Reaction order from rate laws

SAMPLE PROBLEM 16.2 Determining Reaction Order from Rate Laws Problem For each of the following reactions, use the given rate law to determine the reaction order with respect to each reactant and the overall order ... 

Determining Reaction Orders from Rate Laws... 

EXAMPLE 13.2 Determining the reaction orders and rate law from experimental data... 

Wilkinson s method allows the evaluation of the reaction order from data taken during the first half-life. This, as we saw, was not possible from treatment by the integrated rate law. Note, however, that relatively small errors in [A] can lead to a larger error in E at small conversions.17... 

Where does the equation for half-life come from Each rate law has an associated integrated rate law. (A calculus teacher may be able to show you howto arrive at the integrated rate law.) For first-order reactions, the integrated rate law is... 

Rate laws can be derived by measuring concentration variations as function of time or the initial rates as function of the initial concentrations. Unfortunately, there is no general method for finding the rate law and the reaction order from measurements of concentration vs. time or other types of measurements. Usually, a trial-and-error procedure is used, based upon intelligent guesses. 

In an enzyme reaction, initially free enzyme E and free substrate S in their respective ground states initially combine reversibly to an enzyme-substrate (ES) complex. The ES complex passes through a transition state, AGj, on its way to the enzyme-product (EP) complex and then on to the ground state of free enzyme E and free product P. From the formulation of the reaction sequence, a rate law, properly containing only observables in terms of concentrations, can be derived. In enzyme catalysis, the first rate law was written in 1913 by Michaelis and Menten therefore, the corresponding kinetics is named the Michaelis-Menten mechanism. The rate law according to Michaelis-Menten features saturation kinetics with respect to substrate (zero order at high, first order at low substrate concentration) and is first order with respect to enzyme. 

However, when the view is restricted to simple, irreversible reactions obeying an nth order power rate law and, if additionally, isothermal conditions arc supposed, then—together with the results of Section 6.2.3—it can be easily understood how the effective activation energy and the effective reaction order will change during the transition from the kinetic regime to the diffusion controlled regime of the reaction. 

COMBINE (First Order Gas-Phase Reaction in a PFR) I From moie balance From rate law ... 

Deduce rate laws and reaction orders from experimental measnrements of the dependence of reaction rates on concentrations (Section 18.2, Problems 5-8). 

We see that the orders (exponents) in the rate law expression may or may not match the coefficients in the balanced equation. There is no way to predict reaction orders from the balanced overall chemical equation. The orders must be determined experimentally. 

As the size of the electrode was decreased from 25 to 5 gm in diameter, the dissolution reaction was shifted from a position where the initial rate was predominantly diffusion-controlled to a time scale where surface-kinetic limitations became apparent. The procedure for analyzing the rate data was similar to that described above, with boundary conditions that reflected first-and second-order dissolution rate laws under the defined conditions. The dissolution fluxes were found to be governed by a second-order dependence on the interfacial undersaturation ... 

One-electron reduction of NO to HNO is unique because of the spin issues involved. Sequential electron-proton transfer would generate 3NO as an intermediate, and protonation of this species to give UNO is slow.112 These kinetic considerations add to the overall thermodynamic effects favoring H-atom transfer mechanisms. Despite these expectations, evidence in favor of H-atom transfer to NO is quite sparse. NO has been argued to act as a H-atom acceptor in its reaction with hydroxylamine.113 This reaction has a rate law first order in [NO] and first order in [H2NO ], and HNO is inferred as an intermediate. NO also abstracts a hydrogen atom from hyponitrous acid, HONNOH.114 As Table 9.10 shows, NO is now considered to be a very weakhydrogen atom acceptor, so the reports of its reactivity in this mode may bear reexamination. 

The reaction is first order in molecular oxygen and first order in methanol therefore, we say both the reaction and the rate law are elementary. This forn of the rate law can be derived from Collision Theory as shown in the Profes- sion Reference Shelf 3A on the CD-ROM. There are many reactions where the stoichiometric coefficients in the reaction are identical to the reaction orders but the reactions are not elementary owing to such things as pathways involving active intermediates and series reactions. For these reactions that are not elementary but whose stoichiometric coefficients are identical to the reaction orders in the rate law. we say the reaction follows on elememary rate /aw. For example, the oxidation reaction of nitric oxide discussed earlier. 

A key point to remember is that the components of the rate law—rate, reaction orders, and rate constant—must be found by experiment they cannot be deduced from the reaction stoichiometry. Chemists take an experimental approach to finding these components by... 

Sample Problem 16.2 shows how to find the reaction orders from a known rate law. Now let s see how they are found from data before the rate law is known. Consider the reaction between oxygen and nitrogen monoxide, a key step in the formation of acid rain and in the industrial production of nitric acid ... 

Give the individual reaction orders for all substances and the overall reaction order from the following rate law ... 

Consider the zero-, first-, and second-order integrated rate laws. If you have concentration versus time data for some species in a reaction, what plots would you make to "prove" a reaction Is either zero, first, or second order How would the rate constant, k, be determined from such a plot What does thej-intercept equal In each plot When a rate law contains the concentration of two or more species, how can plots be used to determine k and the orders of the species in the rate law ... 

Determining Reaction Order from the integrated Rate Law... 

At this point, we can see that (1) if a plot of [A] versus time is Unear, the reaction is zero order and (2) if a plot of ln[A] versus time is linear, the reaction is first order. From the form of the integrated rate law equations for these cases, you should also be able to see that the slope of the linear plot must be equal to -k. So we can find both the rate constant and the reaction order from our graph. Next we will examine the correct model for second-order kinetics. 

The mathematical form of the reaction rate law for a specific chemical reaction depends on the order of the reaction, which is itself dictated by the reaction mechanism. Reaction order cannot be determined from a simple inspection of a stoichiometric chemical reaction it must be determined empirically from experiment or from detailed knowledge about the underlying reaction mechanism. Analytical rate law expressions are available for zero-, first-, and second-order reaction processes. First- and second-order reaction processes are the most common in everyday occurrence. 

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