Reactions first-order reactions

F-Block Element the lanthanides and actinides, valence electrons in the f orbitals Feedstock a process chemical used to produce other chemicals or products Fine Chemicals chemicals produced in relatively low volumes and at higher prices as compared to bulk chemicals such as sulfuric acid, includes flavorings, perfumes, pharmaceuticals, and dyes First Law of Thermodynamics law that states energy in universe is constant, energy cannot be created or destroyed First Order Reaction reaction in which the rate is dependent on the concentration of reactant to the first power... 

Reactions that have rate equations with a linear dependence on only one concentration are said to be first order reactions. Reactions that depend on the concentration of only one species to the second power or that depend on the product of the concentrations of two species, each to the first power, are second order reactions. If a reaction happens to be independent of concentration, it is a zero order reaction. In general, if a reaction rate is given by... 

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. 

The autocatalator model is in many ways closely related to the FONT system, which has a single first-order exothennic reaction step obeying an Arrhenius temperature dependence and for which the role of the autocatalyst is taken by the temperature of the system. An extension of this is tlie Sal nikov model which supports tliennokinetic oscillations in combustion-like systems [48]. This has the fonn ... 

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. 

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... 

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. 

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... 

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... 

The concentration of phenylacetate can be determined from the kinetics of its pseudo-first-order hydrolysis reaction in an ethylamine buffer. When a standard solution of 0.55 mM phenylacetate is analyzed, the concentration of phenylacetate after 60 s is found to be 0.17 mM. When an unknown is analyzed, the concentration of phenylacetate remaining after 60 s is found to be 0.23 mM. What is the initial concentration of phenylacetate in the unknown ... 

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... 

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. 

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). 

Step 4 of the thermal treatment process (see Fig. 2) involves desorption, pyrolysis, and char formation. Much Hterature exists on the pyrolysis of coal (qv) and on different pyrolysis models for coal. These models are useful starting points for describing pyrolysis in kilns. For example, the devolatilization of coal is frequently modeled as competing chemical reactions (24). Another approach for modeling devolatilization uses a set of independent, first-order parallel reactions represented by a Gaussian distribution of activation energies (25). 

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 ...

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

Even when there is a transport disguise, the reaction order remains one for a first-order reaction. But for reactions that are not intrinsically first order, the transport disguise changes the observed reaction order for an intrinsically zero-order reaction, the observed order becomes 1/2 and for an intrinsically second-order reaction it becomes 3/2 when 0 10. For all reaction orders the apparent activation energy is approximately half the intrinsic... 

A model for coal fluidity based on a macromolecular network pyrolysis model has been developed (33). In that model, bond breaking is described as a first-order reaction having a range of activation energies. A variety of lattices have also been used to describe the bonding in coal. In turn these stmctures... 

As with the case of energy input, detergency generally reaches a plateau after a certain wash time as would be expected from a kinetic analysis. In a practical system, each of its numerous components has a different rate constant, hence its rate behavior generally does not exhibit any simple pattern. Many attempts have been made to fit soil removal (50) rates in practical systems to the usual rate equations of physical chemistry. The rate of soil removal in the Launder-Ometer could be reasonably well described by the equation of a first-order chemical reaction, ie, the rate was proportional to the amount of removable soil remaining on the fabric (51,52). In a study of soil removal rates from artificially soiled fabrics in the Terg-O-Tometer, the percent soil removal increased linearly with the log of cumulative wash time. 

For combustion of simple hydrocarbons, the oxidation reactions appear to foUow classical first-order reaction kinetics sufficiently closely that practical designs can be estabUshed by appHcation of the empirical theory (8). For example, the general reaction for a hydrocarbon ... 

The stabilization of chloromethoxycarbene (234) was intensively studied. It is formed from diazirine (233) in a first order reaction with fi/2 = 34h at 20 C. It reacts either as a nucleophile, adding to electron poor alkenes like acrylonitrile with cyclopropanation, or as an electrophile, giving diphenylcyclopropenone with the electron rich diphenylacetylene. In the absence of reaction partners (234) decomposes to carbon monoxide and methyl chloride (78TL1931, 1935). 

Daily Yield Say the downtime for filhng and emptying a reactor is and no reaction occurs during these periods. The reaction time of a first-order reaction, for instance, is given by = —In (1 — x). The daily yield with n batches per day will be... 

The simplest proWem is when all of the stages have the same kt-, then one of the three variables (kt, n, or Ca ) can be found when the others are specified. For first-order reactions,... 

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