# PART V: REVIEWING PCAT CHEMISTRY in .NET Creation Data Matrix in .NET PART V: REVIEWING PCAT CHEMISTRY

PART V: REVIEWING PCAT CHEMISTRY
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[A] [A] ln 0 = kt 12 + ln[A]0 Rearranging the equation gives: ln 0 ln[A]0 = kt 12 2 2 Using one of the laws of logarithms, the equation can be solved for the half-life: ln 2 0693 = t 12 ln(2) = 0693, so = t 12 k k The half-life of the decomposition of SO2Cl2 with a k of 283 10 3 1 min is: 0693 = 245 min 3 1 283 10 min The half-life is independent of the concentration (this is true only for a rst-order reaction) The half-life remains constant during the course of the reaction The percent remaining as a function of number of half-lives is given in the table below: Number of half-lives elapsed 0 1 2 3 4 5 etc Percentage remaining 100 50 25 125 625 313
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This table allows you to estimate the fraction left by the number of half-lives that have elapsed For example, what percentage of SO2Cl2 remains after 600 min of reaction Two half-lives is 2 245 = 490 min and three half-lives is 3 245 = 785 min Because 600 min of the reaction is between 490 and 735 min , the percentage remaining is between 125 and 25 % A second-order rate law has the form rate = k[A]2 Integrating the rate law for this reaction gives: 1 1 = kt + [A]t [A]o For a second-order reaction, a plot of y intercept of 1 as y and t as x will have slope of +k and a [A]t
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1 The half-life of a second-order reaction can also be derived by [A]o [A]o substituting for [A]t: 2 1 1 1 = kt 12 + Solving for t 12 gives = = t 12 [A]o [A]o k [A]o 2
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The half-life depends on the initial concentration Because the concentration decreases over the course of a reaction, the half-life of a second-order reaction increases with time
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CHAP 10: GENERAL CHEMISTRY
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The Effect of Temperature on k
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The rates of chemical reactions are explained by collision theory, which is an extension of the kinetic molecular theory rst discussed in the description of gases Reactants will be successfully converted to products when the reactant molecules collide with suf cient energy and with the correct orientation These two factors are incorporated into the Arrhenius equation, which gives the value of the rate constant as a function of the temperature: k=
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