The zero-order reaction

A constant rate (zero-order kinetic behaviour) maintained during all, or the greater part of the process may be accounted for [487] by the following reaction models, illustrated in Fig. 5. These alternatives may be distinguished by microscopic observations. 

Reaction rates are related to a and to temperature, T, by different and independent functions and a complete kinetic description of behaviour 

While it is generally true to state that reaction rates increase with temperature, such a qualitative statement is not specific enough to be useful and in some circumstances can be incorrect, e.g. at high a values when the deceleratory character of the reaction may be sufficiently great to offset the acceleratory effect of a slow temperature rise. 

The most accurate method of measuring the influence of temperature on reaction rate is to separate the variables by first determining isothermal rate curves at a series of different temperatures and expressing each set of observations in the form 

The relationship between k and T has then usually been assumed to be of the form 

---

At all temperatures the initial rate R0, was proportional to the first power of the monomer concentration for the zero order reactions this applied to the constant rate which prevails throughout the reaction ... 

For Example 9 the order is 0.7, suggesting a model for which the logL value is between that for Step 2 (0.5 order, log L = 15) and Step 1 (1.0 order, log L = 22). Thus, the rate-determining step may be a reaction on a partially filled surface. Since the log L value calculated in this way for 0.7 order is rather large, some surface mobility and/or rotation is indicated. The zero-order reactions of Examples 11 and 19 are clearly surface reactions for which expected site densities are obtained. For Example 11 Tottrup (25) suggested that the rate-determining step is C-O scission in adsorbed CO. 

The simplest case of compositional dependence is the zero-order reaction, in which the concentration gradient is not affected by concentration. Denoting the molar concentration of the ith element (or component) as c, (and neglecting surface area and volume of solution effects), we have... 

An enzyme which hydrolyzes the cellobiose to glucose, /3-glucosidase is immobilized in a sodium alginate gel sphere (2.5 mm in diameter). Assume that the zero-order reaction occurs at every point within the sphere with k0 = 0.0795 mol/sm3, and cellobiose moves through the sphere by molecular diffusion with Ds = 0.6 x 10 5 cm2 /s (cellobiose in gel). Calculate the effectiveness factor of the immobilized enzyme when the cellobiose concentration in bulk solution is 10 mol/m3. 

Table 3. Temperature range in °C, kinetics, activation energy in kcal/mole and preexponential factor k0 in s l for the first order, in torr/sfor the zero order reaction...

There is one other type however, the y-prn nrrW reaction which is fairly common, particularly in photochemical reactions where the intensity of light is the limiting factor in the reaction rate., or in saturated systems where the concentration of the reacting material is automatically maintained at constant concentration as described later on page 65. The zero order reaction, in which the rate of reaction is constant and independent of concentration, is given simply by equation (12). 

Enantioselective Hydrolysis with Arthrobacter Lipase. Reaction performance with the Arthrobacter lipase was studied in detail. The pH profile curve of the zero-order reaction exhibited a pH-optimum around 7.0, and spontaneous hydrolysis was not significant at pH... 

The consumption of epoxy would equal the breakdown of Ex and be described by the zero order reaction observed in Figure 11... 

All the time-dependent terms in Equation 50 assembled between the braces are independent of the oxygen consumption rate, v. This means that the rate at which the concentration C at any depth approaches a steady-state value (dC/dt) is independent of the zero order reaction rate constant. The time-dependent terms contain, however, the eddy diffusion coefficient and advection velocity, and the rate of approach to steady-state is therefore dependent on these two physical characteristics of the environment. 

A few of the plots for photolyses of CU showed a different behavior several of the log (C0/C) plots show an initial curvature (lower slope at the higher concentrations of CU) becoming linear at longer times (lower concentrations). This behavior is caused by deviation at the higher concentrations of CU from the empirical first order rate law. In the case of these particular runs, the initial concentrations apparently lay in the region between first order and the zero order reaction of optically black solutions. Kf was calculated from the slopes of the linear portions of the plots. 

Keeping in mind the set of simplifying assumptions on which the calculatory process is based, these deviations between model and experiments do not seem to be too dramatic. Specifically,(i) the homogeneity of network, (ii) the zero-order reaction kinetics and (iii) the procedure to estimate Deff may be mentioned in this context, but no attempt was made in this study to develop a more refined mathematical model. 

Note that for the zero-order reaction, Eq. 4.3-6 is recovered. 

If we want to look at the savings account, all we need to do is change the sign in the equation (as we have done for the zero order reaction). 

However, we can determine the amount of S at any time by saying that the amount of S at a given time and the amount of C at the same time must always be the same as our starting C, assuming that no S was present at the start point. As we have done before with the zero order reaction, we can write ... 

As with the zero order reactions we also might be interested in a graphical representation of the rate of the reaction. All we have to use is the equations we used before ... 

Why didn t I tell you about half lives in the zero order reaction For a very simple reason Half lives only work with first order reactions. In all other reactions the half life is dependent on the initial amount and therefore is not a constant, like it is in a first order reaction. 

In other words, it is possible to separate the contribution in the total heat flow from the heat capacity and which arises from the zero-order reaction. It... 

The right-hand side in Eqs. (26) contain the zero-order reaction rates ... 

A third case that is useful to consider in catalysed reactions is the zero-order reaction, in which v apparently does not depend on any concentration ... 

Fig. 1. This illustrates the zero-order reaction kinetics of the oxidation of ascorbic acid by horseradish peroxidase-hydrogen peroxide complex. The disappearance of hydrogen peroxide upon the addition of 3 mM ascorbic acid is recorded by means of the platinum microelectrode (Expt. 574e).

---