Elementaiy reaction rate equation

In deciding whether to write an elementaiy reaction as either a reversible or an irreversible reaction, we take the practical view that if the reverse reaction is negligibly slow on the experimental time scale, the reaction is essentially irreversible. Consider the alkaline hydrolysis of an ester, for which the rate equation is... 

The Arrhenius equation relates the rate constant k of an elementaiy reaction to the absolute temperature T R is the gas constant. The parameter is the activation energy, with dimensions of energy per mole, and A is the preexponential factor, which has the units of k. If Jt is a first-order rate constant, A has the units seconds", so it is sometimes called the frequency factor. 

Most elementary reactions involve either one or two reactants. Elementaiy reactions involving three species are infrequent, because the likelihood of simultaneous three-body encounter is small. In closed, well-mixed chemical systems, the integration of rate equations is straightforward. Results of integration for some important rate laws are listed in Table 2.7, which gives the concentration of reactant A as a function of time. First-order reactions are particularly simple the rate constant k has units of s , and its reciprocal value (1/k) provides a measure of a characteristic time for reaction. It is common to speak in terms of the half-life ( 1/2) for reaction, the time required for 50% of the reactant to be consumed. When... 

This gas-phase reaction is carried out over a zeohte catalyst and follows an elementaiy rate law. The catalyst is packed in a tubular PBR that is 2 m in diameter and 22 m in length. Pure methanol is fed at a molar flow rate of 950 molls, a pressure of 1500 kPa, a concentration of 0.4 mol/ dm, and 490°C. The conversion and pressure at the exit are 0.5 and 375 kPa, respectively. Flow throughout the bed is known to be such that the turbulent contribution in the Eigim equation (i.e., G ) can be neglected. The tubular PBR is to be replaced with a spherical PBR containing an equal amoimt of identical catalyst. The sphericd PBR measirres 5.2 m in diameter and has screens placed 2 dm fiom each end (i.e, L = L =24 dm). 

A catalyst speeds up a reaction by providing a set of elementaiy steps with more favorable kinetics than those that exist in its absence. From Equation 14.8 we know that the rate constant k (and hence the rate) of a reaction depends on the frequency factor (A) and the activation energy ( a)— the larger the value of A (or the smaller the value of E ), the greater the rate. In many cases, a catalyst increases the rate by lowering the activation energy for the reaction. 

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