Rate of appearance

Here, a molecule of C is formed only when a collision between molecules of A and B occurs. The rate of reaction r. (that is, rate of appearance of species C) depends on this collision frequency. Using the kinetic theory of gases, the reaction rate is proportional to the product of the concentration of the reactants and to the square root of the absolute temperature ... 

Assuming this reaction is an elementary reaction, its molecularity is 2 that is, it is a bimolecular reaction. The velocity of this reaction can be determined from the rate of disappearance of either A or B, or the rate of appearance of P or Q ... 

From the mechanism, the rate of appearance of the product is given by rate = E2[ES]. Substituting the preceding equation for [ES], we obtain... 

Another quite general approach is to employ a coupled assay (Figure 7-10). Typically, a dehydrogenase whose substrate is the product of the enzyme of interest is added in catalytic excess. The rate of appearance or disappearance of NAD(P)H then depends on the rate of the enzyme reaction to which the dehydrogenase has been coupled. 

Figure 15-5 also shows that each species has its own rate, but the individual rates are linked by the stoichiometric coefficients. The reaction generates one molecule of N2 O4 for every two molecules of NO2 that are destroyed. That is, the 1 2 stoichiometry of this reaction results in a 1 2 relationship between the rate of disappearance of NO2 and the rate of appearance of N2 O4. The ratio of rates for different species is always equal to the ratio of their stoichiometric coefficients. 

The reaction may be followed by measuring the rate of appearance or disappearance of MADH at 340 nm. In some methods a coupled reaction using diaphorase or phenazine methosulfate plus an indicator dye are used. The amount of pyruvate formed can also be measured colorimetrically. With the general avail-... 

The cerium(IV) oxidation of Mn(II) has been briefly reported on by Aspray et The reaction was followed from the rate of appearance of Mn(III) at... 

Exponential rate expressions are also useful in deriving kinetic equations because they can be substituted into differential equations, which can then be integrated. For example, from Scheme 2 the differential equation describing the rate of appearance of unchanged drug in urine may be written ... 

With Eqs. (104) and (106), the rate of appearance of metabolite into the receiver... 

It is the reaction characterized by fc2(lim) that exhibits the specificity toward the position of the phenyl group substituent, and is responsible for the accelerated rates of appearance of phenol. The rate-limiting step of the overall reaction, however, is the hydrolysis of the acyl-cycloamylose. The overall reaction, then, will be catalytic only if k3 exceeds the rate constant for the alkaline hydrolysis of a particular ester. This situation is true only for highly unreactive esters. If, therefore, the cycloamyloses are to be uti-... 

As a simple model for the enzyme penicillinase, Tutt and Schwartz (1970, 1971) investigated the effect of cycloheptaamylose on the hydrolysis of a series of penicillins. As illustrated in Scheme III, the alkaline hydrolysis of penicillins is first-order in both substrate and hydroxide ion and proceeds with cleavage of the /3-lactam ring to produce penicilloic acid. In the presence of an excess of cycloheptaamylose, the rate of disappearance of penicillin follows saturation kinetics as the cycloheptaamylose concentration is varied. By analogy to the hydrolysis of the phenyl acetates, this saturation behavior may be explained by inclusion of the penicillin side chain (the R group) within the cycloheptaamylose cavity prior to nucleophilic attack by a cycloheptaamylose alkoxide ion at the /3-lactam carbonyl. The presence of a covalent intermediate on the reaction pathway, although not isolated, was implicated by the observation that the rate of disappearance of penicillin is always greater than the rate of appearance of free penicilloic acid. 

The rate of appearance of p-nitrophenolate ion from p-nitrophenyl methylphosphonate (7), an anionic substrate, is moderately accelerated in the presence of cycloheptaamylose (Brass and Bender, 1972). The kinetics and pH dependence of the reaction are consistent with nucleophilic displacement of p-nitrophenolate ion by an alkoxide ion derived from a cycloheptaamylose hydroxyl group to form, presumably, a phosphonylated cycloheptaamylose. At 60.9° and pH 10, the cycloheptaamylose-induced rate acceleration is approximately five. Interestingly, the rate of hydrolysis of m-nitrophenyl methylphosphonate is not affected by cycloheptaamylose. Hence, in contrast to carboxylate esters, the specificity of cycloheptaamylose toward these phosphonate esters is reversed. As noted by Brass and Bender (1972), the low reactivity of the meta-isomer may, in this case, be determined by a disadvantageous location of the center of negative charge of this substrate near the potentially anionic cycloheptaamylose secondary hydroxyl groups. 

Additional support for a discrete binding site is derived from the observation that potassium iodide depresses the rate of appearance of phenol from p-nitrophenyl hexanoate in the presence of 16. In contrast, potassium iodide modestly accelerates the reaction of 17 with p-nitrophenyl hexanoate, in... 

Figure 3. Plot of the pseudo first order rate for reaction of Fe(C0)3 with CO. The rate of disappearance of Fe(C0)3 at 1954 cm l ( ) and the rate of appearance of Fe(C0)4 at 1984 cm ( ) are plotted against pressure of added CO. (Reproduced with permission from reference 8. Copyright 1986 American Institute of Physics.)...

The non-covalently bound BPDEs to DNA formed initially appear to be intercalation complexes (1 6,52-55) Meehan et al. (1 6) report that the BPDE intercalates into DNA on a millisecond time scale while the BPDE alkylates DNA on a time scale of minutes. Most of the BPDE is hydrolyzed to tetrols (53-56). Geacintov et al. (5l ) have shown with linear dichroism spectral measurements that the disappearance of intercalated BPDE l(+) is directly proportional to the rate of appearance of covalent adducts. These results suggest that either there may be a competition between the physically non-covalently bound BPDE l(+) and an externally bound adduct or as suggested by the mechanism in the present paper, an intercalative covalent step followed by a relaxation of the DNA to yield an externally bound adduct. Their results for the BPDE i(-) exhibit both intercalative and externally bound adducts. The linear dichroism measurements do not distinguish between physically bound and covalent bound forms which are intercalative in nature. Hence the assumption that a superposition of internal and external sites occurs for this isomer. 

Atienza et al. [657] reviewed the applications of flow injection analysis coupled to spectrophotometry in the analysis of seawater. The method is based on the differing reaction rates of the metal complexes with 1,2-diaminocycl-ohexane-N, N, N, A/Metra-acetate at 25 °C. A slight excess of EDTA is added to the sample solution, the pH is adjusted to ensure complete formation of the complexes, and a large excess of 0.3 mM to 6 mM-Pb2+ in 0.5 M sodium acetate is then added. The rate of appearance of the Pbn-EDTA complex is followed spectrophotometrically, 3 to 6 stopped-flow reactions being run in succession. Because each of the alkaline-earth-metal complexes reacts at a different rate, variations of the time-scan indicates which ions are present. 

We can, however, consider the stability of each of the three operating points in Example 14-7 with respect to the inevitable small random fluctuations in operating conditions, including cA, in steady-state operation. Before doing this, we note some features of the rate law as revealed in Figure 14.4. There is a maximum value of (- rA) at cA = 1.166 mol m-3. For cA < 1.166, the rate law represents normal kinetics ( rA) increases as cA increases for cA > 1.166, we have abnormal kinetics (—rA) decreases as cA increases. We also note that (-rA) in equation (C), the rate law, represents the (positive) rate of disappearance of A by reaction within the CSTR, and that (—rA) in equation (D), the material balance, represents the (positive) net rate of appearance of A by flow into and out of the reactor. As noted above, in steady-state operation, these two rates balance. 

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