First order rate constant, meaning

Some authors use O] instead of cr as the substituent constant in such correlations.) An example is provided by the aminolysis of phenyl esters in dioxane the substrates RCOOPh were reacted with -butylamine, and the observed first-order rate constants were related to amine concentration by = k2 [amine] kj [amine]. The rate constants kz and k could be correlated by means of Eq. (7-54), the reaction constants being p = +2.14, b = + 1.03 (for A 2) and p = -1-3.03,8 = -1-1.08 (for ks). Thus, the two reactions are about equally sensitive to steric effects, whereas the amine-catalyzed reaction is more susceptible to electronic effects than is the uncatalyzed reaction. 

Figure 2. Inhibition of eel AChE by ANTX-A(S) - the secondary plot. P, the first-order rate constant which was the rate of inhibition at that ANTX-A(S) concentration obtained from the primary plot (insert). The intercept on the 1/P axis is 1/k and the intercept on the 1/[I] axis is -1/K. Figure insert Progressive irreversible inhibition of eel AChE by ANTX-A(S). The inactivation followed first-order kinetics. ANTX-A(S) concentrations, xg/mL (A) 0.083 ( ) 0.166 (o) 0.331 ( ) 0.497 (V) 0.599 ( ) control. Each point represents the mean of 3 or 4 determinations.

Diffusion provides an effective basis for net migration of solute molecules over the short distances encountered at cellular and subcellular levels. Since the diffu-sional flux is linearly related to the solute concentration gradient across a transport barrier [Eq. (5)], a mean diffusion time constant (reciprocal first-order rate constant) can be obtained as the ratio of the mean squared migration distance (L) to the effective diffusivity in the transport region of interest. 

The useful thing about the Lineweaver-Burk transform (or double reciprocal) is that the y intercept is related to the first-order rate constant for decomposition of the ES complex to E + P (7ccat or Vmax) and is equal to the rate observed with all of the enzyme in the ES complex. The slope, in contrast, is equal to the velocity when the predominant form of the enzyme is the free enzyme, E (free meaning unencumbered rather than cheap). 

This means that the rate constants derived from ionizing radiation experiments with bulk monomers are not the second-order k+p given by (2.5), but first-order rate constants, pj, given by (3.1). A comparison of these equations shows that the putative k+p reported... 

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. 

Note that the chemical step (2.75) is totally irreversible, attributed with a pseudo first-order rate constant (s ) defined as Atc =, rCx, where cx has the same meaning as for the CE and EC mechanisms (Sect. 2.4.1). Although this is the simplest case of an electrode mechanism involving chemical reaction, it has particular analytical utihty [53]. The mass transport of the redox species is described by the following model ... 

Although Ymax/ m is traditionally treated as a first-order rate constant for enzyme reactions at low substrate concentration, Northrop recently pointed out that V JK actually provides a measure of the rate of capture of substrate by free enzyme into a productive complex or the complexes destined to go on to form products and complete a turnover at some later time. His analysis serves to underscore the concepts (a) that any catalytic cycle must be characterized by the efficiency of reactant capture and product release, and (b) the Michaelis constant takes on meaning beyond that typically associated with affinity for substrate. Consider the case of an enzyme and substrate operating by the following sequence of reactions ... 

A West Texas gas oil is cracked in a tubular reactor packed with silica-alumina cracking catalyst. The liquid feed mw = 0.255) is vaporized, heated, enters the reactor at 630°C and 1 atm, and with adequate temperature control stays close to this temperature within the reactor. The cracking reaction follows first-order kinetics and gives a variety of products with mean molecular weight mw = 0.070. Half the feed is cracked for a feed rate of 60 m liquid/m reactor hr. In the industry this measure of feed rate is called the liquid hourly space velocity. Thus LHSV = 60 hr Find the first-order rate constants k and k " for this cracking reaction. 

The potentially greater toxicity of peroxynitrite can be readily visualized by comparing the mean diffusion distances that various nitrogen and oxygen-centered species may traverse in one lifetime. The definition of lifetime (t) is the time required for 67% of the initial concentration to decompose, and is readily calculated as the reciprocal of the pseudo-first-order rate constant for the disappearance of the species in question. Distances were calculated from the following equation, which is readily derived from the Fick s laws of diffusion (Nobel, 1983 Pryor, 1992). 

Our aim is to determine the concentration of A in the reactor as a function of time and in terms of the experimental conditions (inflow concentrations, pumping rates, etc.). We need to obtain the equation which governs the rate at which the concentration of A is changing within the reactor. This mass-balance equation will have contributions from the reaction kinetics (the rate equation) and from the inflow and outflow terms. In the simplest case the reactor is fed by a stream of liquid with a volume flow rate of q dm3 s 1 in which the concentration of A is a0. If the volume of the reactor is V dm3, then the average time spent by a molecule in the reactor is V/q s. This is called the mean residence time, tres. The inverse of fres has units of s-1 we will call this the flow rate kf, and see that it plays the role of a pseudo-first-order rate constant. We denote the concentration of A in the reactor itself by a. 

Relative measures of [02(1A8)] could presumably be put on an absolute footing by measurement of the apparent first-order rate constant, k — k7[03]e when ozone is in considerable excess by following relative [Oa(1A9)], and by measurement of the rate constant k = k7[02(tA,)]f. when 02(1A9) is in excess by following ozone concentrations. Then [02(1A9)] = k"[03]elk and a reference point for the excited-state concentration is thus obtained. Although the stoichiometry implied by reaction (7) does not necessarily mean that one molecule of ozone is consumed per molecule of O A,) reacting, allowance can nevertheless be made for the reaction... 

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). 

In NMR spectroscopy, when a species (for example, here [BH+]) is participating in an equilibrium, its spectrum is very dependent on its mean lifetime (t).39,40 The inverse of the mean lifetime is a first-order rate constant, called the rate of exchange (k = 1 It), which can be obtained from the line-shape analysis of the NMR bands if 1 s 1 < k 103 s. Three cases can thus be envisaged ... 

Table 11.3 lists the pseudo first-order rate constants for the decomposition of hydroxybenzoic acids. It shows that the ratio of the mean initial decomposition rate of HBAs under argon, R(HBA)Ar, to that under air, R(HBA)air, is equal to (3.0 + 4.9 + 5.1)/(2.7 + 3.4 + 3.1) = 1.4 (see Table 11.3). The ratio of the rate of OH radical formation under argon to that under air was estimated to be R( OH)Ar/.R( OH)air = 20/15 = 1.3 and is close to the value of R(HBA)Ar/R(HBA)air, which suggests that the decomposition of HBAs is mainly caused by OH radicals, and oxygen molecules have little effect on the decomposition.

By means of backward extrapolation towards time zero, we were able to separate the heat of mixing at the beginning of the experiment from the heat of reaction, as shown in Fig. 8.5a. In this way, and using Equation 8.18, results at 25°C of ArH = —61 2 kj mol-1 and Qmix = —6 kj mol-1 were obtained. At the same time, the pseudo-first-order rate constant, k, was determined to be 2.8 0.1 x 10-3 s-1. The measurements of the enthalpies and the rate constant were repeated at 40 and 55°C. The activation energy was then determined... 

For a pulse-type NMR experiment, the assumption has a straightforward interpretation, since the pulse applied at the moment zero breaks down the dynamic history of the spin system involved. The reasoning presented here, which leads to the equation of motion in the form of equation (72), bears some resemblance to Kaplan and Fraenkel s approach to the quantum-mechanical description of continuous-wave NMR. (39) The crucial point in our treatment is the introduction of the probabilities izUa which are expressed in terms of pseudo-first-order rate constants. This makes possible a definition of the mean density matrix pf of a molecule at the moment of its creation, even for complicated multi-reaction systems. The definition of the pf matrix makes unnecessary the distinction between intra- and inter-molecular spin exchange which has so far been employed in the literature. 

Another way of evaluating enzymatic activity is by comparing k2 values. This first-order rate constant reflects the capacity of the enzyme-substrate complex ES to form the product P. Confusingly, k2 is also known as the catalytic constant and is sometimes written as kcal. It is in fact the equivalent of the enzyme s TOF, since it defines the number of catalytic cycles the enzyme can undergo in one time unit. The k2 (or kcat) value is obtained from the initial reaction rate, and thus pertains to the rate at high substrate concentrations. Some enzymes are so fast and so selective that their k2/Km ratio approaches molecular diffusion rates (108—109 m s-1). This means that every substrate/enzyme collision is fruitful, and the reaction rate is limited only by how fast the substrate molecules diffuse to the enzyme. Such enzymes are called kinetically perfect enzymes [26],... 

M 52] [P 47] The capillary-in-capillary mixer proved functionality for millisecond time-resolved studies by ESI-MS [133]. The experiments were performed in two modes of operation in a spectral mode with recording of entire mass spectra and in a kinetic mode where the intensity of selected ion signals can be monitored as a function of the average reaction time. This enabled new means of resolving kinetic data, i.e. to measure reliably first-order rate constants up to at least 100 s 1. This performance is four times better than for reported ESI-MS experiments. 

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