Reaction rate time dependent

O3 + terpene products Rate =. [03] [terpene] We expect the reaction rate to depend on two concentrations rather than one, but we can isolate one concentration variable by making the initial concentration of one reactant much smaller than the initial concentration of the other. Data collected under these conditions can then be analyzed using Equations and, which relate concentration to time. For example, an experiment could be performed on the reaction of ozone with isoprene with the following initial concentrations ... 

As indicated earlier, the units of the specific reaction rate k depend on the order of the reaction. This is because the overall reaction rate 31 always has the same units (moles per unit time per unit volume). For a first-order reaction of A reacting to form B, the overall reaction rate 31, written for component A, would have units of moles of A/min ft. ... 

Except for radioactive decays, other reaction rate coefficients depend on temperature. Hence, for nonisothermal reaction with temperature history of T(t), the reaction rate coefficient is a function of time k(T(t)) = k(t). The concentration evolution as a function of time would differ from that of isothermal reactions. For unidirectional elementary reactions, it is not difficult to find how the concentration would evolve with time as long as the temperature history and hence the function of k(t) is known. To illustrate the method of treatment, use Reaction 2A C as an example. The reaction rate law is (Equation 1-51)... 

The reaction rate coefficients in the above equations may be related to reaction rates per pair of particles 2/, in nuclear physics (e.g., Fowler et al., 1975 Harris et al., 1983) by k = Xj/(1 + 5/ ), where 8 = 0 except for i= , for which 5/ = 1. That is, for Reactions 2-145 and 2-147 in which two identical particles collide to react, the definition of k is half of defined by nuclear physicists and for reactions in which different particles collide, the definition of k is the same as Xij. The reaction rate coefficients depend on temperature in a complicated way (Table 2-3) and may be calculated as the average value of the product of relative velocity times cross section. The concentrations of the intermediate species can be derived as follows. From Equation 2-155, 145 [ H] = ki4e[ H]pH]. That is. 

In Table 15.7 the reaction quantum yields are given for some selected organic pollutants. As can be seen, reaction quantum yields vary over many orders of magnitude, with some compounds exhibiting very small Oir values. However, since the reaction rate is dependent on both ka and Oir (Eq. 15-34), a low reaction quantum yield does not necessarily mean that direct photolysis is not important for that compound. For example, the near-surface direct photolytic half-life of 4-nitrophenolate (Oir = 8.1 x 10 6) at 40°N latitude is estimated to be in the order of only a few hours, similar to the half-life of the neutral 4-nitrophenol, which exhibits a Oir more than 10 times larger (Lemaire et al., 1985). The reason for the similar half-lives is the much higher rate of light absorption of 4-nitrophenolate as compared to the neutral species, 4-nitrophenol (compare uv/vis spectra in Fig. 15.5 and Illustrative Example 15.3). As a second example, comparison of the near-surface photolytic half-lives (summer, 40°N... 

It has been known for a fairly long time that the reaction rate must depend on the law of energy distribution between reacting molecules. Apparently it was Marcelin who first realized this in 1915 [48, p. 149]. Experiments with molecular beams in the 1960s and 1970s revealed that, in gas-phase systems, a wide variety of reactions take place that cannot be interpreted without... 

Propylene oxidation on a PPFe3+0H/Al203 catalyst corresponds to the case of heterogeneous catalysis, when catalyst forms a unitypical activated complex for substrate transformation in several parallel directions. Hence, the composition of the reaction products depends on the relative reaction rate, time of contact between the substrate and the catalyst, and temperature. 

If the primary process is followed by another reaction or if collisions with other molecules are necessary for the reaction, then the reaction rate will depend on concentration. If it depends only on the concentration of the absorbing material the reaction is of the first order, and if it depends on the square of the concentration it is of the second order. Examples of both are known but in photochemical reactions as in thermal reactions the over-all observed reactions frequently appear to follow neither the first nor the second order, usually on account of the existence of two or more reaction steps. Sometimes a. second reaction is slow in getting started because time is necessary to accumulate some of the product of the first reaction. This situation leads to a time-lag or induction period. Again the second reaction may continue after the primary photo-reaction has stopped, giving rise to after-effects. 

Table 14 Calculation of reaction rate, time law and half-life of a reaction in dependence of its order...

If diffusion phenomena are not involved, the formation and deactivation of polymerization centers should reflect in rate-time dependences, other conditions being constant. Rate acceleration period of very widely differing lengths is often observed, followed either by a more or less steady rate or by a deceleration (rate decay) period. As for the polymerization center deactivation, it is quite important to know whether a macromolecule or a metal-polymer bond is formed due to this reaction (see Sect. 4). 

The reaction rate will depend on the stirring and nitrogen purge rates. The reaction should be monitored for completion (>98% conversion) by GC using the method described in (Note 2) the retention time for hydroxyketone 3 is 4.9 min. 

After the homogenization process, a 2ml of TEOS (99.9%, Aldrich Chemical Co., USA) was added and mixed into the catalyst-included mixed solvents. As reaction time goes on after ftie TEOS addition, the hydrolysis and condensation reactions initiated, so that the transparent solution became white and white. The reaction rate highly depended on the reaction conditions such as the volume ratio of H2O to EtOH and the addition amount of NH3. The synftiesis temperature and time were room temperature and 4hrs, respectively. After the synthesis reaction had proceeded for 4 hours, the synthesized silica gel was washed with water three times by repeated centrifuging and dispersion in water, and then dried at 110°C for 72hrs. All the chemicals used in the present study were used without any furthermore purification. 

Equation (2 26) is a form of the design equation for constant volumetric flow rate Uq that may prove more useful in determining the space time or reactor volume for reaction rates that depend only on the concentration of one species. 

Methyl Acrylate (MA). The y-emulsion polymerization of MA was studied most intensively in our investigations. The dependence of the reaction rate/time function, and the maximum reaction rate, on composition of the mixture, dose rate, and temperature was studied. 

Agrawal. P.M. and Raff. L.M. (1981) Calculation of reaction probabilities and rate cocfficicnrs for collincar three-body exchange reactions using time-dependent wave packet methods J. Chem. Phys. 74. 5076-5081. 

Our concern in the last chapter was to get a feel for the way in which the reaction rate varies with composition and temperature. Here we wish to sec how the composition varies in time as the reaction proceeds isothermally in a batch reactor. When we come to discuss different types of reactor we shall have to deal with variations of temperature and hence of the rate constants, but here they will be assumed to be constant throughout the reaction. The reaction rate will depend only on the composition, but this of course will vary during the reaction and we shall have to solve differential equations. Sometimes we shall work with the extent of reaction, sometimes with concentrations of reactants or products. No apology is made for this variety of approach since it is important that the student be versatile with the use of different variables and develop an eye for those that will give the simplest form of a solution. The use of the extent is a routine matter, useful for avoiding mistakes in complex situations, but in simpler cases it is often possible to write down the differential equations for concentrations by inspection. From Sec. 5.2 onward, the rate constants will be denoted by lower case fc s with a variety of suffixes, the concentrations by or the lower case letter corresponding to the species. 

A stimulating paper deals with a revision of the familiar, and widely used, monomer-excimer kinetics by treating such systems as examples of reactions with time dependent rate constants. The simple mathematical formulations usually employed in systems where excimers are involved are shown to be inadequate. No doubt future efforts will be directed to rectifying the situation. Strong transient effects arising from nonstationary diffusion which occur during excimer formation through reactions with time dependent rate coefficients have been used as a scheme to test different models used in convolution kinetics . Time dependent excimer... 

A compilation of available kinetic models shows that, in most cases, the calculated reactive surface areas are one to three orders of magnitude less than the estimated physical surface areas. Commonly, geometric and BET surface areas are used interchangeably in kinetic studies to measure physical surface areas. The models that did produce closer fits were for open systems with short residence times. Comparisons assumed experimentally correct reaction rates and dependent reactive surface areas. In reality, the reaction rate and the reactive surface area are explicitly linked on the basis of surface controlled reactions. The product of these two terms determines the mass transfer for a specific system. 

MTBE is eliminated with pseudo-first order reaction kinetics [108-111]. The reaction rate is dependent on the frequency and power density of the ultrasound. At higher frequency, the elimination of MTBE is much faster. For each frequency the power density shows an optimum, since the interaction of and influence on cavitation bubble size, collapse time, transient temperature and internal pressure is very complex. Initial MTBE concentration was also observed to be of influence the reaction rate decreased with increasing MTBE concentration. This indicates that the reaction is limited by OH radical diffusion. 

Enzymes themselves can be analyzed by measuring the amount of substrate transformed in a given time or the product that is produced in a given time. The substrate, houldJ2eJn ccess so that the reaction rate depends oiily on the enzyme concentration. The results are expressed as international units of enzyme. For example, the activity of a glucose oxidase preparation can be determined by measuring manometrically or amperometrically the number of micromoles of oxygen consumed per minute. On the other hand, the use of enzymes to develop specific procedures for the determination of substrates, particularly in clinical chemistry, has proved to be extremely useful. In this case, the enzyme concentration is in excess so the reaction rate is dependent on the substrate concentration. 

The rate of a chemical reaction is defined as the rate of change of the concentration of one of its components, either a reactant or a product. The experimental investigation of reaction rates therefore depends on being able to monitor the change of concentration with time. Classical procedures for reactions that take place in hours or minutes make use of a variety of techniques for determining concentration, such as spectroscopy and electrochemistry. Very fest reactions are studied spectroscopically. Spectroscopic procedures are available for monitoring reactions that are initiated by a rapid pulse of electromagnetic radiation and are over in a few femtoseconds (1 fe = 10 s). 

The rate of a reaction is time dependent. It is therefore important that we know how to measure the period of time during which the observed change in concentration has taken place. Time may look like the easiest parameter to record, but this is not so. In foct the definition of time in kinetic studies deserves to be re-examined in much more detail. 

For a first-order reaction in spherical catalyst particles the effectiveness factor (and hence the observed reaction rate constant) depends on the Thiele Modulus (0 = R k/D), which is in essence the square root of the ratio of the time constants for reaction and diffusion. Then, the effectiveness factor is ... 

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