The denaturation of a-la and /Mg in milk follows first- and second-order kinetics, respectively (Figure 9.15). Both proteins show a change in the temperature-dependence of denaturation at about 90°C (Figure 9.15). [Pg.283]

When even second-order reactions are included in a group to be analyzed, individual integration methods maybe needed. Three cases of coupled first- and second-order reactions will be touched on. All of them are amenable only with difficulty to the evaluation of specific rates from kinetic data. Numerical integrations are often necessary. [Pg.695]

FIGURE 3.18. Semi-Batch versus Batch Operations for First- and Second-Order Kinetics. [Pg.133]

There are, however, other options for treating data from both first- and second-order kinetics. Collectively, they are known as time lag methods. These methods are primarily of historical interest, although the mathematical rearrangements provide insights into the nature of the functions involved. [Pg.26]

The second and third terms in equation (2.86) describe kinetics of annihilation of radicals corresponding to above processes developing in the first and second order of magnitude with respect to chemisorbed radicals. Note that the rate constant A" may be dependent on concentration of free radicals in volume. [Pg.150]

Figure 7 Kinetic analysis of a typical ionogenic reaction (Experiment SGC 9) by means of first and second order plots, p is the ratio [SD ions]t/[SD ions]m. The change of order occurs at about 300 s when p = 70%. |

E. Nakashima, A. Tsuji, M. Nakamura, T. Yamana, Physicochemical Properties of Amphoteric beta-Lactam Antibiotics. IV. First- and Second-Order Degradations of Cefaclor and Cefatrizine in Aqueous Solution and Kinetic Interpretation of the Intestinal Absorption and Degradation of the Concentrated Antibiotics , Chetn. Pharrn. Bull. 1985, 33, 2098-2106. [Pg.248]

Regions of stable and unstable operation determined by numerical simulation of mass and heat balances equations first- and second-order, autocatalytic, and product-inhibited kinetics graphically presented boundaries in co-ordinates

Levi and associates (26) showed that the decay kinetics in the Dember effect measured on a (S+Au)-sensitized iodobromide emulsion could be expressed by the sum of first- and second-order reactions. They attribute the first-order process to the reaction of electrons and interstitial silver ions [Pg.363]

These equations are similar to those of first- and second-order chemical reactions, I being a photon concentration. This applies only to isotropic radiation. The coefficients A and B are known as the Einstein coefficients for spontaneous emission and for absorption and stimulated emission, respectively. These coefficients play the roles of rate constants in the similar equations of chemical kinetics and they give the transition probabilities. [Pg.23]

Satisfaction of kinetic order. Carriers follow Michaelis-Menten-type saturation kinetics or first-order kinetics. Ion channels follow the type of respective structure—unimolecular transmembrane channels and bimolecular half-channels follow first- and second-order kinetics, respectively. The kinetic order of supramolecular channels depends on the assembly number. However, this principle can be applied only when the association constants are small. If the association becomes strong, the kinetic order decreases down to zero. Then the validity becomes dubious in view of the absolute criterion of the mechanism. Decreased activation energy compared to the carrier transport mechanism and competitive inhibition by added other cations stand as criteria. [Pg.204]

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides [Pg.2947]

Applying a chromatographic method it is sometimes possible to separate copolymer molecules according to their size Z and composition [5]. The SCD found in such a way can be compared with that calculated within the framework of the chosen kinetic model. The first- and second-order statistical moments of SCD are of special importance. [Pg.165]

Since more than one of these dissolution processes might occur in the coal extraction experiments, it is necessary to allow for concurrent chemical reactions when constructing a rate equation. Since reactions are either first or second order, a kinetic expression having concurrent reactions of first and second order must be derived. [Pg.430]

The kinetic data based on the demonstration of specific acid catalysis in buffers, solvent isotope effects and acidity functions all support mechanisms where the proton-transfers are fast. It is possible to write equations which accommodate these facts together with the first-order dependence on hydrazo-compound and the concurrent first and second-order dependence on acidity. These are [Pg.442]

Conversion rate data obtained under a wide range of operating conditions may be worked out to provide a kinetic expression, most typically expressed according to well established models for bioprocess kinetics first and second order, Monod, Haldane, product-inhibited, etc. [Pg.113]

Simpler evidence for the presence of a tetrahedral intermediate is adduced from a study of the kinetics of alkaline hydrolysis of amides such an anilides26-28, chloroacetamide30, N,N-diacylamines31, and urea32. The rate equations for these reactions contain both first- and second-order terms in hydroxide ion. A reasonable explanation is that the hydrolysis mechanism involves a tetrahedral intermediate, rather than that the second-order term is due to base catalysis of the addition of the hydroxide ion to the carbonyl group. Such a mechanism is [Pg.213]

It is obvious that to quantify the rate expression, the magnitude of the rate constant k needs to be determined. Proper assignment of the reaction order and accurate determination of the rate constant is important when reaction mechanisms are to be deduced from the kinetic data. The integrated form of the reaction equation is easier to use in handling kinetic data. The integrated kinetic relationships commonly used for zero-, first-, and second-order reactions are summarized in Table 4. [The reader is advised that basic kinetic [Pg.155]

A kinetic model which accounts for a multiplicity of active centres on supported catalysts has recently been developed. Computer simulations have been used to mechanistically validate the model and examine the effects on Its parameters by varying the nature of the distrlbultons, the order of deactivation, and the number of site types. The model adequately represents both first and second order deactivating polymerizations. Simulation results have been used to assist the interpretation of experimental results for the MgCl /EB/TlCl /TEA catalyst suggesting that [Pg.403]

Interestingly, in the experiments devoted solely to computational chemistry, molecular dynamics calculations had the highest representation (96-98). The method was used in simulations of simple liquids, (96), in simulations of chemical reactions (97), and in studies of molecular clusters (98). One experiment was devoted to the use of Monte Carlo methods to distinguish between first and second-order kinetic rate laws (99). One experiment used DFT theory to study two isomerization reactions (100). [Pg.127]

The differential (rate) forms are (1.16), (1.18) and (1.20), and the corresponding integrated forms are (1.17), (1.19) (or (1.19a)) and (1.21). The designations [A]q and [A], represent the concentrations of A at zero time and time /. Linear plots of [A], In [A], or [A], vs time therefore indicate zero-, first, or second order dependence on the concentration of A. The important characteristics of these order reactions are shown in Fig. 1.1. Notwithstanding the appearance of the plots in 1.1 (b) and 1.1 (c), it is not always easy to differentiate between first-and second-order kinetics.Sometimes a second-order plot of kinetic data might be mistaken for successive first-order reactions (Sec. 1.6.2) with similar rate constants. [Pg.6]

In Chapter 8, we addressed proton transfer reactions, which we have assumed to occur at much higher rates as compared to all other processes. So in this case we always considered equilibrium to be established instantaneously. For the reactions discussed in the following chapters, however, this assumption does not generally hold, since we are dealing with reactions that occur at much slower rates. Hence, our major focus will not be on thermodynamic, but rather on kinetic aspects of transformation reactions of organic chemicals. In Section 12.3 we will therefore discuss the mathematical framework that we need to describe zero-, first- and second-order reactions. We will also show how to solve somewhat more complicated problems such as enzyme kinetics. [Pg.462]

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