Reaction, order

An example of a two-stage hydrolysis is that of the sequence shown in Eq. IV-69. The Idnetics, illustrated in Fig. IV-29, is approximately that of successive first-order reactions but complicated by the fact that the intermediate II is ionic [301]... 

A monolayer undergoes a first-order reaction to give products that also form monolayers. An equation that has been used under conditions of constant total area is (t - K°°)/(ifi - t") = exp(-)kr). Discuss what special circumstances are implied if this equation holds. 

Figure A3.4.3. Methyl radical recombination as a second-order reaction (after [22, 23]).

Let us compare computations of the effectiveness factor, using each of the three approximations we have described, with exact values from the complete dusty gas model. The calculations are performed for a first order reaction of the form A lOB in a spherical pellet. The stoichiometric coefficient 10 for the product is unrealistically large, but is chosen to emphasize any differences between the different approaches. 

More computational results are provided by Hite [75], including a second order reaction with different stoichiometry, and slab, as well as sphere geometry for the pellet. Overall it can be concluded that the approximate procedure of Hite and Jackson gives results of quite adequate... 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

First-order nitrations in nitromethane are also markedly accelerated by addition of sulphuric acid, the effect being very similar to that observed with zeroth-order reactions. 

Unlike the effect of sulphuric acid upon nitration in nitric acid ( 2.2.3 where zeroth-order reactions are unknown), the form of the catalysis of zeroth-order nitration in nitromethane by added sulphuric acid does not deviate from a first-order dependence with low concentrations of catalyst. ... 

The most crucial observation concerning the effects of added species is that nitrate ion anticatalyses nitration without changing the kinetic form of the reaction. This shows that nitrate does not exert its effect by consuming a proportion of the nitronium ion, for, as outlined above, this would tend to bring about a kinetically first-order reaction. Nitrate ions must be affecting the concentration of a precursor of the nitronium... 

When large concentrations of water are added to the solutions, nitration according to a zeroth-order law is no longer observed. Under these circumstances, water competes successfully with the aromatic for the nitronium ions, and the necessary condition for zeroth-order reaction, namely that all the nitronium ions should react with the aromatic as quickly as they are formed, no longer holds. In these strongly aqueous solutions the rates depend on the concentrations and reactivities of the aromatic compound. This situation is reminiscent of nitration in aqueous nitric acid in which partial zeroth-order kinetics could be observed only in the reactions of some extremely reactive compounds, capable of being introduced into the solution in high concentrations ( 2.2.4). 

The effect of nitrous acid on the nitration of mesitylene in acetic acid was also investigated. In solutions containing 5-7 mol 1 of nitric acid and < c. 0-014 mol of nitrous acid, the rate was independent of the concentration of the aromatic. As the concentration of nitrous acid was increased, the catalysed reaction intervened, and superimposed a first-order reaction on the zeroth-order one. The catalysed reaction could not be made sufficiently dominant to impose a truly first-order rate. Because the kinetic order was intermediate the importance of the catalysed reaction was gauged by following initial rates, and it was shown that in a solution containing 5-7 mol 1 of nitric acid and 0-5 mol 1 of nitrous acid, the catalysed reaction was initially twice as important as the general nitronium ion mechanism. 

Anisole] = 0 4 mol 1 zeroth-order reactions, except for that with added nitrate, which was of the first order with respect to the concentration of anisole. 

II [Anisole] = 2 x lo mol i" first-order reactions. For the experiment using pure nitric acid the half-life was about i min, but for that using fuming nitric acid reaction was complete in < 30 s. 

Fixed-time integral methods are advantageous for systems in which the signal is a linear function of concentration. In this case it is not necessary to determine the concentration of the analyte or product at times ti or f2, because the relevant concentration terms can be replaced by the appropriate signal. For example, when a pseudo-first-order reaction is followed spectrophotometrically, when Beer s law... 

In a curve-fitting method the concentration of a reactant or product is monitored continuously as a function of time, and a regression analysis is used to fit an appropriate differential or integral rate equation to the data. Eor example, the initial concentration of analyte for a pseudo-first-order reaction, in which the concentration of a product is followed as a function of time, can be determined by fitting a rearranged form of equation 13.12... 

Eor a pseudo-zero-order reaction a plot of [A]( versus time should be linear with a slope of -k, and a y-intercept of [A]o (equation 13.8). A plot of the kinetic data is shown in figure 13.7. Linear regression gives an equation of... 

We know from equation 13.6 that for a pseudo-first-order reaction, the concentration of picrate at time t is... 

For a first-order reaction we can write, from equations 13.2, 13.21, and 13.22... 

Equation 13.14 shows how [A]o is determined for a two-point fixed-time integral method in which the concentration of A for the pseudo-first-order reaction... 

First-Order Reactions The simplest case is a first-order reaction in which the rate depends on the concentration of only one species. The best example of a first-order reaction is an irreversible thermal decomposition, which we can represent as... 

Reaction A5.5 is not the only possible form of a first-order reaction. Eor example, the reaction... 

Proceeding in the same manner as for a first-order reaction, the integrated form of the rate law is derived as follows... 

Thus, for a second-order reaction, a plot of [A] versus f is linear, with a slope of k and an intercept of [A]o h Alternatively, a reaction can be shown to be second-order in A by observing the effect on the rate of changing the concentration of A. In this case, doubling the concentration of A produces a fourfold increase in the reaction s rate. 

To determine the reaction order we plot ln(%p-methoxyphenylacetylene) versus time for a first-order reaction, and (%p-methoxyphenylacetylene) versus time for a second-order reaction (Figure A5.1). Because the straight-line for the first-order plot fits the data nicely, we conclude that the reaction is first-order in p-methoxyphenylacetylene. Note that when plotted using the equation for a second-order reaction, the data show curvature that does not fit the straight-line model. 

Pseudo-Order Reactions and the Method of Initial Rates Unfortunately, most reactions of importance in analytical chemistry do not follow these simple first-order and second-order rate laws. We are more likely to encounter the second-order rate law given in equation A5.11 than that in equation A5.10. 

A variation on the use of pseudo-ordered reactions is the initial rate method. In this approach to determining a reaction s rate law, a series of experiments is conducted in which the concentration of those species expected to affect the reaction s rate are changed one at a time. The initial rate of the reaction is determined for each set of conditions. Comparing the reaction s initial rate for two experiments in which the concentration of only a single species has been changed allows the reaction order for that species to be determined. The application of this method is outlined in the following example. 

Chemical Properties. Vacuum thermal degradation of PTFE results in monomer formation. The degradation is a first-order reaction (82). Mass spectroscopic analysis shows that degradation begins at ca 440°C, peaks at 540°C, and continues until 590°C (83). 

The activation parameters for an initiator can be deterrnined at normal atmospheric pressure by plotting In vs 1/T using initiator decomposition rates obtained in dilute solution (0.2 M or lower) at several temperatures. Rate data from dilute solutions are requited in order to avoid higher order reactions such as induced decompositions. The intercept for the resulting straight line is In and the slope of the line is —E jR therefore both and E can be calculated. 

In the normal process ( ), step (J) occurs very rapidly and step (/) is the rate-determining step, whereas in the inhibition process (B), step (3) occurs very slowly, generally over a matter of days, so that it is rate determining. Thus it has been demonstrated with AChE that insecticides, eg, tetraethyl pyrophosphate and mevinphos, engage in first-order reactions with the enzyme the inhibited enzyme is a relatively stable phosphorylated compound containing one mole of phosphoms per mole of enzyme and as a result of the reaction, an equimolar quantity of alcohoHc or acidic product HX is hberated. 

The reaction/mass-transfer technique is based on Danckwerts theory of mass transfer accompanied by a fast pseudo first-order reaction (10) ... 

Numerous kinetic mechanisms have been proposed for oil shale pyrolysis reactions (11—14). It has been generally accepted that the kinetics of the oil shale pyrolysis could be represented by a simple first-order reaction (kerogen — bitumen — oil), or... 

For weU-defined reaction zones and irreversible, first-order reactions, the relative reaction and transport rates are expressed as the Hatta number, Ha (16). Ha equals (k- / l ) where k- = reaction rate constant, = molecular diffusivity of reactant, and k- = mass-transfer coefficient. Reaction... 

Fig. 15. Temperature vs heat generation or removal in estabHshing stationary states. The heavy line (—) shows the effect of reaction temperature on heat-generation rates for an exothermic first-order reaction. Curve A represents a high rate of heat removal resulting in the reactor operating at a low temperature with low conversion, ie, stationary state at a B represents a low rate of heat removal and consequently both a high temperature and high conversion at its stationary state, b and at intermediate heat removal rates, ie, C, multiple stationary states are attainable, c and The stationary state at c ...

---