Wednesday, March 27, 2024

Lec XXVIII

Chem 1200


Angel C. de Dios

Kinetics VI

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As we near the end of the lectures on kinetics, it is important to reiterate the experimental side of kinetics. In the laboratory, the methods of initial rates require several runs for the same reaction. Each run begins with known initial concentrations of reactants. As you notice, when we do this on paper, it helps if the initial concentrations are chosen such that only one reactant is changing its concentration between runs. It is likewise helpful if this reactant is changing its concentration by an integral multiple. In the other method, where we simply monitor how a reactant is changing its concentration, it is necessary to draw test plots. We need to check which graph yields the best straight line. The test plots are [A] vs. time (zero order), square root of [A] vs. time (half order), ln[A] vs. time (first order), and 1/[A] vs. time (second order). All these plots except for the second order have a negative slope, from which we extract the rate constant. Drawing these plots is good exercise since this is how it is done in the real world. On paper, as in an exam, we will take advantage of the half-life as a clue to the order of a reaction. When we do not have time to draw all these test plots and given that the choices are limited to zero, first and second order, we can use the half-life to determine quickly the order of the reaction. In zero order, since the rate is constant, it should take shorter times to successively half the concentration of the reactant. The half-life is therefore decreasing as the reaction progresses in zero order. First order reactions are special, its half-life is constant all throughout the reaction. In second order, the rate of the reaction slows down a lot faster as the reactant is consumed thus making the successive half-lives longer. An increasing half-life as a reaction progresses therefore suggests a second order process. All of these, both test plots and using half-life as a clue, work if there is only one reactant. In the case of two reactants (like the fading of phenolphthalein), these approaches can still be applied by using one of the reactants in very large excess. This excess reactant will therefore maintain its concentration as the reaction progresses. This allows us to monitor the rate of the reaction as a function of the concentration of the limiting reactant. In this case, we will make test plots for the concentration of the limiting reactant. Whichever plot gives us a straight line provides a rate constant. But we need to keep in mind that this rate constant may still have a dependence on the concentration of the reactant in excess. That is why we call this a pseudo rate constant. We then have to repeat the experiment at different concentrations of the excess reactant to see the dependence of the pseudo rate constant on the excess reactant. The experience in the laboratory course is important since this is where you will see it first-hand, and go through the entire scheme of determining the rate law experimentally.