Second order reaction with different reactants

Second order reaction with different reactants 

In the previous chapter we developed the equations for a second order rate kinetics, in which both reactants were identical. This scenario is very common in dimerization reactions. However, in many second order reactions there ate two different reactants present. The aim of this chapter is to look at the relevant equations for this case. Additionally, we will look at an experimental way to simplify such general second order kinetics. 

The aim of this chapter is to extend the second order kinetics discussed in the previous chapter to a more general concept, in which the two reactants are not identical. Furthermore, the principal of pseudoorders will be introduced. By the end of the chapter you should be able to  

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Second order reaction with different reactants... 

For such a second-order reaction, a plot of Ijc against t is linear (Fig. 18.7). The factor 2 multiplying kt in this expression arises from the stoichiometric coefficient 2 for NO2 in the balanced equation for the specific example reaction. For other second-order reactions with different stoichiometric coefficients for the reactant (see the thermal decomposition of ethane described on page 755), we must modify the integrated rate law accordingly. 

Second Order Reaction with Reactants having Different Initial Concentrations Let the reaction... 

The simplest case of parallel second-order steps is that of formation of two different dimers of a reactant A, corresponding to the network 5.23 and rate equations 5.24 (see next page). At all times, both products are formed in the same ratio rP rQ = kAP kAQ, so that the decay of A is an ordinary second-order reaction with rate coefficient k = kAP + kAQ. Likewise, the product formations are ordinary second-order reactions. (One could think of the initial amount of A as divided into two portions in the ratio kAV kAQ that react independently of one another and at the same rate, one to P and the other to Q.) All equations and plots for irreversible second-order reactions thus are valid (see Section 3.3.1). 

Not many redox reactions on mineral surfaces follow the two basic assumptions of Eq. 18 outer-sphere transfer and regeneration of the surface during the reaction. Fast reductive dissolutions with powerful reducing agents may potentially lead to an additional test of Eq. 18. In many cases the surface species arc consumed during the reaction. Astumian and Schelly (1984) developed a theory to compare a second-order reaction of two reactants in solution (Eq. 14) with u heterogeneous reaction of a dissolved species A and an adsorbed species B. The two different reaction environments are outlined in Figure 5. Here we denote the surface complex as =MO-B ... 

Apply the rate-law equations to show the difference between a first-order reaction with a single reactant and a second-order reaction with a single reactant. 

Figure 3.1 Conversion for a second-order batch reaction with different reactant ratios. 

Strategy (a) The relationship between the concentrations of a reactant at different times is given by the integrated rate law. Because this is a second-order reaction with a single reactant, we must use Equation 14.11. (b) The half-life for a second-order reaction is given by Equation 14.12. 

Let us consider a second order reaction which is first order with respect to each reactant and the reactants have different initial concentrations. 

It is important to recognize the difference between the order of a reaction with respect to a specific reactant and the overall order of a reaction. The /order of a reaction with respect to a particular reactant is the power to which the concentration of that reactant must be raised to have direct proportionality between concentration and reaction rate. According to Equation 8-2 the rate of the chloromethane-hydroxide ion reaction is first order with respect to chloromethane and first order with respect to hydroxide ion. In Equation 8-1 the rate is first order with respect to chloromethane and zero order with respect to hydroxide ion because [OH0]0 = 1. The overall order of reaction is the sum of the orders of the respective reactants. Thus Equations 8-1 and 8-2 express the rates of overall first-order and second-order reactions, respectively. 

The same general conclusions apply since backmixing of products with reactants should be avoided, a tubular plug-flow reactor or a batch reactor is preferred. However, there is one respect in which a series reaction involving a second reactant B does differ from simple series reaction with one reactant, even when the orders are the same. This is in the stoichiometry of the reaction the reaction cannot proceed completely to the product Q, even in infinite time, if less than two moles... 

This is the most common mode of addition. For safety or selectivity critical reactions, it is important to guarantee the feed rate by a control system. Here instruments such as orifice, volumetric pumps, control valves, and more sophisticated systems based on weight (of the reactor and/or of the feed tank) are commonly used. The feed rate is an essential parameter in the design of a semi-batch reactor. It may affect the chemical selectivity, and certainly affects the temperature control, the safety, and of course the economy of the process. The effect of feed rate on heat release rate and accumulation is shown in the example of an irreversible second-order reaction in Figure 7.8. The measurements made in a reaction calorimeter show the effect of three different feed rates on the heat release rate and on the accumulation of non-converted reactant computed on the basis of the thermal conversion. For such a case, the feed rate may be adapted to both safety constraints the maximum heat release rate must be lower than the cooling capacity of the industrial reactor and the maximum accumulation should remain below the maximum allowed accumulation with respect to MTSR. Thus, reaction calorimetry is a powerful tool for optimizing the feed rate for scale-up purposes [3, 11]. 

The rate constants of second-order reactions in which the two reactants, although different, have the same initial concentration, are also determined with the help of Eq. 2.26. 

The rate constants of reactions without gaseous reactants have the following (or comparable) units mol/cm s (zeroth-order), 1/s or s (first-order), and cmVmol s (second-order). Shown in Fig. 2.3 for zeroth-, first-, and second-order reactions is the time-dependence of the concentration of a reactant A, and its linear and log rate of change with concentration. The appearance of the plots, and particularly the log rate versus log (A) plots, differs uniquely for each reaction order. This sug-... 

Note that the half-life of a second-order reaction is inversely proportional to the initial reactant concentration. This result makes sense because the half life should be shorter in the early stage of the reaction when more reactant molecules are present to collide with each other. Measnring the half-lives at different initial concentrations is one way to distinguish between a first-order and a second-order reaction. 

The torch front and plane front are also formed during the simple mixing of coloured flows without any chemical reactions [8-11]. Thus, these fronts of liquid flow mixing can appear both during fast chemical reactions and without any reactions. This fact led to further investigation into the influence of the reaction rate constant on the conditions of quasi-plug flow mode formation in turbulent flows (plane front of reaction). Solutions of reactants were prepared which interacted with each other, at different rate constants, with the formation of coloured products these solutions were introduced into the tubular reactor for the formation of reaction front macrostructures. The second-order reactions, which occur at rate constants in the range of = 10 -10 1/mol-s, were studied ... 

ER.7 The following irreversible reaction A—>3R was studied in the PER reactor. Reactant A is fed with an inert gas (40%) at 10 atm and 600 K and a flow rate of l.OL/min. Product R was measured in the exit gas for different space velocities, as presented in the following table. The rate is a second-order reaction. Calculate the... 

As we move from first-order to second-order reactions, complexity increases sig-nifieantly. To begin, there are several different types of second-order reactions. A second-order reaction can either be second order with respect to a single reactant or first order with respect to two distinct reactants (and therefore second order overall). In order to illustrate these possibilities, eonsider the following general reaction ... 

Pseudo-First-Order Reactions Under certain circumstances, second-order reactions can sometimes be approximated as first-order reactions. For example, consider a second-order reaction that depends on the concentrations of two different reactants (each to the first order). If one of the reactant concentrations is much larger than the other reactant concentration, then it will remain essentially constant (only slightly depleted) during the reaction process while the concentration of the other reactant is fully consumed. In this situation, the second-order rate law can be rewritten as a pseudo-first-order rate law. As an example, consider a second-order reaction that is first order with respect to two reactants A and B. The rate law for this reaction is... 

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