Second order rate constant meaning

Another means is available for studying the exchange kinetics of second-order reactions—we can adjust a reactant concentration. This may permit the study of reactions having very large second-order rate constants. Suppose the rate equation is V = A caCb = kobs A = t Ca, soAtcb = t For the experimental measurement let us say that we wish t to be about 10 s. We can achieve this by adjusting Cb so that the product kc 10 s for example, if A = 10 M s , we require Cb = 10 M. This method is possible, because there is no net reaction in the NMR study of chemical exchange. 

What about reactions of the type A + B — C This is a second-order reaction, and the second-order rate constant has units of M min-1. The enzyme-catalyzed reaction is even more complicated than the very simple one shown earlier. We obviously want to use a second-order rate constant for the comparison, but which one There are several options, and all types of comparisons are often made (or avoided). For enzyme-catalyzed reactions with two substrates, there are two Km values, one for each substrate. That means that there are two kcJKm values, one for each substrate. The kcJKA5 in this case describes the second-order rate constant for the reaction of substrate A with whatever form of the enzyme exists at a saturating level B. Cryptic enough The form of the enzyme that is present at a saturating level of B depends on whether or not B can bind to the enzyme in the absence of A.6 If B can bind to E in the absence of A, then kcJKA will describe the second-order reaction of A with the EB complex. This would be a reasonably valid comparison to show the effect of the enzyme on the reaction. But if B can t bind to the enzyme in the absence of A, kcat/KA will describe the second-order reaction of A with the enzyme (not the EB complex). This might not be quite so good a comparison. 

In many cases K is small, such that this equation simplifies to kobs = ETZ [Red], which means that the observed second-order rate constant and the associated activation parameters are composite quantities, viz. AV = AV ( et) + A VCK). When K is large enough such that 1 + 2 [Red] > 1, it is possible to separate ET and K kinetically and also the associated activation parameters, viz. AV (kv r) and AV(K) (141). A series of reactions were studied where it was possible to resolve K and ET, i.e., AV(K) and AV (kKT). In this case oppositely charged reaction partners were selected as indicated in the following reactions (142444 ) ... 

However, if for two different solvents the kinetics and the initiator efficiencies are the same, and if equilibrium (2) is the only one involved, and if the more polar solvent gives a faster reaction, this means that the experimental second-order rate-constant [ + a kp+ - kjp)] in equation (vb) is greater for the more polar solvent. Since theory (and experiment) tell us that for the more polar solvent kp+ and p are smaller than for a less... 

Vary fast reactions, both in gaseous and liquid phases, can be studied by this method. In flash photolysis technique, a light flash of very high intensity and very short duration ( 10 6 sec) is produced in the neighborhood of the reaction vessel. This produces atoms, free radicals and excited species in the reaction system. These species undergo further reactions which can be followed by spectroscopic means. The method is also known as kinetic spectroscopy. The first order rate constant as large as 105 sec-1 and second order rate constants as large as 1011 mol dm sec-1 can be measured by this technique. 

The individual contributions of the H20, H+, and HO- catalysts to the mechanism of the reaction were further evaluated by means of the kinetics parameters (Table 6.4). At neutral pH, Reactions a and c were both dominated by fcH2<> The second-order rate constants ku+ and kHO- were identical, indicating similar efficiencies of the H+ and HO catalysts. Interestingly, the second-order rate constants for the hydrolysis of Gly-D-Val (6.48) to yield Gly and D-Val (6.49) (Reaction b) could also be calculated (Table 6.4). The similarity to the corresponding rate constants of Reactions a and c suggests that the rate of peptide bond hydrolysis is not particularly sensitive to substitution at or protonation of the flanking amino and carboxy groups [69],... 

Second-order rate constants for MTSEA-, MTSET-, and MTSES-modification of residues within the loop D region of the GABA-binding site. Second-order rate constants (IC2) represent the mean standard deviation. NR, no reaction. The free solution rates were reported by Karlin and Akabas (1998) and reflect the rates of MTS reaction with 2-mercaptoethanol. Adapted from Holden and Czajkowski (2002) with permission from the American Society of Biochemistry and Molecular Biology... 

For the case where R is a methyl group, the reaction is in the falloff region at 1 atm, and for C2H5, it is close to the high-pressure limit. For C3H7 and above, a value for the effective second-order rate constant, k.r, of (0.8-2) X 10 11 cnr1 molecule 1 s 1 means that the lifetime of an alkyl radical at 1 atm in air is 10 ns. 

Recognizing this, Richard and Jencks, proposed using azide ion as a clock for obtaining absolute reactivities of less stable cations. The basic assumption is that azide ion is reacting at the diffusion limit with the cation. Taking 5 x 10 M s as the second-order rate constant for this reaction, measurement of the selectivity fcaz Nu for the competition between azide ion and a second nucleophile then provides the absolute rate constant since feaz is known. The clock approach has now been applied to a number of cations, with measurements of selectivities by both competition kinetics and common ion inhibition. Other nucleophiles have been employed as the clock. The laser flash photolysis (LFP) experiments to be discussed later have verified the azide clock assumption. Cations with lifetimes in water less than about 100 ps do react with azide ion with a rate constant in the range 5-10x10 M- s-, " which means that rate constants obtained by a clock method can be viewed with reasonable confidence. 

Reactions in 1.83M Sulfuric Acid. In a medium of 1.83M sulfuric acid the reaction of or-Cr(OH2) 2(0204)2 with cerium(IV) was found to be of apparent second order, being first order in each reactant. Second-order rate plots based on spectro-photometric measurements at 25° are shown in Figure 2. The average of 11 kinetic runs which covered the reactant concentration ranges [Ce(IV)]o = 2.00 X 10-2 to 2.50 X 10-3Af and [cis-]0 = 1.00 X 10-2 to 2.50 X 10 W gave a mean value for the apparent second-order rate constant, k (= — [Ce(IV) / /[Ge(IV)][cis-]) of 1.06 ( 0.10) X 10-1 liter mole-1 sec.-1 The value in parenthesis refers to the standard deviation from the mean. 

Significance of the Michaelis Constant, Km. The Michae-lis constant Km has the dimensions of a concentration (molarity), because k x and k2, the two rate constants in the numerator of equation (23), are first-order rate constants with units expressed per second (s 1), whereas the denominator fc is a second-order rate constant with units of m-is-1. To appreciate the meaning of Km, suppose that [S] = Km. The denominator in equation (25) then is equal to 2[S], which makes the velocity v = VmaJ2. Thus, the Km is the substrate concentration at which the velocity is half maximal (fig. 7.6). 

The spectral changes observed during oxidation provide a means for monitoring the kinetics of the oxidation process. The reactions follow a rate law that is first order in [Ni] and first order in [02] Rate = fc[Ni(L)CN] [02] (79). The reaction is relatively slow and not very sensitive to the nature of the N-substituent (k = 1.4-3.1 X 10 2 M 1 s-1 in dimethylformamide (DMF) at 30 °C). The reaction rates are independent of the presence of a singlet oxygen scavenger or radical traps. The activation parameters AH and AS were measured by using the temperature dependence of the second-order rate constants in DMF... 

Chaimovich and coworkers have prepared large unilamellar vesicles of DODACl by a vaporization technique which gives vesicles of ca 0.5 pm diameter. These vesicles are much larger than those prepared by sonication, where the mean diameter is 30 nm, and their effects on chemical reactivity are very interesting. The reaction of p-nitrophenyl octanoate by thiolate ions is accelerated by a factor of almost 10 by DODACl vesicles (Table 2), but this unusually large effect is due almost completely to increased concentration of the very hydrophobic reactants in the small region of the vesicular surface and an increased extent of deprotonation of the thiol. There is uncertainty as to the volume element of reaction in these vesicles, but it seems that second-order rate constants at the vesicular surface are similar to those in cationic micelles or in water (Cuccovia et al., 1982b Chaimovich et al., 1984). 

Apply Equation 1.53 to calculate the mean residence time needed to achieve 90% conversion in a CSTR for (a) a first-order reaction and (h) a second-order reaction of the type A -I- B - products. The rate constant for a first-order reaction has units of reciprocal time. For the current example, assume k = 0.1 s. The rate constant for a second-order reaction has units of reciprocal time and reciprocal concentration. It is common practice to multiply a second-order rate constant by the initial or inlet concentration of the stoichiometrically limiting coefficient. This gives a rate constant with units of reciprocal time. For the second-order reaction suppose ajnk = 0.1 s . ... 

---