# ln18s08 - Lecture 18 Introduction to Kinetics First a CH...

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1 Lecture 18: Introduction to Kinetics First a CH 302 Kinetics Study Guide (Memorize these first three pages, they are all the background you need) Reaction Rate: The most important issue in kinetics is a determination of the rate of a reaction and the data that comes from a plot of the rate data. In the concentration-time plot below for the reaction aA ! bB [ ] The rate is simply how fast A disappears (note the negative sign) and B appears as a function of time. The instantaneous rate is simply the tangent line at any time (the slope.) The lower case a and b are the reaction coefficients and are constants that make sure that rates at which things appear and disappear are the same (conservation of matter.) Rate Laws (what affects the rate.) Of course you can ask the question, what factors affect the rate. There are four factors : [A] x which is the concentration of A, the pre-exponential factor, A , which depends on the state of the reactants, T , the temperature, and E a , the activation barrier. With these factors we make a RATE LAW. - __ "# A] __ = __ "# B] __ = rate = A exp (-E a /RT ) [A] x = k [A] x a " t b " t The first three terms A exp (- E a /R T ) combine to make the rate constant , k . Half the problems you do in kinetics use this differential rate expression . Among problems you can do: \$ Calculate the instantaneous rate at any given time: measuring the slope of the tangent line \$ Determining the order of a reaction (the exponent x ) using a method of initial rates \$ Calculate k, T, E a , A, [ ] or x given known values. HINT: This third type of problem is simple plug-and-chug except that you need to be able to manipulate the exp term effortlessly. Remember this is done using the inverse relationship ln (exp x) = x [B] [A] time - __ "# A] __ = _ "# B] __= rate a " t b " t

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2 Integrated Rate Law. You might think the differential rate expression above tells us just about all we need to know about reaction kinetics. Almost. The one thing it can’t answer is the following simple but important question: Suppose a certain amount of compound reacts over time; how much is left at some later time? (for example, I have 100 molecules of A which reacts with a rate constant of 2x10 -2 sec -1 . How much A is left after 1 s?) To work this problem we need to integrate the differential rate expression. Those of you who have had calculus can do this easily. The answers for the three most important reaction orders are shown below. order x = 0 order x = 1 order x = 2 differential rate law - __ "# A] __ = k a " t - __ "# A] __ = k [A] 1 a " t - __ "# A] __ = k [A] 2 a " t integrated rate law [A] = [A o ] - akt ln [A] = ln[A o ] - akt 1/[A] = 1/[A o ] + akt In each case, you can calculate how much is left from starting materials or formed as products given the starting amount, [A o ], the rate constant, k, and the reaction time, t. Reaction half life.
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ln18s08 - Lecture 18 Introduction to Kinetics First a CH...

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