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# fa01lec02 - Review of Chemical Kinetics 7.51 September 2001...

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© RT Sauer 1999 1 Review of Chemical Kinetics 7.51 September 2001 Kinetic experiments study the rate at which reactions occur, that is how the concentration of some molecular species changes as a function of time. In a plot of concentration vs. time, the rate of the reaction is simply the slope. In the kinetic experiment shown below, the rate of the reaction decreases as the reaction proceeds. 30 20 10 0 0.00 0.25 0.50 0.75 1.00 time (min) concentration of product The exact way in which reaction rates change as a function of time and how these rates vary with the concentration of reactants depends on the reaction mechanism. Kinetic studies can be used, therefore, to test proposed mechanisms. Rate equations or rate laws show the change in the concentration of one molecular species with respect to time (the rate ) as a mathematical function of a rate constant or kinetic constant, specified by a lower case k, and the concentrations of each molecular species that participates in the reaction. The examples shown below are rate laws for reactions that proceed in a single direction (i.e., back reactions are not considered). In some of the cases shown, certain rates have been adjusted to be consistent with the stoichiometry of the reaction. Thus, for 2A A 2 , the monomer concentration changes twice as fast as the dimer concentration. rxn (1) U N rate = -d[U]/dt = d[N]/dt = k[U] rxn (2) AB A+ B rate = -d[AB]/dt = d[A]/dt = k[AB] rxn (3) A+ B AB rate = -d[A]/dt = -d[B]/dt = k[A][B]

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© RT Sauer 1999 2 rxn (4) 2A A 2 rate = -d[A]/dt = 2d[A 2 ]/dt = k[A] 2 rxn (5) 2A+ B A 2 B rate = -d[A]/dt = -2d[B]/dt = 2d[A 2 B]/dt = k[A] 2 [B] Note that in each of the reactions shown above, the reactants and products are different molecular species. This means that all of the reactants have participated in the reaction. This is not true, however, for the following reaction. rxn (6) A+B+C AB + C rate = -d[A]/dt = -[B]/dt = k[A][B] Here, the rate law is identical to rxn (3) and the concentration of [C] doesn’t appear in the rate expression because C does not participate in this reaction. Rates are expressed in units of concentration/time (for example, M•sec -1 , µ M•min -1 , nM•sec -1 , etc.). The units of the rate constant always contain reciprocal time (sec -1 , min -1 , etc.) and depending on the reaction may also contain one or more reciprocal concentrations. For example, if the right side of the rate equation is k[A][B], then the rate constant must have units of M –1 •time -1 so that the entire expression will have units of M•time -1 . Order of reaction . The overall kinetic order of a reaction is defined by how many concentrations appear on the right side of the rate expression. The order of the reaction with respect to a particular species is defined by whether that species appears one or more times. For example, if the right side of the rate law is [A] m [B] n , then the overall order of the reaction is m+n and the reaction is m’th order with respect to [A] and n’th order with respect to [B]. Zeroth order means that the reaction rate does not change as the concentration of a species is changed.
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## This note was uploaded on 11/11/2011 for the course BIO 7.344 taught by Professor Bobsauer during the Spring '08 term at MIT.

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fa01lec02 - Review of Chemical Kinetics 7.51 September 2001...

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