Order of reaction

The order of the overall reaction is the sum of exponents of species on the rate expression. 

We will consider three types of chemical reaction  

The rate (in molecules cm 3 s ) of a first-order reaction is expressed as 

Few reactions are truly first-order, in that they involve decomposition of a molecule without intervention of a second molecule. The classic example of a true first-order reaction is radioactive decay, such as 222Rn — 218Po + a-particles. In the atmosphere, by far the most important class of first-order reactions is photodissociation reactions in which absorption of a photon of light (hv) by the molecule induces chemical change. Photodissociation, or photolysis, reactions are written as 

Thermal decomposition of a molecule is often represented as first-order, but the energy required for decomposition is usually supplied through collision with another molecule. If the other molecule is an air molecule, it is denoted as M, and the actual reaction is A + M— B + C + M. Since M is at great excess relative to A, its concentration is constant, and the concentration of M can be implicitly included in the reaction rate coefficient then, the reaction is written simply as A — B + C. 

Atmospheric Chemistry and Physics From Air Pollution to Climate Change, Second Edition, by John H. Seinfeld and Spyros N. Pandis. Copyright 2006 John Wiley Sons, Inc. 

From the law of mass action. based on experimental observation and later explained by the collision theory, it is found that the rate of reaction (1.1-1) can often be expressed as 

The proportionality factor k,. is called the rate coefficient or rate constant By definition, this rate coefficient is independent of the quantities of the reacting species, but dependent on the other variables that influence the rate. When the reaction mixture is thermodynamically nonideal, k, will often depend on the 

It can also be verified that the dimensions of the rate coefficients used with conversions are the same as those given for use with concentrations. Partial pressures may also be used as a measure of the quantities of the reacting species, 

In this case, the dimensions of the rate coefficient are hr kmol m atm -  

With thermodynamically nonideal conditions (e.g., high pressures) partial pressures may have to be replaced by fugacities. When use is made of mole fractions, the corresponding rate coefficient has dimensions hr kmol m . According to the ideal gas law  

In kinetics, reactions are classified as being first, second, third, etc. order depending on the way the rate of the reaction is related to the concentration terms in the rate equation. If the rate of reaction is apparently independent of concentration, the reaction is said to be of zero order. 

It is extremely important to note that the reaction orders a, / , k. are not the same as the stoichiometric coefficients a, b, c. Reaction order cannot be simply determined from inspection of the balanced chemical equation. It requires detailed information about the kinetic mechanisms underlying the reaction and can generally only be determined experimentally or through careful kinetic studies (see the dialog box on reaction mechanism for details). The overall order of the reaction is given by the sum of the reaction orders with respect to the various reactants. In other words. 

In general, first- and second-order reactions are most commonly seen, but reactions of other orders are also important. Direct analytical solutions are easily acquired for zero-order, first-order, and second-order reactions. Reactions of third-order or higher generally require numerical methods for solution. In the sections that follow, we will cover several examples of zero-order, first-order, and second-order homogeneous chemical reactions. 

The concentration of ozone in Earth s upper atmosphere is regulated by the following reaction  

This rate law is an example of a mixed-order reaction. The reaction is second order with respect to O3 and inverse first order (-1 order) with respect to O2. It is clear that this rate law cannot be obtained from a simple inspection of the chemical reaction So from where does this seemingly strange rate law come  

Many chemical reactions, including the ozone-oxygen reaction above, do not occur in a single step as written. Instead, they proceed by a number of smaller intermediate reaction steps. These are known as the elementary reaction steps, and it is these individual elementary reaction steps which determine the rate law for the overall chemical reaction. 

In the simplest case in chemical kinetics only one substance is changing, and the rate at which it changes is at all times directly proportional to the amount of material reacting. When these conditions obtain the reaction is said to be of the first order. Mathematically expressed this relation is 

Change in Concentration (pressure in mm.) of Nitrogen Pentoxide with Time at 45°. 

These formulas are nicely illustrated in Table I and in Figs. 1, 2 and 3 with data taken from the next following chapter on the decomposition of nitrogen pentoxide at 45°. 

It is seen in Table I and Fig. 1 that the concentration, expressed as gas pressure in millimeters of mercury, decreases and approaches zero as the time increases, doing so at a decreasing rate. The average rates of decrease between two concentrations are represented by the slopes of straight lines joining the points in Fig. 1. When they are plotted against the average concentra- 

This is a simple example of a first order reaction. Nexfcf n simplicity comes the second order reaction in which the rate of disappearance of one of the reactants is proportional not just to 

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Cfeed = molar concentration of FEED in the reactor di, 0-2 = constants (order of reaction) for primary and secondary reactions... 

K Rate coefficient Units dependent on order of reaction Units dependent on order of 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. 

Figure 3-9. Overaii order of reaction from a series of haif-iife experiments each at different initiai concentration of reactant.

The power a is called the order of reaction with respect to reactant A, b is the order with respect to B, and the sum (a + b. ..) is the overall order of the reaction. Many rate equations are of forms different from Eq. (1-11)—for example, concentration teims may appear in the denominator—and then the concept of reaction order is not applicable. 

A plot according to Eq. (2-35) is useful in confirming the absence of another rate term, because the line should pass through the origin. The log-log plot of Eq. (2-36) is valuable because the slope of the line is the order of reaction, for any order. Figure 2-5 is a plot of Eq. (2-36) for the addition of sulfite to the double bond of cinnamoylsalicylic acid. At low concentrations of sulfite the reaction appears to be first-order in sulfite, but at higher sulfite concentrations some deviation is observed. 

At the outset it should be clear that, in order to apply these methods, the order of reaction must be known. Most of the following applies to first-order reactions. 

Previously, the same author [52] reported that compounds containing the tricoordinated sulfur cation, such as the triphenylsulfonium salt, worked as effective initiators in the free radical polymerization of MMA and styrene [52]. Because of the structural similarity of sulfonium salt and ylide, diphenyloxosulfonium bis-(me-thoxycarbonyl) methylide (POSY) (Scheme 28), which contains a tetracoordinated sulfur cation, was used as a photoinitiator by Kondo et al. [63] for the polymerization of MMA and styrene. The photopolymerization was carried out with a high-pressure mercury lamp the orders of reaction with respect to [POSY] and [MMA] were 0.5 and 1.0, respectively, as expected for radical polymerization. 

Order of Reaction with More Than One Reactant... 

Kinetic observations of the homogeneous part of the reaction in water12,13 do not provide any substantially new element to the knowledge of this system. The obvious observations that the rate of resinification increases with increasing temperature and decreasing pH of the mixture only provide technically useful correlation parameters and the zero-order of reactions carried out to small conversion of 2-furfuryl alcohol13 does not indicate anything except an elementary kinetic approximation (the use of colour build-up as a criterion for the extent of alcohol consumed is also questionable since no firm relationship has ever been established between these two quantities). 

One of the main assumptions which have been made in the study of polyesterifications is the concept of equal reactivity of functional groups. It was first postulated by Flory1 who, studying various polyesterifications and model esterifications, found the same orders of reaction and almost the same rate constants for the two systems. He concluded that the reaction rate is not reduced by an increase in the molecular weight of the reactants or an increase in the viscosity of the medium. The concept of equal reactivity of functional groups has been fully and carefully analyzed by Solomon3,135 so that we only discuss here its main characteristics. Flory clearly established the conditions under which the concept of equal reactivity can be applied these are the following ... 

The observations that addition of pyridine increases the rate of decomposition, shifts the order of reaction from unity to zero, and considerably diminishes formation of 4-nitrophenol also warrants attention. This is compatible with the superior electron-donor properties of pyridine as compared to DMSO (Gutmann, 1976, 1977) generation of the corresponding diazopyridinium cation in one or several of the forms corresponding to 8.59 and 8.60 competes with formation of 8.58. 

Writing the rate equation in the logarithmic form for an nth order of reaction, we have... 

The order of reaction with respect to aluminium chloride was ill-defined. Since nitrobenzene and aluminium chloride form a 1 1 complex which exhibits the simple monomeric molecular weight in nitrobenzene solution185, and since even in solutions of aluminium chloride and benzoyl chloride in nitrobenzene the aluminium chloride is preferentially associated with the solvent184, then in nitrobenzene solutions of aluminium chloride and benzenesulphonyl chloride the lesser basicity of the latter relative to benzoyl chloride means that the aluminium chloride must be mainly associated with nitrobenzene and in equilibrium with aluminium chloride associated with the sulphonyl chloride184. By analogy with... 

Kinetic studies using acidified hypochlorous acid are rather more complicated than these with hypobromous acid. Much higher concentrations of mineral acid are necessary so that the activities of the reacting entities do not correspond closely to their molecular concentrations, and the kinetic order of reaction varies according to the acid concentration and the reactivity of the aromatic. 

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