Order of overall reaction

This also accounts for the production of the small amount of butane. If the reaction mechanism were steps 1, 2, 3, 4, 5a, and 5b, then applying the steady state approximations would give the overall order of reaction as 1/2. 

The rate constant fe in equation 4.1-3 is sometimes more fully referred to as the specific reaction rate constant, since r = k( when c,- = 1 (i = 1,2,.. . , N). The units of Inland of A) dependon the overall order of reaction, n, rewritten from equation 3.1-3 as... 

If the concentration of a reactant changes and that has no effect on the rate of reaction, then the reaction is zero-order with respect to that reactant ([2]° = 1). Many times, we calculate the overall order of reaction it is simply the sum of the individual coefficients, third order in this example. 

Then the reaction would be said to be (Xth order with respect to A, [3th order with respect to B,. . . and the overall order of reaction would be a + 3 +. Thus, order of reaction with respect to a reactant is the power to which the concentration of the reactant is raised into the rate law, and the overall order of reaction is the sum of the powers of the concentrations involved in the rate law. 

In this expression, k is the rate constant—a constant for each chemical reaction at a given temperature. The exponents m and n, called the orders of reaction, indicate what effect a change in concentration of that reactant species will have on the reaction rate. Say, for example, m = 1 and n = 2. That means that if the concentration of reactant A is doubled, then the rate will also double ([2]1 = 2), and if the concentration of reactant B is doubled, then the rate will increase fourfold ([2]2 = 4). We say that it is first order with respect to A and second order with respect to B. If the concentration of a reactant is doubled and that has no effect on the rate of reaction, then the reaction is zero order with respect to that reactant ([2]° = 1). Many times the overall order of reaction is calculated it is simply the sum of the individual coefficients, third order in this example. The rate equation would then be shown as ... 

For most hydrocarbon flame or reacting systems the overall order of reaction is about 2, E/R is approximately 20,000 K, and the flame temperature is about 2000 K. Thus,... 

Figure 3.5 Overall order of reaction from a series of half-life experiments, each at a different initial concentration of reactant.

Figure 22 presents the change of over-all reaction rate with change in partial pressure of carbon dioxide in the main gas stream. Nitrogen was used as the diluent, and the total flow rate was maintained constant. The over-all order of reaction is found to be ca. 0.5 from 950 to 1200°. An overall order of reaction of ca. 0.5 close to the start of Zone II has been interpreted to mean a true reaction order of zero (70, 79). In this case, however, as has been shown in Fig. 19, the true order is not zero at 1200°. Therefore, the above reasoning is not valid. An over-all order of 0.5 would be expected (for reaction in Zone II) if the mechanism of the reaction is represented by... 

The overall order of reaction as determined from the pressure fall... 

Astarita, G., Lumping Nonlinear Kinetics Apparent Overall Order of Reaction, AIChE J. 35, 529 (1989). 

Just because the overall order of reaction is third- or fourth-order, it does not mean that all the species must simultaneously collide in the rate-determining step. You saw in Chapter 13 that the rate law actually reveals all the species that are involved up to and including the rate-determining step. 

It is also worthwhile to notice that the overall order of reaction is 2 when a = 1, that is, with an exponential distribution. The only value of a for which (f>(a,0) is finite is a = 1. This result can be generalized to any initial distribution by simply making use of the limit properties of the Laplace transform C(t) at large times becomes proportional to t if and only if c(x,0) at small x becomes proportional to x h > 0. Now if 0 < f2 < 1, c(0,0) = and if 13 > 1 c(0,0) = 0. It follows that c(0,0) is finite only if f3 = 1, in which case C(t) at large times becomes proportional to 1/t, which is the behavior typical of sound-order kinetics (Kram-beck, 1984b). The question of the large-time asymptotic behavior of the overall kinetics is discussed later in more general terms. 

Let s discuss Eq. (109) in some detail. First of all, it satisfies the SCI requirement, because when a approaches < it yields —dCldt = C/(l + K C). The intrinsic kinetics are always of nonnegative order, and approach order zero only when the reactant concentration approaches °o. In contrast with this, Eq. (109) yields an apparent overall order of reaction that may well be negative at high C if /3 > 1. 

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