Reaction rates instantaneous

Reaction Rates Average Reaction Rate Instantaneous Rate Stoichiometry and Reaction Rate... 

Tubular Reactors. The tubular reactor is exceUent for obtaining data for fast thermal or catalytic reactions, especiaHy for gaseous feeds. With sufficient volume or catalyst, high conversions, as would take place in a large-scale unit, are obtained conversion represents the integral value of reaction over the length of the tube. Short tubes or pancake-shaped beds are used as differential reactors to obtain instantaneous reaction rates, which can be computed directly because composition changes can be treated as differential amounts. Initial reaction rates are obtained with a fresh feed. Reaction rates at... 

Rates of Reaction. The rates of formation and dissociation of displacement reactions are important in the practical appHcations of chelation. Complexation of many metal ions, particulady the divalent ones, is almost instantaneous, but reaction rates of many higher valence ions are slow enough to measure by ordinary kinetic techniques. Rates with some ions, notably Cr(III) and Co (III), maybe very slow. Systems that equiUbrate rapidly are termed kinetically labile, and those that are slow are called kinetically inert. Inertness may give the appearance of stabiUty, but a complex that is apparentiy stable because of kinetic inertness maybe unstable in the thermodynamic equihbrium sense. 

It is important that the formaldehyde addition rate be balanced with the alkali content of the system and the engineering control capability. At high alkali contents, the exotherm will be more vigorous and create more load on the heat exchangers. At low alkali contents, the reaction rate may be quite slow. While this temporarily reduces the difficulty in instantaneous heat load, it may permit potentially hazardous levels of unreacted formaldehyde to accumulate. Such accumulations could become dangerous as batch temperature rises. In both cases. 

Determination of the instantaneous rate at a particular concentration. To determine the rate of reaction, plot concentration versus time and take the tangent to the curve at the desired point. For the reaction N20s(g) — 2N02(g) + 02(g), it appears that the reaction rate at [N205] = 0.080 M is 0.028 mol/L - min. 

The solution that is obtained for the instantaneous reaction rate per unit area is ... 

The maintenance of product formation, after loss of direct contact between reactants by the interposition of a layer of product, requires the mobility of at least one component and rates are often controlled by diffusion of one or more reactant across the barrier constituted by the product layer. Reaction rates of such processes are characteristically strongly deceleratory since nucleation is effectively instantaneous and the rate of product formation is determined by bulk diffusion from one interface to another across a product zone of progressively increasing thickness. Rate measurements can be simplified by preparation of the reactant in a controlled geometric shape, such as pressing together flat discs at a common planar surface that then constitutes the initial reaction interface. Control by diffusion in one dimension results in obedience to the... 

To determine the reaction rate at a given instant in the course of the reaction, we should make our two concentration measurements as close together in time as possible. In other words, to determine the rate at a single instant we determine the slope of the tangent to the plot of concentration against time at the time of interest (Fig. 13.4). This slope is called the instantaneous rate of the reaction. The instantaneous reaction rate changes in the course of the reaction (Fig. 13.5). 

From now on, whenever we speak of a reaction rate, we shall always mean an instantaneous rate. The definitions in Eqs.l and 2 can easily be adapted to refer to the instantaneous rate of a reaction. 

The instantaneous reaction rate is the slope of a tangent drawn to the graph of concentration as a function of time for most reactions, the rate decreases as the reaction proceeds. 

Patterns in reaction rate data can often be identified by examining the initial rate of reaction, the instantaneous rate of change in concentration of a species at the instant the reaction begins (Fig. 13.6). The advantage of examining the initial rate is that the products present later in the reaction may affect the rate the interpretation of the rate is then quite complicated. There are no products present at the start of the reaction, and so any pattern due to the reactants is easier to find. 

Moreover, a dramatic increase of the reaction rate was observed when the coupUng of aromatic imines mediated by samariiun diiodide was carried out in the presence of both water and a tertiary amine or tetramethylethylene-diamine (TMEDA) [29], causing the almost instantaneous formation of the 1,2-diamine, although with undetermined diastereoselectivity. Similarly, the samarium diiodide promoted reductive coupling of iminiiun ions formed in situ by reacting ahphatic aldehydes with secondary amines and benzotriazole occurred at temperatures as low as - 70 °C [30]. Even in this case a mixture of diastereomers with undetermined ratio was obtained nevertheless, the item of diastereoselectivity induced by a chiral amine (auxiliary) is worthy of investigation. 

In closed systems (batch reactors), the instantaneous overall rate of accumulation of the reactant S is related to the reaction rate by the following expression ... 

Thermal methods in kinetic modelling. Methods for the estimation of thermokinetic parameters based on experiments in a reaction calorimeter will be discussed below. As mentioned in section 5.4.4.3, instantaneous heat evolved due to a single reaction is directly proportional to the reaction rate. Assume that the reaction is of first order. Then for isothermal operation ... 

Since the reaction rate almost invariably changes with time, it is necessary to use the time derivative to express tfye instantaneous rate of reaction. 

The principles of stoichiometry may be used to write the reaction rate in terms of the fraction conversion. The desired conversion level is expressed in terms of the initial substrate level. Thus CAo = 24 kg/m3. At any time the instantaneous concentration of substrate can be written as... 

The instantaneous reaction rate can be expressed in terms of the fraction conversion by combining equations A, C, and D. 

In order to determine the product distribution quantitatively, it is necessary to combine material balance and reaction rate expressions for a given reactor type and contacting pattern. On the other hand, if the reactor size is desired, alternative design equations reflecting the material balances must be employed. For these purposes it is appropriate to work in terms of the fractional yield. This is the ratio of the amount of a product formed to the amount of reactant consumed. The instantaneous fractional yield of a product V (denoted by the symbol y) is defined... 

For those cases where the rate expressions for all reactions taking place in the system under study are known, the use of the instantaneous yield in the above equations does not contribute significantly to understanding the system behavior. In such cases it is easier to determine the overall yield by substituting the appropriate ratio of reaction rate expressions for the instan-... 

In many applications, due to the large value of k, the first reaction is essentially instantaneous compared to the characteristic flow time scales. Thus, if the transport equation is used to solve for Y, the chemical-source term iS) will make the CFD code converge slowly. To avoid this problem, Y can be written in terms of by setting the corresponding reaction-rate expression (S ) equal to zero as follows ... 

Fig. 16.1. Results of reacting quartz sand at 100°C with deionized water, calculated according to a kinetic rate law. Top diagram shows how the saturation state Q/K of quartz varies with time bottom plot shows change in amount (mmol) of quartz in system (bold line). The slope of the tangent to the curve (fine line) is the instantaneous reaction rate, the negative of the dissolution rate, shown at one day of reaction.

A definition of instantaneous fractional yield is based on the ratio of reaction rates... 

Since the reaction rate is instantaneous, this is set equal to the feed rate of ammonia. 

The other basic type of explosion depends on a chain reaction. In some chain reactions, each chain carrier produces more than one free radical in propagation steps resulting in a rapid increase in the concentration of active species with time with a consequent rapid increase in the reaction rate. This in turn would further increase the production of free radicals. The reaction thus occurs instantaneously and an explosion takes place. The chain is called to branch when an active species or chain carrier produces more than one free radical or carrier, e.g. 

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