, the rate of the reaction decreases as the reaction proceeds. A kinetic plot involves two variables: one independent (time in this case) and one dependent (on the independent variable, concentration in this case). Thus, our graph contains (i) a plot describing graphically the dependence of product concentration on time, and (ii) a plot for the instantaneous rate as a function of time, given by the derivative of the mathematical function describing the dependence in (i). rate ca-Prot_Enz

First order (unimolecular) reaction k + :  by convention Empirical rate law or phenomenological equation: at any time t, the rate of disappearance of the substrate A (= - d[A]/dt) is equal to that of the appearance of the product B (= + d[B]/dt) and proportional to [A]. The factor of proportion k is referred to as the rate constant. Here, the first order rate constant has units of s-1. We need to solve a differential equation (the phenomenological equation) to yield a value for the independent variable [A] at any time t. This can be done by applying a set of laws (chemical, translated to mathematics), and assuming some conditions related to the system investigated. [A] + [B] = Constant = [A0] d[A] + d[B] = 0 Mass conservation t = 0: [A] = [A0]; [B] = 0 Initial conditions ca-Prot_Enz

Integrated solution (pseudo) first order k Variables separation Integration/initial conditions A0/2 [A] = [A0] e-kt [B] = [A0] - [A] = [A0] - [A0] e-kt [B] = [A0] (1 - e-kt) ca-Prot_Enz

First order reversible (uni-uni) reaction k1 k-1 A B Phenomenological equation [A] + [B] = Constant = [A0] Mass conservation d[A] + d[B] = 0 t = 0: [A] = [A0]; [B] = 0 Initial conditions Substituting B Variables separation Variable change Substituting A ca-Prot_Enz

Integrated solution (uni-uni) first order k1 k-1 A B Rearrangement Integration Substituting a Rearrangement Limits Molar fraction at equilibrium = relative rate of formation and ca-Prot_Enz

Integrated solution (uni-uni) first order k1 k-1 A B k1=0.1 s-1; k-1=0.03 s-1 k1=0.03 s-1; k-1=0.1 s-1 5.33 s 5.33 s 0.023 M 0.077 M 0.077 M 0.023 M ca-Prot_Enz