Third-order reactions examples

An example of a third-order reaction is the formation of nitrogen oxy-chloride according to tire reaction... 

Similar expressions can be written for third-order reactions. A reaction whose rate is proportional to [A] and to [B] is said to be first order in A and in B, second order overall. A reaction rate can be measured in terms of any reactant or product, but the rates so determined are not necessarily the same. For example, if the stoichiometry of a reaction is2A-)-B—>C- -D then, on a molar basis, A must disappear twice as fast as B, so that —d[A]/dt and -d[B]/dr are not equal but the former is twice as large as the latter. 

Gas phase third-order reactions are rarely encountered in engineering practice. Perhaps the best-known examples of third-order reactions are atomic recombination reactions in the presence of a third body in the gas phase and the reactions of nitric oxide with chlorine and oxygen (2NO T Cl2 -> 2NOC1 2NO + 02 -> 2N02). 

Bromination data became accessible over a large reactivity range when it became possible to follow low bromine concentrations. All the modern kinetic techniques are based on the fact that, since bromination is a second- or third-order reaction, bromination half-lives of a few milliseconds to several seconds can be obtained by working at very low reagent concentrations. For example, second-order rate constants as high as 109 m 1 s 1 can be readily measured if the reagent concentrations are 10-9m, the half-life of the bromine-olefin mixture then being 1 s. 

Unimolecular and trimolecular or first and third-order reactions are also known, but these are less frequent in occurrence than bimolecular reactions. Examples of each of the three orders of gaseous reaction are ... 

Termination occurs when two radicals recombine they need not be similar to those shown in the H2 Br2 case. Termination can also occur when a radical reacts with a molecule to give either a molecular species or a radical of lower activity that cannot propagate a chain. Since recombination processes are exothermic, the energy developed must be removed by another source, as discussed previously. The source can be another gaseous molecule M, as shown in the example, or a wall. For the gaseous case, a termolecular or third-order reaction is required consequently, these reactions are slower than other types except at high pressures. 

As we have seen earlier, even third-order reactions can be reduced to pseudo-first-order reactions by keeping the concentrations of all species except A constant and in great excess compared to A. This technique of using pseudo-first-order conditions is by far the most common technique for determining rate constants. Not only does it require monitoring only one species, A, as a function of time, but even absolute concentrations of A need not be measured. Because the ratio [A]/[A]0 appears in Eq. (T), the measurement of any parameter that is proportional to the concentration of A will suffice in determining k l7, since the proportionality constant between the parameter and [A] cancels out in Eq. (T). For example, if A absorbs light in a convenient... 

Run Example 1 with the mechanism (meccm.rad) modified to include HONO formation. While heterogeneous chemistry is not included in this mechanism, it can be crudely approximated by including it as a third-order reaction ... 

Kinetic traces are now exponential and the first-order treatment yields /cv, which will exhibit a linear dependence on [B]. The true rate constant k can then be easily obtained from the relationship/c Ar, (/ B. A similar treatment is applicable to other reaction types as well. A third-order reaction, for example, can be run under pseudo-first- or pseudo-second-order conditions, depending on the precise rate law and the chemistry involved. 

Let us now consider the problem from the standpoint of calcite precipitation kinetics. At saturation states encountered in most natural waters, the calcite reaction rate is controlled by surface reaction kinetics, not diffusion. In a relatively chemically pure system the rate of precipitation can be approximated by a third order reaction with respect to disequilibrium [( 2-l)3, see Chapter 2]. This high order means that the change in reaction rate is not simply proportional to the extent of disequilibrium. For example, if a water is initially in equilibrium with aragonite ( 2c=1.5) when it enters a rock body, and is close to equilibrium with respect to calcite ( 2C = 1.01), when it exits, the difference in precipitation rates between the two points will be over a factor of 100,000 The extent of cement or porosity formation across the length of the carbonate rock body will directly reflect these... 

Problem 9 What are third order reactions Derive the rate expressions and discuss their characteristics. Give examples of third order reactions. 

Example Staring from the full rate equation, determine the units of the rate constant k for (a) a zero-order reaction (b) a first-order reaction (c) a second-order reaction (d) a third-order reaction and (e) a half-order reaction. Assume that concentrations are expressed in molar units and time in seconds. 

The mathematics involved for higher-order reactions become more difficult and such a treatment is beyond the scope of this book. For example, the integrated rate equations for the three types of third-order reactions are given in Table 3.2. 

Third-order reactions are quite rare, the most famous examples being the reactions of NO with O2, 2NO + 02- 2NO2 and with CI2, 2N0 + CI2 2N0C1. ... 

It has also been shown that the gas-phase recombinations of atoms (for example, H, Cl, Br, O) and simple free radicals such as OH are third-order reactions. ... 

If one wished to observe solvent effects in less ambiguous fashion, the best chance would lie in going to higher-order reactions. For a third-order reaction (n = 3), Rn = 450. Strangely enough, there are no examples of third-order reactions (or equilibria) which have been studied in both gas phase and in solution. The reactions of NO with O2, CI2, and Br2 are third-order in the gas phase, and it would appear that their study in solution could prove very interesting and profitable. 

Third-order reactions are uncommon. Fractional orders exist when the reaction represents a sequence of several elementary steps. Procedures for establishing the order and rate constants for these cases are similar to those given above. Experimental data that suggest fractional-order rate equations should be examined carefully for effects of physical resistances. Sometimes these effects, rather than a sequence of elementary processes, can be responsible for the fractional order. An example is the study of the hydrochlorination of lauryl alcohol with zinc chloride as a homogeneous catalyst ... 

Second and third order reactions (A + B — products and A + B + C —> products are commonly reduced to a pseudo first order form to examine the chemical lifetime. For example,... 

Another example is provided by the chain hydrogenation of acetylene (8). One step in the chain, H + C2H2 C2H3, will be essentially a third-order reaction and have a negative activation energy of as much as —17 kcal/mole at 1 atm and 1400°K. Since there is no simple way of... 

The above relationships appear deceptively simple since they would seem to be predictable from a glance at tbe chemical equation. This is not, however, the case. The decomposition of arsine could have just as well been found to quadruple in rate were arsine s concentration doubled. In this hypothetical case, the reaction rate would be proportional to [AsH3]. Van t Hoff noted that first-order and second-order reactions are relatively common, and third-order reactions are uncommon. He provided the example of the oxidation of hydriodic acid by hydrogen peroxide ... 

The simplest of the third-order reactions is the recombination of atoms in presence of a third body for example 2H-1-M = Hj-l-M. 

Gas-phase third-order reactions are rarely encountered in engineering practice. Perhaps the best-known examples... 

We may develop similar expressions for second- and third-order reactions in which two or three molecules of A collide in the rate-limiting step. See, for example, Gordon, A. J. Ford, R. A. The Chemist s Companion lohn Wiley Sons New York, 1972 p. 135 for a listing of the differential and integrated forms of zero-, first-, and second-order rate equations. 

Derive an expression for the half-life of (a) a third order reaction (b) a reaction whose order is = -1 (c) a reaction whose order is j. (In these last two cases, examples are rare but known.)... 

Give some examples of Third Order Reactions and one example of a Fourth Order Reaction. 

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