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<br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br /> <br />31 <br /> <br />Subtraoting eq. 3.1.10 from eq. 3.1.11 and taking the logarithm, <br /> <br />k' 2[Alo <br />In([Yl.-[Ylt) · III k'l - k'lt. (3.1.12) <br /> <br />A plot of In([Yl. - [Ylt) versus <br /> <br />time will yield a straight line of <br /> <br />k'2(Alo k'2(Alo <br />In k' (-In 1 ). It is the <br />1 s ope <br /> <br />object of the chemioal kinetic methodology to obtain straight line plots <br /> <br />slope equal to k'l and intercept <br /> <br />in order to determine the order of reaotion and rate constants. <br /> <br />After the proper rate relationship and constants have been <br /> <br />determined, the mechanism of the prooess can be deduoed. This is <br /> <br />somewhat of an intuitive prooess but there are certain guidelines. For <br /> <br />instanoe, the conoentration dependences in the rate law establish the <br /> <br />speoies that are involved in the mechaniBIII of the reaotion or prooess. <br /> <br />Rate laws for oomplex reaotions can take on various forms. '!'be number <br /> <br />of additive terms in a rate law indioate the number of parallel pathways <br /> <br />in the mechanism. A rate law with a denominator indicate sucoessive and <br /> <br />reversible pathways. The most important concept is that of the rate- <br /> <br />l1mi ting, or rate-determining step. In sequential steps of a mechanism <br /> <br />this is the slowest step with the lowest valued rate constant, k. It <br /> <br />controls the progress of the entire reaotion since faster subsequent <br /> <br />steps cannot prooeed until the rate limiting step has oocurred. A final <br /> <br />rule is that any given mechanistio interpretation of a rate law is not <br /> <br />unique to that rate. Alternative meohanisms leading to a given rate law <br /> <br />are kinetically indistinguishable and oannot be ruled out. <br /> <br />Chemical reactions and physical prooesses often display a <br /> <br />temperature dependenoe. TYpically the rate constant is logarithmically <br /> <br />dependent on the inverse of temperature. Three theories have made use <br />