Reaction rates instantaneous rate

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

When the stoichiometric coefficients, va, vy, etc., are included in the rate law, as in Equation 3.5, the reaction has a unique rate constant (k) under specified conditions regardless of whether the rate is measured by monitoring the changing concentration of A, B or C. It also follows from Equation 3.5 that (except for zero-order reactions) the instantaneous rate of a reaction changes as the reaction proceeds, as will be illustrated later in Fig. 3.1. Thus, k is the parameter which measures whether the reaction (imprecisely expressed) is fast or slow . In any case, it follows that any property of a reacting system which relates (preferably directly) to the concentration of any component in the chemical reaction maybe monitored to measure the rate and, hence, to investigate the rate law and quantify the rate constant. 

For fast and intermediate reactions, the time-averaged reaction source term will contain some additional terms. These additional terms need to be modeled to close the set of equations. For example, consider the case of a single second-order reaction with instantaneous rate given by... 

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. 

A further factor which must also be taken into consideration from the point of view of the analytical applications of complexes and of complex-formation reactions is the rate of reaction to be analytically useful it is usually required that the reaction be rapid. An important classification of complexes is based upon the rate at which they undergo substitution reactions, and leads to the two groups of labile and inert complexes. The term labile complex is applied to those cases where nucleophilic substitution is complete within the time required for mixing the reagents. Thus, for example, when excess of aqueous ammonia is added to an aqueous solution of copper(II) sulphate, the change in colour from pale to deep blue is instantaneous the rapid replacement of water molecules by ammonia indicates that the Cu(II) ion forms kinetically labile complexes. The term inert is applied to those complexes which undergo slow substitution reactions, i.e. reactions with half-times of the order of hours or even days at room temperature. Thus the Cr(III) ion forms kinetically inert complexes, so that the replacement of water molecules coordinated to Cr(III) by other ligands is a very slow process at room temperature. 

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. 

To set up expressions for the instantaneous rate of a reaction, we consider At to be very small so that t and t + At are close together we determine the concentration of a reactant or product at those times and find the average rate from Eq. 1. Then we decrease the interval and repeat the calculation. We can imagine continuing the process until the interval At has become infinitely small (denoted d/) and the change in molar concentration of a reactant R has become infinitesimal (denoted d R]). Then we define the instantaneous rate as... 

FIGURE 13.4 The rate ol reaction is the change in concentration of a reactant (or product) divided by the time interval over which the change occurs (the slope of the line AB, for instance). The instantaneous rate is the slope of the tangent to the curve at the time of interest. 

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 ... 

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