Reaction rates change with time

The rate is defined as an intensive variable, and the definition is independent of any particular reactant or product species. Because the reaction rate changes with time, we can use the time derivative to express the instantaneous rate of reaction since it is influenced by the composition and temperature (i.e., the energy of the material). Thus,... 

Because the reaction rate changes with time, and because the rate may be different for the various reactants and products (by factors that depend on the coefficients in the balanced equation), we must be very specific when we describe a rate for a chemical reaction. 

This need not be true in vivo where the concentrations of reactants and their enzymes in some cases are nearly comparable. Under these conditions, the nominal concentration of substrate could be significantly greater than the level of unbound substrate, and the reaction rate calculated with nominal concentrations inserted into the rate law clearly would overestimate the rate observed in vivo (Wright et al., 1992 Shiraishii and Savageau, 1993). This condition does not alter the basic chemical kinetic equations that describe the mechanism, but it does mean that the quasi-steady state assumption (e.g., see Peller and Alberty, 1959 Segel and Slemrod, 1989) may be inappropriate when reaction rates change with time in vivo. 

This remains true in vivo for systems that are in steady-state. However, it is not true in general when reaction rates change with time. The conditions (see above) that can make it a valid assumption in vitro do not necessarily pertain to the situation... 

In general, for a homogeneous reaction for which the reaction rate changes with time and also it is not uniform over a volume of a reactor the reaction rate is... 

We have seen that the rate of a reaction is typically not constant. Most reaction rates change with time. This is so because the concentrations change with time (Fig. 12.1). 

If the flow is accompanied with CBA decomposition, the G value in Eq. (5) should be substituted with its time function, G(t). In the general case, thermal decomposition of a solid substance with gas emission is a heterogeneous topochemical reaction [22]. Kinetic curves of such reactions are S -shaped the curves representing reaction rate changes in time pass a maximum. At unchanging temperature, the G(t) function for any CBA is easily described with the Kolrauch exponential function [20, 23, 24] ... 

In a static reactor the rate changes with time as the reactants are consumed, and the initial rate is often used. In a dynamic reactor under steady state conditions the rate is independent of time, and with a known flow of reactant into the reactor the observed fractional conversion is readily changed into a rate. What is of great interest in understanding a catalysed reaction is the response of the rate to variations in operating conditions, especially the concentrations or pressures of the reactants, and temperature. It is frequently observed that, at least over some limited range of temperature, the Arrhenius equation in the form... 

Lundberg and Doty (16) further studied the polymerization of S-, RS- and R-NCA initiated by the terminal amino group of preformed S-polymer. As shown in Fig. 11, the polymerization of S-NCA proceeds with a high rate from the initial stage, while R-NCA polymerizes slowly with increasing rate at the later stage. The optical rotation of the reaction mixture changes with time, as shown in Fig. 12,... 

Reaction rates decrease with time because the reaction rate depends on the concentration of the reactants. As the reaction proceeds, the reactant is consumed and its concentration declines. This change in concentration, in turn, decreases the reaction rate. 

The reaction was performed in a static reactor and was followed by pressure measurements (55). Change of pressure with time (initial pressure of nitrous oxide, 148 torr) and the corresponding yield for the reaction at 250° on a freshly prepared sample of NiO(250°) are reported in Fig. 39. The reaction rate decreases with time according to the kinetic law already proposed by Winter (86)... 

Semibatch Operation In semibatch operation the rates of mass flow into and out of the system are unequal (see Fig. 3-1 c). For example, benzene may be chlorinated in a stirred-tank reactor by first adding the charge of liquid benzene and catalyst and then continuously adding chlorine gas until the required ratio of chlorine to benzene has been obtained. Operation of this kind is. batch from the standpoint that the composition of the reaction mixture changes with time. However, from a process standpoint the chlorine is added continuously. The system is still an ideal stirred-tank reactor if the... 

An alternative approach is to express the results in analogy with those for catalytic systems, in terms of an effectiveness factor (Ishida and Wen, 1968). Unlike in catalytic pellets, here the rate changes with time. Hence, the effectiveness factor also changes with time (i.e., with r,), and the following equation can be derived for a first-order reaction in a sphere ... 

Define reaction rate. Assuming constant temperature and a closed reaction vessel, why does the rate change with time ... 

Although racemization appeared to obey first-order kinetics during the early stages of the reaction, the apparent rate changed with time. The rate constants we used for calculation of thermo- namic and linear free-energy parameters were derived from the initial, linear rates. 

What is meant by the term rate of a chemical reaction Why does the rate of a reaction normally change with time When does the rate of a chemical reaction equal the rate constant ... 

This means that the rate at which the intermediate, I, is formed and the rate of its disappearance are practically equal. Strictly speaking, the steady-state is reached almost immediately after initiation of the reaction. Figure 1.12.1 schematically depicts this situation curve (a) shows how the concentration of the final reaction products changes with time, curve (b) shows the rate of reactant disappearance, and curve (c) represents the rate of formation of the reaction intermediate (I). We can see that during most of the reaction the concentration of I is practically constant and very low point S is a small... 

The course of a surface reaction can in principle be followed directly with the use of various surface spectroscopic techniques plus equipment allowing the rapid transfer of the surface from reaction to high-vacuum conditions see Campbell [232]. More often, however, the experimental observables are the changes with time of the concentrations of reactants and products in the gas phase. The rate law in terms of surface concentrations might be called the true rate law and the one analogous to that for a homogeneous system. What is observed, however, is an apparent rate law giving the dependence of the rate on the various gas pressures. The true and the apparent rate laws can be related if one assumes that adsorption equilibrium is rapid compared to the surface reaction. 

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