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Arrhenius equation, kinetic theory, and reaction mechanisms

# Arrhenius equation, kinetic theory, and reaction mechanisms...

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1 Kinetics Lecture 3: The Arrhenius Equation and reaction mechanisms. As we wrap up kinetics we will: Briefly summarize the differential and integrated rate law equations for 0, 1 and 2 order reaction Learn how scientists turn model functions like the integrated rate laws into straight lines from which useful information can be found in the slope and y-intercept Learn about the three factors found in the rate constant: A, E a and T are related in the Arrhenius equation Learn how the activation energy can be extracted from concentration time data using the combined Arrhenius equation Learn about two theories developed to explain kinetics: collision and transition state theory Learn about how the rate law for a reaction is created from the reaction mechanism Look at some famous catalysts First, a summary of the differential and integrated rates laws from Lectures 1 and 2 in a handy little table . In addition to the equations we have derived, note the comparison curves for first and second order integrated equations are also provided. In plot (a) note that in the first t 1/2 of 1.73 s, the concentration of A falls from 1.0M to 0.5M. It falls again by half from 0.5M to 0.25M in the next 1.73 s. And on and on. Contrast this with a second order reaction in (b) where during the first 2.5 s t 1/2 , the concentration falls from 1.0M to 0.5M. However the second t 1/2 takes 5 s for the concentration to be cut in half; the third t 1/2 takes 10 s. Note the concentration dependence of t 1/2 for all reactions that are not order one.

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3 Curve Fitting: Graphing the integrated rate equation. Something scientists do a lot is to try to find a best fit of a theoretical equation to experimental data. Let’s see if there is any value in doing it for the integrated rate equations that were and are shown in the table above. Remember these are the equations that let us find out how much stuff we have after a reaction has been going on awhile. In trying to fit experimental data, it is important to know what kind of function will fit the data. Scientists hope to find simple relationships like straight lines or parabolas because they aren’t crazy about doing hard math either. Well the good news for the integrated rate equations is that each of them can be arranged to fit a straight line. Remember that a straight line has the form: y = mx + b with two constants, a slope, m, and a y-intercept, b. The dependent y-variable is plotted as a function of the independent x-variable.

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4 One of the reasons scientists try to fit their data is that parameters like the slope or y-intercept actually correspond to important scientific information. For example, in doing kinetics, a couple important pieces of information are the rate constant, k, and the amount of starting material in a reaction, [A o ]. Wouldn’t it be great if we could extract that kind of information from a kinetics plot?
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