Second-order reactions Characteristics

Figure 14.10 Second-order reaction characteristics (a) Decrease of reactant concentration with time.

Characteristics of Zero-, First-, and Second-Order Reactions... 

The characteristics of zero-, first-, and second-order reactions are summarized in Table 11.2. To determine reaction order, the properties in either of the last two columns at the right of the table can be used (Example 11.5). 

FIGURE 13.14 The characteristic shapes of the time dependence of the concentration of a reactant during a second-order reaction. The larger the rate constant, k, the greater is the dependence of the rate on the concentration of the reactant. The lower gray lines are the curves for first-order reactions with the same initial rates as for the corresponding second-order reactions. Note how the concentrations for second-order reactions fall away much less rapidly at longer times than those for first-order reactions do. 

Consequently, the characteristic dimensionless rate group for the second-order reaction and initial conditions is given by... 

Fig. 1.1 The characteristics of (a) zero- (b) first- and (c) second-order reactions. In (a) the concentration of A decreases linearly with time until it is all consumed at time T. The value of the zero-order rate constant is given by Aq/T. In (b) the loss of A is exponential with time. The plot of In [A], vs time is linear, the slope of which is k, the first-order rate constant. It obviously does not matter at which point on curve (b) the first reading is taken. In (c) the loss of A is hyperbolic with time. The plot of [A], vs time is linear with a slope equal to k, the second-order rate constant.

Since the k vs [B] plot illustrated in Fig. 1.5 is identical to that obtained with unidirectional concurrent first- and second-order reactions of A (Fig. 1.4(c)) confusion might result if the equilibria characteristics are not carefully assessed. The pseudo first-order rate constant k for the reaction... 

Kinetic and equilibrium studies of the sorption of methanol on various coals and on partially acety-lated samples of these coals have been used to elucidate a mechanism for this process. The data are interpreted in terms of partial acetylation blocking surface sites and perhaps interfering with intermolecular hydrogen bonding. It is proposed that the rate-determining step is a set of parallel, competing, second-order reactions involving transfer of methanol from the surface to the interior of the coal. All types of surface sites appear to participate, and the pressure-independent rate constant is considered to be the sum of the rate constants for each type of surface site. The dependence of the experimental rate constant on methanol pressure is a characteristic of the coal rank. 

Strictly speaking, except for the explicitly appearing reaction time r or rate mn, the form of the function depends on the concrete kinetics of the chemical reaction, i.e., on whether we are dealing with a first- or second-order reaction or with an autocatalytic reaction, just as, except for the characteristic dimension d, the form of the functions depends on the concrete geometric properties of the system and will be different for a round capillary and a plane slit. 

Characteristics of First- and Second-Order Reactions of the Type A----- Products... 

In perchloric acid, hexoses and pentoses are oxidized by Ce(IV) via formation of two complex intermediates. The first is partly oxidized following Michaelis-Menten kinetics and partly dissociated to the second, which is oxidized more slowly than the former.180 The first step in the oxidation of aldoses by Tl(III) in the same medium involves the C-l-C-2 cleavage of the aldehydo form of the sugar. Thus, D-glucose gives D-arabinose and formic acid. With an excess of oxidant the final product is carbon dioxide.181 In the presence of a catalytic amount of sulfuric acid in acetic acid, Tl(III) oxidizes maltose and lactose to the corresponding disaccharide aldonic acids. The reaction showed activation enthalpies and enthropies characteristic of second-order reactions.182... 

Problem 7 What is a second order reaction Derive the rate expression for a second order reaction. Discuss the characteristics of a second order reaction. Write some examples of second order reactions and study the kinetics of any one reaction. (Meerut 2002,2000)... 

A distinctive characteristic of styrene polymerization is its thermal selfinitiation at high temperatures (without the presence of a chemical initiator). The mechanism of styrene thermal initiation was first described by Mayo [12]. The kinetics of thermal initiation were described by Weickert and Thiele [13] as a second-order reaction, while Hui and Hamielec [14], Husain and Hamielec... 

Fig. 7. The characteristic functions of rj vs.

Effect of reaction order on diffusion factor y. Calculation of the characteristic function of y applicable to the case of an n order reaction yields similar functional relationships, in which the modulus

concentration term. For example, the case of second-order reaction involves the modulus... 

One of the major problems encountered in maximizing the flavor yields from cysteine-sugar systems is the high instability of the thiols diat are generated. The thiols do not only react with melanoidins but also widi each other (6, 2S). The result is that the characteristic meaty flavor disappears and a rubbery off-flavor is formed. Since the rates of the second-order reactions between the thiols are proportional to the square of the thiol concentrations, it is clear that products... 

Using Eq. 3.5.4, for a second-order reaction, the characteristic reaction time is... 

The quotient k JK represents the apparent rate coefficient of a second-order reaction whose rate density is determined by the frequency of (effective) collisions between enzyme and substrate molecules. For the same concentrations of enzyme and substrate, respectively, the catalytic efficiency can be described by the quotient koJKM- With the help of the values of k /K, we can investigate which among several substrates the enzyme prefers is therefore a measure of the substrate specificity of an enzyme where high values indicate high specificity. Typical values lie between 10 and 10 mol L s . Table 19.1 is a compilation of characteristic quantities of the enzymes urease and catalase. 

The influence of the transformation rate, respectively the characteristic reaction time on the temperature profile in multi-injection reactors, is shown in Figure 5.28 for a second order reaction. For nearly all instantaneous reactions, the... 

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