Rate constant meaning

FIGURE 13.21 The equilibrium constant for a reaction is equal to the ratio of the rate constants for the forward and reverse reactions, (a) A forward rate constant (A) that is relatively large compared with the reverse rate constant means that the forward rate matches the reverse rate when the reaction has neared completion and the concentration of reactants is low. (b) Conversely, if the reverse rate constant (A ) is larger than the forward rate constant, then the forward and reverse rates are equal when little reaction has taken place and the concentration of products is low. 

If [B] is in excess and effectively constant throughout reaction, then [B]/J is also effectively constant throughout reaction, and can be taken with k to give rate = k [A] where k is called the pseudo-rate constant - meaning as if. ... 

A positive cross-relaxation rate constant means that if spin S deviates from equilibrium cross-relaxation will increase the magnetization on spin I. This leads to an increase in the signal from I, and hence a positive NOE enhancement. This situation is typical for small molecules is non-viscous solvents. 

Superoxide anion and nitrogen monoxide engender peroxynitrite at almost diffusion-controlled rates (6.7x10 M" . s" Huie and Padmaja 1993 for review see Ducrocq et al. 1999). Its high rate constant means that NO competes effectively with superoxide dismutase for reaction with O2 " (Hogg et al. 1992). 

This proportionality constant is called the rate constant (see Chapter 7, Section 7.9). A large rate constant means that the starting material is rapidly converted to product. For a second-order reaction, the rate constant is determined from a plot of time versus a concentration term that includes both starting materials. Formally, the 2 in an 8 2 reaction indicates that it follows second-order kinetics, but a second-order reaction is usually associated with the collision process of the nucleophile with the electrophilic carbon atom. As a practical matter, the fact that the S 2 reaction is second order means that if the reaction is slow, increasing the concentration of the nucleophile will increase the rate of the reaction (the rate constant remains the same). Similarly, increasing the concentration of the halide will increase the rate. 

This rate constant is correlated to the fluoroacidity of each bath and allows sorting this property for different mixtures. A low rate constant means that the silicon ions are stable in the bath, and correlatively that the mixture tends to be basic. In the next paragraph, optimization of the operating conditions will be presented, first concerning the composition and then the mixture choice. 

Having separated the dynamical from equilibrium (or, more accurately, quasi-equilibrium) effects, one can readily discover the origin of the activation free energy and define the concept of the potential of mean force by analysis of the expression for the TST rate constant, k in (A3.8.3). The latter can be written as [7]... 

RRKM theory assumes a microcanonical ensemble of A vibrational/rotational states within the energy interval E E + dE, so that each of these states is populated statistically with an equal probability [4]. This assumption of a microcanonical distribution means that the unimolecular rate constant for A only depends on energy, and not on the maimer in which A is energized. If N(0) is the number of A molecules excited at / =... 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

Relative rate meaning, here, simply the ratio of nitro-alkylbenzene to nitrobenzene, multiplied by the initial ratio of alkylbenzene to benzene. This is not precisely the same as the ratio of rate constants for nitration. ... 

Nucleophilic reactivity of the sulfur atom has received most attention. When neutral or very acidic medium is used, the nucleophilic reactivity occurs through the exocyclic sulfur atom. Kinetic studies (110) measure this nucleophilicity- towards methyl iodide for various 3-methyl-A-4-thiazoline-2-thiones. Rate constants are 200 times greater for these compounds than for the isomeric 2-(methylthio)thiazole. Thus 3-(2-pyridyl)-A-4-thiazoline-2-thione reacts at sulfur with methyl iodide (111). Methyl substitution on the ring doubles the rate constant. This high reactivity at sulfur means that, even when an amino (112, 113) or imino group (114) occupies the 5-position of the ring, alkylation takes place on sulfiu. For the same reason, 2-acetonyi derivatives are sometimes observed as by-products in the heterocyclization reaction of dithiocarba-mates with a-haloketones (115, 116). 

Km for an enzymatic reaction are of significant interest in the study of cellular chemistry. From equation 13.19 we see that Vmax provides a means for determining the rate constant 2- For enzymes that follow the mechanism shown in reaction 13.15, 2 is equivalent to the enzyme s turnover number, kcat- The turnover number is the maximum number of substrate molecules converted to product by a single active site on the enzyme, per unit time. Thus, the turnover number provides a direct indication of the catalytic efficiency of an enzyme s active site. The Michaelis constant, Km, is significant because it provides an estimate of the substrate s intracellular concentration. 

The foregoing conclusion does not mean that the rate of the reaction proceeds through Table 5.1 at a constant value. The rate of reaction depends on the concentrations of reactive groups, as well as on the reactivities of the latter. Accordingly, the rate of the reaction decreases as the extent of reaction progresses. When the rate law for the reaction is extracted from proper kinetic experiments, specific reactions are found to be characterized by fixed rate constants over a range of n values. 

The vapor pressure ratio measures the intrinsic tendency of component 1 to enter the vapor phase relative to component 2. Likewise, ri measures the tendency of Mi to add to Mi - relative to M2 adding to Mi-. In this sense there is a certain parallel, but it is based on Mi - as a reference radical and hence appears to be less general than the vapor pressure ratio. Note, however, that ri = l/r2 means kn/ki2 = k2i/k22- In this case the ratio of rate constants for monomer 1 relative to monomer 2 is the same regardless of the reference radical examined. This shows the parallelism to be exact. 

Droplet trajectories for limiting cases can be calculated by combining the equations of motion with the droplet evaporation rate equation to assess the likelihood that drops exit or hit the wall before evaporating. It is best to consider upper bound droplet sizes in addition to the mean size in these calculations. If desired, an instantaneous value for the evaporation rate constant may also be used based on an instantaneous Reynolds number calculated not from the terminal velocity but at a resultant velocity. In this case, equation 37 is substituted for equation 32 ... 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

The thiol ( -dodecyl mercaptan) used ia this recipe played a prominent role ia the quaUty control of the product. Such thiols are known as chain-transfer agents and help control the molecular weight of the SBR by means of the foUowiag reaction where M = monomer, eg, butadiene or styrene R(M) = growing free-radical chain k = propagation-rate constant = transfer-rate constant and k = initiation-rate constant. 

The electrocatalytic activity of novel redox films in regeneration of NAD/NADH has been investigated by means of chronoamperometry, hydrodynamic and potentiodynamic methods. In order to achieve the most efficient electrocatalytic properties indicated as both the highest heterogeneous rate constant and maximum sensitivity, the further optimization of electropolymerisation conditions has been made. 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

As the temperature drops, (5.80) starts to incorporate quantum corrections. When friction increases, T u decreases and the prefactor in (5.80) increases. This means that the reaction becomes more adiabatic. However, the rise of the prefactor is suppressed by the strong decrease in the leading exponent itself The result (5.80) may be recast in a TST-like form. If the transition were classical, the rate constant could be calculated as the average flux towards the product valley... 

Now, if (kd) is the desorption rate constant, then the mean desorption time (td) for... 

A reading of Section 2.2 shows that all of the methods for determining reaction order can lead also to estimates of the rate constant, and very commonly the order and rate constant are determined concurrently. However, the integrated rate equations are the most widely used means for rate constant determination. These equations can be solved analytically, graphically, or by least-squares regression analysis. 

---