FundChemReaxEngCh2

FundChemReaxEngCh2 - _________ ~~___....2...,f~ Rate...

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Unformatted text preview: _________ ~~___....2...,f~ Rate Constants of Elementary Reactions 2.1 I Elementary Reactions Recall from the discussion of reaction networks in Chapter 1 that an elementary re- action must be written as it proceeds at the molecular level and represents an irre- ducible molecular event. An elementary reaction normally involves the breaking or making of a single chemical bond, although more rarely, two bonds are broken and two bonds are formed in what is denoted a four-center reaction. For example, the reaction: is a good candidate for possibly being an elementary reaction, while the reaction: is not. Whether or not a reaction is elementary must be determined by experimentation. As stated in Chapter 1, an elementary reaction cannot be written arbitrarily and must be written the way it takes place. For example (see Table 1.4.3), the reaction: (2.1.1) cannot be written as: (2.1.2) since clearly there is no such entity as half a molecule of dioxygen. It is important to note the distinction between stoichiometric equations and elementary reactions (see Chapter 1) is that for the stoichiometric relation: (2.1.3) S4 CHAPTER 2 Rate Constants of Elementary Reactions one can write (although not preferred): NO + ~02 = N0 2 (2.1.4) The remainder of this chapter describes methods to determine the rate and tem- perature dependence of the rate of elementary reactions. This information is used to describe how reaction rates in general are appraised. 2.2 I Arrhenius Temperature Dependence of the Rate Constant The rate constant normally depends on the absolute temperature, and the functional form of this relationship was first proposed by Arrhenius in 1889 (see Rule III in Chapter 1) to be: k = Ii exp[-E/(RgT)J (2.2.1) EXAMPLE 2.2.1 I where the activation energy, E, and the pre-exponential factor, A, both do not de- pend on the absolute temperature. The Arrhenius form of the reaction rate constant is an empirical relationship. However, transition-state theory provides a justification for the Arrhenius formulation, as will be shown below. Note that the Arrhenius law (Equation 2.2.1) gives a linear relationship between In k and T~ 1• The decomposition reaction: can proceed at temperatures below 100°C and the temperature dependence of the first-order rate constant has been measured. The data are: 288 298 313 323 338 1.04 X 1O~5 3.38 X 1O~5 2.47 X 1O~4 7.59 X 1O~4 4.87 X 10 3 Suggest an experimental approach to obtain these rate constant data and calculate the acti- vation energy and pre-exponential factor. (Adapted from C. G. Hill, An Introduction to Chem- ical Engineering Kinetics & Reactor Design. Wiley, New York, 1977.) • Answer Note that the rate constants are for a first-order reaction. The material balance for a closed system at constant temperature is: dt CHAPTER 2 Bate Constants of Elementary Reactions 55 where nN,o, is the number of moles of NzOs. If the system is at constant volume (a closed vessel), then as the reaction proceeds the pressure will rise because there is a positive mole...
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This note was uploaded on 07/19/2011 for the course ENG 101 taught by Professor Calt during the Spring '11 term at Caltech.

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FundChemReaxEngCh2 - _________ ~~___....2...,f~ Rate...

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