Faster and FasterCertain foods such as beans, cabbage, and broccoli contain complexsugars known as oligosaccharides. Although these compounds arebroken down to simple sugars during the digestive process, somepeople have a problem breaking them down completely. This failurecan lead to a condition known politely as flatulence, because theundigested material is eventually fermented by anaerobic organismsin the colon to produce gases such as CO2, H2, CH4, and smallamounts of smelly compounds.To help people who have this problem, a commercial productcalled Beano was developed. Its maker’s advertising material statesthat Beano “is a food enzyme from a natural source that breaksdown the complex sugars in gassy foods, making them more digestible.”As you will learn in this chapter, which describes the factorsaffecting the speed of chemical reactions, enzymes are biologicalcatalysts. Their role is to speed up chemical reactions. One of theenzymes in Beano, galactosidase, accelerates the breakdown of the15—Principles of Reactivity:Chemical Kinetics Charles D. WintersThe Control of Chemical ReactionsHard-to-digest foods. Foods such asbeans, cabbage, and broccoli are known toproduce flatulence in some people due toincomplete digestion of complex sugars.However, an enzyme, when added to thefood, can help break down these complexsugars and avoid “problem gas.”698(a) (b) (d) (e)(c)t  0 t  9 sec t  34 sec t  37 sect  28 secFigure A CO2in water. (a) A cold solution of CO2in water. (b) A few drops of a dye (bromthymol blue) are added to the cold solution.The yellow color of the dye indicates an acidic solution. (c) A less than stoichiometric amount of sodium hydroxide is added, convertingH2CO3to HCO3(and CO32). (d) The blue color of the dye indicates a basic solution. (e) The blue color begins to fade after some seconds asCO2slowly forms more H2CO3.TheamountofH2CO3formed is finally sufficient to consume the added Na0H and the solution is again acidic.Charles D. WintersChapter Outline15.1 Rates of Chemical Reactions15.2 Reaction Conditions and Rate15.3 Effect of Concentration on Reaction Rate15.4 Concentration–Time Relationships: Integrated RateLaws15.5 A Microscopic View of Reaction Rates15.6 Reaction MechanismsChapter GoalsSee Chapter Goals Revisited (page 741). Test your knowl-edge of these goals by taking the exam-prep quiz on theGeneral ChemistryNow CD-ROM or website.•Understand rates of reaction and the conditions affectingrates.•Derive the rate equation, rate constant, and reaction orderfrom experimental data.•Use integrated rate laws.•Understand the collision theory of reaction rates and therole of activation energy.•Relate reaction mechanisms and rate laws.again takes on O2, it releases H ions. These ions and HCO3 re-formH2CO3, from which CO2is liberated and exhaled.A simple experiment illustrates the effect of carbonic anhydrase.First, add a small amount of NaOH to a cold, aqueous solution of CO2(Figure A). The solution becomes basic immediately, because there isnotenough H2CO3in the solution to use up the NaOH. After someseconds, however, dissolved CO2slowly produces more H2CO3, whichconsumes NaOH, and the solution again becomes acidic.Now try the experiment again, this time adding a few drops ofblood to the solution (Figure B). Carbonic anhydrase in blood speedsup reactions 1 and 2 by a factor of about 107, as evidenced by themore rapid reaction that occurs under these conditions.To learn more about Beano and enzymes, see J. R. Hardee, T. M. Montgomery, and W. H. Jones: Journal of Chemical Education,Vol. 77, p. 498, 2000. For a more detailed discussion of the rate ofconversion of aqueous CO2, see J. Bell: Journal of ChemicalEducation, Vol. 77, p. 1098, 2000.(a) t  0 t  3 sec t  15 sec t  17 sec t  21 sec(b)(c) (d) (e)Figure B Action of carbonic anhydrase. (a) A few drops of blood are added to a cold solution of CO2in water. (b) The dye indicatesan acidic solution. (c, d) A less than stoichiometric amount of sodium hydroxide is added, converting H2CO3to HCO3(and CO32). Thedye’s blue color indicates a basic solution. (e) The blue color begins to fade after a few seconds as more H2CO3forms, and the solutionagain becomes acidic. The formation of H2CO3is more rapid in the presence of an enzyme.oligosaccharides in certain foods to the simple sugars galactose andglucose.Oligosaccharide H2O galactose glucoseCarbonic anhydrase is one of the many enzymes that play im-portant roles in biological processes (see page 732). Carbon dioxidedissolves in water to a small extent to produce carbonic acid, whichionizes to give H and HCO3ions.CO2gCO2aq 1CO2aq H2OH2CO3aq 2H2CO3aq H aq HCO3aq 3Carbonic anhydrase speeds up reactions 1 and 2. Many of theH ions produced by ionization of H2CO3(reaction 3) are picked upby hemoglobin in the blood as hemoglobin loses O2. The resultingHCO3 ions are transported back to the lungs. When hemoglobin212121¡212121¡2/1212121¡21uuuuuygalactosidase699Charles D. Winters700 Chapter 15 Principles of Reactivity: Chemical KineticsTo Review Before You Begin• Review reaction stoichiometry (Chapters 4 and 5)• Understand the distribution of molecular energies in a gas (Figure 12.14) and in aliquid (Figure 13.14)When carrying out a chemical reaction, chemists are concerned with two issues:the rate at which the reaction proceeds and the extent to which the reaction isproduct-favored. Chapter 6 began to address the second question, and Chapters 16and 19 will develop that topic further. In this chapter we turn to the other part ofour question, chemical kinetics, the study of the rates of chemical reactions.The study of kinetics is divided into two parts. The first part concerns the macro-scopic level, which addresses rates of reactions: what the reaction rate means, how todetermine a reaction rate experimentally, and how factors such as temperature andthe concentrations of reactants influence rates. The second part considers chemi-cal reactions at the particulate level. Here, the concern is with the reaction mecha-nism, the detailed pathway taken by atoms and molecules as a reaction proceeds.The goal is to reconcile data in the macroscopic world of chemistry with an under-standing of how and why chemical reactions occur at the particulate level—andthen to apply this information to control important reactions.15.1—Rates of Chemical ReactionsThe concept of rate is encountered in many