Rate law for elementary steps

We characterize elementary steps by their molecularity, the number of reactant particles involved in the step. The most common molecnlarities are unimolecular and bimolecular  

Elementary steps in which three reactant particles collide, called termolecular steps, are very rare because the probability of three particles simultaneously colliding is small. 

Although we cannot deduce the rate law for an overall chemical reaction from the balanced chemical equation, we can dednce the rate law for an elementary step from its eqnation. Since we know that an elementary step occurs through the collision of the reactant particles, the rate is proportional to the product of the concentrations of those particles. For example, the rate for the bimolecular elementary step in which A reacts with B is proportional to the concentration of A multiplied by the concentration of B  

Similarly, the rate law for the bimolecnlar step in which A reacts with A is proportional to the square of the concentration of A  

Rate-Determining Steps and Overall Reaction Rate Laws 

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These rate laws for elementary steps are related to the experimental rate law for the overall reaction in a way that depends on which step in the mechanism is rate-determining. 

Determining Molecularity and Rate Laws for Elementary Steps... 

While it is not possible to determine the rate law of a reaction by inspecting its balanced equation, it is possible to deduce the rate law if you know the elementary steps for the reaction or, in other words, the reaction mechanism. Knowing the molecularity of the elementary step will help you determine the rate law for that step. For example, consider the elementary step that involves the decomposition of substance A into one or more product ... 

When writing rate laws for these steps, we treat each step as an elementary reaction the only difference is that the species concentrations in the gas phase are replaced ly their respectiven tial pressures ... 

Plan We find the overall equation from the sum of the elementary steps. The molecularity of each step equals the total number of reactant particles. We write the rate law for each step using the molecularities as reaction orders. 

Elementary step rate law for the step can be written from the molecularity of the reaction... 

The initial reactant product conversion rate should increase at higher temperature because kinetic rate constants for elementary steps, particularly the desorption of gas D, increase at higher temperature. In summary, there is no total pressure dependence of the initial reactant product conversion rate when (1) A -h B C -h D, (2) single-site adsorption is appropriate for each component, and (3) desorption of one of the products controls the Hougen-Watson kinetic rate law. 

The individual steps in a reaction mechanism are called elementary steps. Unlike the overall stoichiometric equation, the coefficients for reactants in an elementary step do provide the exponents in the rate law for that step. According to our reasoning above, only three types of elementary steps are likely to occur, those involving one, two, or three molecules. Steps with one reactant are called unimolecular, and those with two and three reactants are called bimolecular and termolecular, respectively. The molecularity tells us the overall order of the rate law for the elementary step, as summarized in Table 11.1. 

In Section 143 we stressed fliat rate laws must be determined experimentally tiiey cannot be predicted from die coefficients of balanced chemical equations. We are now in a position to understand why this is so Every reaction is made up of a series of one or more elementary steps, and the rate laws and relative speeds of tiiese steps will dictate die overall rate law. Indeed, the rate law for a reaction can be determined from its mechanism, as we will see shortly. Thus, our next challenge in kinetics is to arrive at reaction mechanisms that lead to rate laws that are consistent widi diose observed experimentally. We will start by examining die rate laws of elementary steps. 

How is the order and rate of an overall chemical reaction related to the orders and rates of the elementary processes that comprise the reaction The answer is simple for most reactions. Since the overall reaction can be no faster than its slowest step (called the rate-determining step), the rate law for the overall reaction is closely related to the rate law for this step. 

Since a proposed mechanism consists of elementary steps, we can write a rate law for each step from the fact that for an elementary process the order equals the molecularity. Every multistep mechanism leads to a set of simultaneous differential equations analogous to those for the simple mechanism of Eq. (11.5-1). There is one independent differential equation for each elementary step of the mechanism. 

Setup Intermediates are species that are generated in an earlier step and consumed in a later step. We can write rate laws for elementary reactions simply by using the stoichiometric coefficient for... 

Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

To construct an overall rate law from a mechanism, write the rate law for each of the elementary reactions that have been proposed then combine them into an overall rate law. First, it is important to realize that the chemical equation for an elementary reaction is different from the balanced chemical equation for the overall reaction. The overall chemical equation gives the overall stoichiometry of the reaction, but tells us nothing about how the reaction occurs and so we must find the rate law experimentally. In contrast, an elementary step shows explicitly which particles and how many of each we propose come together in that step of the reaction. Because the elementary reaction shows how the reaction occurs, the rate of that step depends on the concentrations of those particles. Therefore, we can write the rate law for an elementary reaction (but not for the overall reaction) from its chemical equation, with each exponent in the rate law being the same as the number of particles of a given type participating in the reaction, as summarized in Table 13.3. 

STRATEGY Construct the rate laws for the elementary reactions and combine them into the overall rate law for the decomposition of the reactant. If necessary, use the steady-state approximation for any intermediates and simplify it by using arguments based on rapid pre-equilibria and the existence of a rate-determining step. 

When a reaction proceeds in a single elementary step, its rate law will mirror its stoichiometry. An example is the rate law for O3 reacting with NO. Experiments show that this reaction is first order in each of the starting materials and second order overall NO + 03- NO2 + O2 Experimental rate = i [N0][03 J This rate law is fully consistent with the molecular view of the mechanism shown in Figure 15-7. If the concentration of either O3 or NO is doubled, the number of collisions between starting material molecules doubles too, and so does the rate of reaction. If the concentrations of both starting materials are doubled, the collision rate and the reaction rate increase by a factor of four. 

This chapter presents the underlying fundamentals of the rates of elementary chemical reaction steps. In doing so, we outline the essential concepts and results from physical chemistry necessary to provide a basic understanding of how reactions occur. These concepts are then used to generate expressions for the rates of elementary reaction steps. The following chapters use these building blocks to develop intrinsic rate laws for a variety of chemical systems. Rather complicated, nonseparable rate laws for the overall reaction can result, or simple ones as in equation 6.1-1 or -2. 

This chapter provides an introduction to several types of homogeneous (single-phase) reaction mechanisms and the rate laws which result from them. The concept of a reaction mechanism as a sequence of elementary processes involving both analytically detectable species (normal reactants and products) and transient reactive intermediates is introduced in Section 6.1.2. In constructing the rate laws, we use the fact that the elementary steps which make up the mechanism have individual rate laws predicted by the simple theories discussed in Chapter 6. The resulting rate law for an overall reaction often differs significantly from the type discussed in Chapters 3 and 4. 

Notice that if you add these two steps together, you get the overall reaction. We have determined that the first step is the slow step in the mechanism, the rate-determining step. If we write the rate law for this elementary step it is Rate = k[N02]2, identical to the experimentally determined rate law for the overall reaction. 

Based on the equations for the elementary reactions, the molecularity of these reactions, and the rate law for the rate-determining step, the reaction mechanism seems reasonable. 

In summary, when a reaction is said to be an elementary reaction, the reaction rate law has been experimentally investigated and found to follow the above rate law. One special case is single-step radioactive decay reactions, which are elementary reactions and do not require further experimental confirmation of the reaction rate law. For other reactions, no matter how simple the reaction may be, without experimental confirmation, one cannot say a priori that it is an elementary reaction and cannot write down the reaction rate law, as shown by the complicated reaction rate law of Reaction 1-34. On the other hand, if the reaction rate law of Reaction 1-36 is found to be Equation 1-37, Reaction 1-36 may or may not be an elementary reaction. For example, Reaction 1-32 is not an elementary reaction even though the simple reaction law is consistent with an elementary reaction (Bamford and Tipper, 1972, p. 206). 

In studying any particular reaction, one does not really know a priori if it is an elementary reaction or not, unless it involves four or more species, in which case it cannot be elementary. Determination of the rate law for the reaction is the first step in assessing whether it could be elementary. 

The experimentally observed rate law for an overall reaction depends on the reaction mechanism—that is, on the sequence of elementary steps and their relative rates. If the overall reaction occurs in a single elementary step, the experimental... 

Because the rate law for an overall reaction depends on the reaction mechanism, it provides important clues to the mechanism. A plausible mechanism must meet two criteria (1) The elementary steps must sum up to give the overall reaction, and (2) the mechanism must be consistent with the observed rate law for the overall reaction. 

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