Rate constant for first-order reactions

Thus, rate constants for first-order reactions can be obtained directly from a plot of In b versus t. 

Ki = reaction rate constant for first order reaction, 1/sec l = pore length, cm... 

Special integrated rate equations have been derived for the situation where neither the initial concentrations nor the equilibrium values of the concentrations need be known to determine the rate constant. For first-order reactions, Guggenheim [3] has described a method in which measurements of some physical property of the system are made at constant time intervals A. Then... 

From the units fo the rate constants (min" ), we know that both kl and k2 are the rate constants for first order reactions. We therefore can write ... 

The reaction half-times and rate constants accessible by the various techniques are summarised in Table 1.1. The smallest half-times, from about 10 s down to 10 or even 10 " s, have been determined by the flash-photolysis, fluorescence-quenching, ultrasonic-absorption, and esr methods next come the temperature-jump and electric-impulse techniques (approximately 10 s). In terms of rate constants, for first-order reactions the upper limit for a given technique is approximately the reciprocal of the least half-time that can be measured (k for second-order rate constants, however, the upper limit depends... 

The constants Aa, Ah and Ea were calculated from Arrhenius plots of the parameters a and b. The assumption that the parameter b in the original Seo model is independent of temperature conflict obviously with the fact that the rate constant of first-order reaction k(t) is a function of temperature since k(t) approaches b at the initial time, t—>0. The corresponding activation energy obtained from parameter a should be the energy barrier for the transition state and parameter b represents the rate constant for the imidization reaction. 

Graphical methods can also be used to determine the rate constant for zero-order reactions. Table 14.2 snmmarizes this and the other relationships discnssed in this section for zero-order, first-order, and second-order reactions. 

The half-life (tm) of a reaction is the time it takes for half of a reactant to be consumed. The half-life is constant for first-order reactions, and it can be used to determine the rate constant of the reaction. 

The rate constants for second-order reactions can be expressed in dm mol sec, or, if the rate is measured from the change of gas pressure at constant volume, as described in eq. (2.12), in (pressure) V(time)". The conversion between units of pressure and those of concentration for gas phase reactions which are not first order, can be obtained from the perfect gas equation, from which, for the general case of a reaction of order n, the variation in the total gas pressure can be related to the change in the total gas concentration hy p = cRT... 

A plot of the first-order rate constant for equilibration in reaction (3-23) is shown as a function of [Co(edta)2 ]. the reagent present in large excess. The plot is linear as expected from Eq. (3-23). Data, from Ref. 1. are given in Table 3-1. 

FIGURE 13.14 The characteristic shapes of the time dependence of the concentration of a reactant during a second-order reaction. The larger the rate constant, k, the greater is the dependence of the rate on the concentration of the reactant. The lower gray lines are the curves for first-order reactions with the same initial rates as for the corresponding second-order reactions. Note how the concentrations for second-order reactions fall away much less rapidly at longer times than those for first-order reactions do. 

Therefore, if a plot of In [A] against t is linear, the reaction is first order and k can be obtained from the slope. For first-order reactions, it is customary to express the rate not only by the rate constant k but also by the half-life, which is the time required for half of any given quantity of a reactant to be used up. Since the half-life ti/2 is the time required for [A] to reach Aq/2, we may say that... 

In summary, the simple Michaelis-Menten form of Equation (12.1) is usually sufficient for first-order reactions. It has two adjustable constants. Equation (12.4) is available for special cases where the reaction rate has an interior maximum or an inflection point. It has three adjustable constants after setting either 2 = 0 (inhibition) or k = 0 (activation). These forms are consistent with two adsorptions of the reactant species. They each require three constants. The general form of Equation (12.4) has four constants, which is a little excessive for a... 

The material balance was calculated for EtPy, ethyl lactates (EtLa) and CD by solving the set of differential equation derived form the reaction scheme Adam s method was used for the solution of the set of differential equations. The rate constants for the hydrogenation reactions are of pseudo first order. Their value depends on the intrinsic rate constant of the catalytic reaction, the hydrogen pressure, and the adsorption equilibrium constants of all components involved in the hydrogenation. It was assumed that the hydrogen pressure is constant during... 

The half-life is thus seen to depend on the initial concentration for the second order reaction considered. This is in contrast to first-order reaction where the half-life is independent of concentration. For this reason half-life is not a convenient way of expressing the rate constant of second-order reactions. 

The rate of the electrode process—similar to other chemical reactions— depends on the rate constant characterizing the proportionality of the rate to the concentrations of the reacting substances. As the charge transfer reaction is a heterogeneous process, these constants for first-order processes are mostly expressed in units of centimetres per second. 

The initial concentrations of A and B in the feedstream are each 10 moles/m3. The remainder of the stream consists of inerts at a concentration of 30 moles/m3. The reaction is reversible and substantial amounts of all species exist at equilibrium under the pressure and temperature conditions employed. The forward reaction is first-order with respect to A and first-order with respect to B. At 120 °C the rate constant for the forward reaction is 1.4 m3/ mole-ksec. The reverse reaction is first-order in C, first-order in D, and inverse first-order in B. The rate constant for the reverse reaction is 0.6 ksec-1. 

Assuming that AE AG, the rate constants for the quenching reaction and its reverse (kj and k i in eq. 8) can be written using the theoretical results of eq. 5-7. In order to make the situation clear it is useful to consider two limiting cases. In the first limit, k i << back electron transfer to give the... 

SAQ 8,22 A simple first-order reaction has a forward rate constant of 120 s 1 while the rate constant for the back reaction is 0.1 s F Calculate the equilibrium constant K of this reversible reaction by invoking the principle of microscopic reversibility. 

The authors [1] studied kinetics of poly (amic acid) (PAA) solid-state imidization both in the presence of nanofiller (layered silicate Na+-montmorillonite) and without it. It was found, that temperature imidization 1] raising in range 423-523 K and nanofiller contents Wc increase in range 0-7 phr result to essential imidization kinetics changes expressed by two aspects by essential increase of reaction rate (reaction rate constant of first order k increases about on two order) and by raising of conversion (imidization) limiting degree Q im from about 0,25 for imidization reaction without filler at 7 i=423 K up to 1,0 at Na -montmorillonite content 7... 

Early attempts at observing electron transfer in metalloproteins utilized redox-active metal complexes as external partners. The reactions were usually second-order and approaches based on the Marcus expression allowed, for example, conjectures as to the character and accessibility of the metal site. xhe agreement of the observed and calculated rate constants for cytochrome c reactions for example is particularly good, even ignoring work terms. The observations of deviation from second-order kinetics ( saturation kinetics) allowed the dissection of the observed rate constant into the components, namely adduct stability and first-order electron transfer rate constant (see however Sec. 1.6.4). Now it was a little easier to comment on the possible site of attack on the proteins, particularly when a number of modifications of the proteins became available. 

Figure 4.15 Rates of oxygen consumption by shaken suspensions of anaerobic soils. Points are measured data, lines are fits to two first-order rate equations. The apparent rate constant for the initial reaction is common to all sods that for the main reaction varies 30-fold between the soils and is well correlated with [Fe +] (Reddy et al., 1980). Reproduced by permission of Soil Sci. Soc. Am.

The ratio of a first-order rate constant for an intramolecular reaction (involving two functional groups or moieties within the same molecular entity) to the second-... 

There is competition between conventional and AM ROPs. Initiation in conventional ROP is first-order each in protonated monomer and unprotonated monomer. AM ROP is first-order each in protonated monomer and alcohol. The ratio of the rates of AM-to-conventional ROP depends on [ROH]/[M] and the ratio of the rate constants for the two reactions. Assuming that the two rate constants are comparable, AM ROP becomes the dominant process at high [ROH] and low [M], Thus, AM ROP is carried out under monomer-starved conditions. The instantaneous monomer concentration is very low, but monomer is continuously added to the reactor at a rate equal to its rate of consumption. 

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