Half second order reaction

Even when there is a transport disguise, the reaction order remains one for a first-order reaction. But for reactions that are not intrinsically first order, the transport disguise changes the observed reaction order for an intrinsically zero-order reaction, the observed order becomes 1/2 and for an intrinsically second-order reaction it becomes 3/2 when 0 10. For all reaction orders the apparent activation energy is approximately half the intrinsic... 

A second-order reaction has a long tail of low concentration at long reaction times. The half-life of a second-order reaction is inversely proportional to the concentration of the reactant. 

The half-life for the second-order reaction of a substance A is 50.5 s when [A] = 0.84 mol-L. Calculate the time needed for the concentration of A to decrease to (a) one-sixteenth (b) one-fourth (c) one-fifth of its original value. 

For the same value of K, first-order reactions proceed much more rapidly than second-order reactions. The reaction rate for a hrst-order reaction will decrease to half its original value when the concentration has decreased to half the original concentration. For a second-order reaction, the reaction rate will decrease to a quarter the original rate when the concentration has decreased to half the original concentration compare Equations (1.16) and (1.17). 

The initial half-life of a second-order reaction corresponds to a decrease from Oq to UqI2 and is given by... 

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 half-life of a reactant is the time required for half of that reactant to be converted into products. For a first order reaction, the half-life is independent of concentration so that the same time is required to consume half of any starting amount or concentration of the reactant. On the other hand, the half-life of a second-order reaction does depend on the starting amount of the reactant. 

The half-life of the reaction depends on the concentration of A and, thus, this reaction cannot be first-order. For a second-order reaction, the half-life varies inversely with the... 

A zero-order reaction has a half life that varies proportionally to [A]0, therefore, increasing [A]0 increases the half-life for the reaction. A second-order reaction s half-life varies inversely proportional to [A]0, that is, as [A]0 increases, the half-life decreases. The reason for the difference is that a zero-order reaction has a constant rate of reaction (independent of [A]0). The larger the value of [A]0, the longer it will take to react. In a second-order reaction, the rate of reaction increases as the square of the [A]0, hence, for high [A]0, the rate of reaction is large and for very low [A]0, the rate of reaction is very slow. If we consider a bimolecular elementary reaction, we can easily see that a reaction will not take place unless two molecules of reactants collide. This is more likely when the [A]0 is large than when it is small. 

A second-order reaction may typically involve one reactant (A -> products, ( -rA) = kAc ) or two reactants ( pa A + vb B - products, ( rA) = kAcAcB). For one reactant, the integrated form for constant density, applicable to a BR or a PFR, is contained in equation 3.4-9, with n = 2. In contrast to a first-order reaction, the half-life of a reactant, f1/2 from equation 3.4-16, is proportional to cA (if there are two reactants, both ty2 and fractional conversion refer to the limiting reactant). For two reactants, the integrated form for constant density, applicable to a BR and a PFR, is given by equation 3.4-13 (see Example 3-5). In this case, the reaction stoichiometry must be taken into account in relating concentrations, or in switching rate or rate constant from one reactant to the other. 

A second order reaction, A + B 4- Products, is found to be 25% complete in 50 minutes when both starting concentrations are 0.2 mol/liter. Find the specific rate and the half life of the reaction. 

For second-order reactions, the half-life does depend on the reactant concentration. We calculate it using the following formula ... 

Determine the half-life of a second-order reaction if the rate constant is 1.78 M-1s-1. The initial concentration is 0.575 M. 

Problem 1.18 A second order reaction with initial concentration of each reactant as 0.5 mol dm 3 was carried out in presence of acid as catalyst. At pH 4.0 the half-life of reaction was found to be 60 min. Calculate the observed and true rate constant for the reaction. 

Now half-life period for second order reaction is given as... 

This means that as a second-order reaction proceeds, the half-life increases. 

Very rarely are measurements themselves of much use or of great interest. The statement "the absorption of the solution increased from 0.6 to 0.9 in ten minutes", is of much less use than the statement, "the reaction has a half-life of 900 sec". The goal of model-based analysis methods presented in this chapter is to facilitate the above translation from original data to useful chemical information. The result of a model-based analysis is a set of values for the parameters that quantitatively describe the measurement, ideally within the limits of experimental noise. The most important prerequisite is the model, the physical-chemical, or other, description of the process under investigation. An example helps clarify the statement. The measurement is a series of absorption spectra of a reaction solution the spectra are recorded as a function of time. The model is a second order reaction A+B->C. The parameter of interest is the rate constant of the reaction. 

V = V max [S]// m- A reaction of higher order is called pseudo-first-order if all but one of the reactants are high in concentration and do not change appreciably in concentration over the time course of the reaction. In such cases, these concentrations can be treated as constants. See Order of Reaction Half-Life Second-Order Reaction Zero-Order Reaction Molecularity Michaelis-Menten Equation Chemical Kinetics... 

A zero-order reaction thus becomes a half-order reaction, a first-order reaction remains first-order, whereas a second-order reaction would have an apparent order 3/2 for diffusion-limited conditions. 

Fig. 10. Fractional conversion versus Damkohler number for half,-, first- and second-order reactions taking place in a single ideal CSTR. Shaded areas represent possible conversion ranges lying between perfectly micromixed flow (M) and completely segregated flow (S). Data taken from reference 32. A = R —...

For reactions with a different order, the half-life depends on the initial concentrations. For example, for a second-order reaction, 2A product, with d[A]/ dt=-2k[A], then... 

The concentration evolution curves of Figures 2-la and 2-lb may be used to estimate the half-life or mean reaction time. When Figures 2-la and 2-lb are compared, the mean reaction time is found to differ by four orders of magnitude Hence, for second-order reactions, the timescale to reach equilibrium in general depends on the initial conditions. This is in contrast to the case of first-order reactions, in which the timescale to reach equilibrium is independent of the initial conditions. 

Half-Life Method For a zero-order reaction the half-life (tll2) is proportional to the initial concentration. The half-life for a first-order reaction is independent of the initial concentration while a second-order reaction is proportional to 1/initial concentration. 

What are the dimensions of a (i) zero-order, (ii) first-order, and (iii) second-order reaction rate constant What is the half-life of a given compound with respect to a given reaction In which case(s) is the half-life independent of the concentration of the compound ... 

What are the dimensions of the rate constant for zero-, first-, and second-order reactions If a first-order reaction is half completed in 2 min, what is its rate constant ... 

A zero-order reaction thus becomes a half-order reaction, a first-order reaction remains first order, whereas a second-order reaction has an apparent order of 3/2 when strongly influenced by diffusional effects. Because k and n are modified in the diffusion controlled region then, if the rate of the overall process is estimated by multiplying the chemical reaction rate by the effectiveness factor (as in equation 3.8), it is imperative to know the true rate of chemical reaction uninfluenced by diffusion effects. 

We can obtain an expression for the half-life of a second-order reaction by substituting [A]f = [A]0/2 and t = ti/2 into the integrated rate law ... 

FIGURE 12.8 Concentration of a reactant A as a function of time for a second-order reaction. Note that each half-life is twice as long as the preceding one because... 

In contrast with a first-order reaction, the time required for the concentration of A to drop to one-half of its initial value in a second-order reaction depends on both the rate constant and the initial concentration. Thus, the value of h/2 increases as the reaction proceeds because the value of [A]0 at the beginning of each successive half-life is smaller by a factor of 2. Consequently, each half-life for a second-order reaction is twice as long as the preceding one (Figure 12.8). 

Beginning with the integrated rate law, derive a general equation for the half-life of a zeroth-order reaction of the type A — Products. How does the length of each half-life compare with the length of the previous one Make the same comparison for first-order and second-order reactions. 

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