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Chemical KineticsThe Study of Reaction RatesChemical KineticsKinetics involves the study of several factors that affect the rates of chemical reactions.The final goal is to use all of the data to develop a step-by-step reaction mechanism.The mechanism is a possible path by which reactants become products.Factors Affecting Reaction RatesScientists typically examine how each of the following factors affect the rate of a particular reaction.n n Concentration of Reactantsn n Temperaturen n Solvent(if applicable)n n Catalysts(if applicable)Reaction RatesThe rate of reaction is typically expressed in the rate of disappearance of reactants,or the rate of formation of products.Since the stoichiometry of the reaction is known,the concentration of only one component of the reaction needs to be measured.Reaction RatesNote that the concentration of NO increases by the same amount that NO2 decreases.Reaction RatesO2=NOSo only one component of the reaction need be measured.Reaction RatesFor the reaction:2NO2(g)2NO(g)+O2(g)rate of loss of NO2=rate of formation of NO =2(rate of formation of O2)Reaction RatesFor the reaction:2NO2(g)2NO(g)+O2(g)rate of loss of NO2=rate of formation of NO =2(rate of formation of O2)-NO2 =NO =2(O2)t t tNote the negative sign for the rate of loss of reactant.Reaction Rates-NO2 =NO =2(O2)t t tThis relationship can also be seen in a graphical presentation of concentration versus time.2NO2(g)2NO(g)+O2(g)Note that the rate of reaction varies as the reaction proceeds.Reaction Rates:2NO2(g)2NO(g)+O2(g)The rate of reaction of NO2 is most rapid at the beginning of the reaction.It slows considerably as the reaction proceeds.Reaction RatesReaction rates vary with time,and also depend upon the temperature and stoichiometry of the reaction.As a result,we must be very specific in what we mean by a reaction rate.Initial rates are often used.This is the rate of reaction just after the reaction begins.The tangent to the curve during the initial moments of the reaction provides the rate.Reaction RatesThis graph for the decomposition of N2O5 to form NO2 and O2 shows an initial rate of 5.4 x 10-4 mol/L-sReaction RatesThe convention for dealing with the stoichiometry of the reaction is that for a general reaction:aA+bB cC+dDRate=-1 A =-1 B=1(C)=1(D)a t b t c t d tRate LawsOne of the goals of kinetics is to determine the rate law for a reaction.The rate law is the mathematical relationship that shows how the reaction rate depends upon the concentration of reactants.Rate=kAxByk is the rate constant,and is highly temperature dependentRate LawsFor a decomposition reaction such asA productsthe rate law will beRate=kAnn is the reaction order,and is usually equal to 0,1 or 2.The value of n must be determined experimentally.Rate LawsThe value of n can be obtained by graphing concentration versus time.Rate LawsThe relationship between reaction rate and concentration also illustrated the effect of reaction order.Rate LawsNote that the reaction rate doesnt depend upon concentration of reactant for a zero order rate law.Rate LawsRate=kAxByx and y are called the order of the reaction with respect to reactant A and B respectively.They will usually have the value of 0,1 or 2,though other values are possible.Rate laws must be determined experimentally.Rate LawsThe exponents in the rate law provide information on which reactants may be involved in critical steps of the reaction mechanism.The mechanism is the step-by-step process by which reactants become products.Rate laws must be determined experimentally.Rate LawsThe rate law of a reaction,along with information about temperature effects and solvent effects can be used to develop a possible reaction mechanism.The goal of kinetics is often to determine a possible reaction mechanism for a known reaction.Determination of Rate LawsAll rate laws are experimentally determined.There are two basic methods used:1.The Method of Initial Rates2.Graphical Techniques using the Integrated Rate LawThe Method of Initial RatesThe reaction rate is measured for several different experiments.In each trial,on reactant concentration is changed(usually doubled)while the others are held constant.The change in rate will depend only upon the reactant with the changed concentration.The Method of Initial RatesThe Method of Initial RatesNO2-doublesOThe Method of Initial RatesNO2-doublesRate doublesOThe Method of Initial RatesNO2-doublesRate doublesRate NO2-1OThe Method of Initial RatesNH4+doublesRate doublesRate NH4+1OThe Method of Initial Ratesrate NH4+NO2-orrate=k NH4+NO2-The reaction is first-order in ammonium ion,first-order in nitrite ion,and second-order overall.The Method of Initial RatesThe Method of Initial RatesBrO3-doublesrate doublesrate BrO3-1 The Method of Initial RatesH+doublesrate quadruplesrate H+2The Method of Initial RatesBr-doublesrate doublesrate Br-1Method of Initial Ratesrate BrO3-Br-H+2The rate law is usually written with the rate constant,k,included:rate=kBrO3-Br-H+2The reaction is first order in bromate,first order in bromide,and second order in hydronium ion.Method of Initial Ratesrate=kBrO3-Br-H+2The data for any reaction trial can be used to calculate the value of k,the rate constant.The reaction rate has the units mol/liter-time,so the units of k depend upon the exponents in the rate law.Usually the value of k for several trials is averaged.Graphical TechniquesThe Integrated Rate LawsThe Integrated Rate LawIn general,rate laws will be first or second order.In either case,the rate law can be integrated to provide a linear equation of the form:y=mx+b.This permits graphical presentation of the data and determination of the value of the rate constant.The Integrated Rate LawOnce concentration versus time data have been collected,the scientist constructs one or more graphs to determine both the order of the reaction and the value of the rate constant.The Integrated Rate LawWe need not measure concentration.Any property that is proportional to concentration(intensity of color,pressure or volume of gases,pH,etc.)may be graphed.HCO2H(aq)+Br2(aq)2Br1-(aq)+CO2(g)The Integrated Rate Law-First Order Reactionsrate=-dA=kA1 dtRearranging,we obtain:-dA =kdt A When this expression is integrated from time=0 to time t,we obtain:lnA=-kt+lnAoThe Integrated Rate Law-First Order ReactionslnA=-kt+lnAoThis is the integrated rate law for first-order reactions.It has the linear form y=mx+b.If the reaction is first-order,a graph of lnA versus time will be linear with a slope equal to k.The Integrated Rate Law-First Order ReactionsThe linearity indicates that the reaction is first-order with respect to N2O5.The rate constant(-slope)has the units of(time)-1.The Integrated Rate Law-First Order ReactionslnA=-kt+lnAoIf a graph isnt linear,a second-order plot must be prepared.The Integrated Rate Law-First Order ReactionsThe curvature of the graph of lnA vs time indicates that this reaction is not first order.The Integrated Rate Law 2nd Order Reactionsrate=-dA=kA2 dtRearranging,we obtain:-dA =kdt A2 When this expression is integrated from time=0 to time t,we obtain:1 =kt+1_ A AoThe Integrated Rate Law 2nd Order Reactions 1 =kt+1_ A AoThis equation has a linear(y=mx+b)form.If a reaction is second-order,a plot of 1/A versus time is linear,with the slope equal to the rate constant.The rate constant has the units(M)-1(time)-1.The Integrated Rate Law 2nd Order ReactionsThe linearity of the graph of A-1 indicates that the reaction is second-order with respect to NO2.The Integrated Rate Law-2nd Order ReactionsThe linearity of the graph of 1/A versus time indicates that the reaction is second-order with respect to C4H6.Zero-Order Rate LawsMost reactions involving a single reactant exhibit first or second-order kinetics.Rarely,a reaction will have zero-order kinetics.In this case,Rate=kA0=k(1)=kZero-Order Rate LawsRate=kA0=k(1)=kThe integrated rate law is:A=-kt+Aoand a graph of A versus time is linear.Zero-Order Rate LawsUnlike the rate laws for other reactions,for a zero-order reaction,a graph of A versus time is linear.The slope=-k.Graphical TechniquesHalf-life and 1st Order ReactionsThe half-life is the time it takes for the concentration of a reactant to halve.It is represented by the symbol t.The half-life for a 1st-order reaction doesnt depend upon concentration.First-order reactions have a constant half-life.That is,it takes the same length of time for the concentration to halve throughout the reaction.Half-life and 1st Order ReactionsHalf-life and 1st Order ReactionsFirst order reactions have a constant half-life throughout the course of the reaction.First-Order Half-LifeHalf-life and 1st Order ReactionsThe first order rate law can be rearranged:lnA=-kt+lnAo Since A=Ao at the half-life,ln(Ao/.5Ao)=ktln(2.00)=kt0.693=ktlnAoA=ktHalf-life and 1st Order Reactions0.693=ktort=0.693 kThe half-life is constant throughout a first order reaction.All radioactive decay exhibits first-order kinetics.Half-life Problemn nA mummys shroud has a 14C activity of 8.9 dis/min/gC.Living things have a 14C activity of 15.2 dis/min/gC.The half-life of 14C is 5,730 years.Estimate the age of the shroud.Half-life and 2nd Order Reactions For a 2nd order reaction,each successive half-life is twice the previous one.Half-life and 2nd Order ReactionsThe half-life of second-order reactions depends upon the concentration of reactant.As the concentration decreases,the half-life increases.Half-life and 2nd Order ReactionsThe integrated rate law for a 2nd order reaction is:1 =kt+1_ A AoAt the half life,A=Ao,and t=t.1 =k t+1_ .5Ao Ao Half-life and 2nd Order Reactions 1 =k t+1_ .5Ao Ao 1 =k t Ao t=1/k AoThe half-life changes with concentration of reactant for a second-order reaction.SummaryRate Laws for Multiple ReactantsFor reactions with two or more reactants,the reaction order for each reactant can be determined graphically by monitoring the concentration of one reactant while ensuring that all other reactants are in very large(at least ten-fold)excess.In this way,the rate will depend only upon the reactant studied.The concentrations of other reactants will not change much during the reaction.Energy&Reaction RatesCollisions with the proper orientation also need sufficient energy to form products.For all reactions,exothermic or endothermic,a minimum amount of energy is required for the reactants to form products.This minimum amount of energy is called the activation energy.Energy&Reaction RatesThe activation energy,Ea,is used to help weaken the bonds of reactants and help form the bonds in products.Energy&Reaction RatesEnergy&Reaction RatesSince the Since the kinetic energy of kinetic energy of the collisions the collisions influences the influences the reaction rate,reaction rate,there is a there is a relationship relationship between between temperature temperature and the value of and the value of the rate the rate constant.constant.Energy&Reaction RatesThe experimentally based Arrhenius equation relates temperature and activation energy to the rate constant.k=Ae-Ea/RTwhere k is the rate constant;Ea is the activation energy(J/mol);R=8.314 J/K-mol;T is temperature in Kelvins;and A is the frequency factor.Energy&Reaction Ratesk=Ae-Ea/RTA,the frequency factor,(or pre-exponential factor)takes into account the frequency of collisions and the fraction with proper orientation to form products.Energy&Reaction Ratesk=Ae-Ea/RTThe Arrhenius equation is best used in logarithmic form:ln(k)=-+ln(A)This equations has the linear form y=mx+b.A graph of ln k versus 1/T has a slope of-Ea/R.Ea 1R TEnergy and Chemical ReactionsReaction rates depend upon concentrations of reactants because molecules need to collide with each other in order to form products.Not all molecular collisions lead to product formation.The collisions must have sufficient energy to weaken existing bonds and also the proper orientation to produce product(s).Determination of EaChemists usually determine the value of the rate constant for a reaction at several temperatures.A graph of ln(k)versus 1/T will be linear,with the slope equal to Ea/R.Temperature and Reaction RateChemical reactions always go faster when the temperature is increased.However,increasing the temperature of a reaction may be costly,or cause unwanted side reactions to occur.Collision TheoryReaction MechanismsThe goal of kinetics is to determine the series of steps by which reactants become products.This series of steps is called a reaction mechanism.The reaction mechanism is a series of elementary steps that represent single chemical events such as a collision,decomposition,etc.Reaction MechanismsBecause each elementary step represents a single event,we can write rate laws for each of the steps.For example,if an elementary step involves the collision of molecule A with molecule B,than the rate will depend upon both the concentration of A and the concentration of B.Rate=kABReaction MechanismsRate laws can only be written for elementary steps.They cannot be written for chemical reactions unless experiments are performed to determine the relationship between rate and concentration.Elementary Steps and their Rate LawsReaction MechanismsScientists study a particular reaction and experimentally determine the rate law.Using other experimental information,they propose a reaction mechanism.The reaction mechanism is a series of elementary steps that represent single chemical events such as a collision,decomposition,etc.Reaction MechanismsThe proposed reaction mechanism must meet two criteria:1.The proposed mechanism for the reaction must be consistent with the observed rate law.2.The sum of the elementary steps must give the overall balanced equation for the chemical reaction.Reaction MechanismsConsider the reaction between NO2(g)and CO(g).The balanced equation is:NO2(g)+CO(g)NO(g)+CO2(g)The experimentally determined rate law for the reaction is:Rate=kNO22 Reaction MechanismsThe proposed mechanism for the reaction is:NO2(g)+NO2(g)NO3(g)+NO(g)NO3(g)+CO(g)NO2(g)+CO2(g)k1k2Reaction MechanismsThe sum of the steps must add up to the overall balanced equation:NO2(g)+NO2(g)NO3(g)+NO(g)NO3(g)+CO(g)NO2(g)+CO2(g)k1k2Reaction MechanismsThe sum of the steps must add up to the overall balanced equation:NO2(g)+NO2(g)NO3(g)+NO(g)NO3(g)+CO(g)NO2(g)+CO2(g)NO2(g)+CO(g)NO(g)+CO2(g)k1k2Reaction IntermediatesThis is a species that is neither a reactant nor a product.It is produced during the course of the reaction and consumed in a later step.NO2(g)+NO2(g)NO3(g)+NO(g)NO3(g)+CO(g)NO2(g)+CO2(g)NO2(g)+CO(g)NO(g)+CO2(g)k1k2Reaction MechanismsNO2(g)+NO2(g)NO3(g)+NO(g)NO3(g)+CO(g)NO2(g)+CO2(g)Reaction MechanismsNO3 is a reaction intermediate.It is formed and consumed during the course of the reaction.Reaction MechanismsNO2(g)+CO(g)NO(g)+CO2(g)The proposed two-step mechanism provided the overall balanced equation for the reaction.For the mechanism to be valid,the experimental or observed rate law must match the rate law derived from the proposed reaction mechanism.Reaction MechanismsNO2(g)+CO(g)NO(g)+CO2(g)The experimentally determined rate law for the reaction is:Rate=kNO22 Reaction MechanismsThe proposed mechanism for the reaction is:NO2(g)+NO2(g)NO3(g)+NO(g)NO3(g)+CO(g)NO2(g)+CO2(g)k1 and k2 are the rate constants for the two steps of the mechanism.Many reaction mechanisms contain a rate determining step.k1k2Reaction MechanismsIf a multi-step process has one step which is much slower than all of the other steps,the slow step will determine the overall rate.The slow step is called the rate determining step.The overall reaction can be no faster than its slowest step.Reaction MechanismsThe proposed mechanism for the reaction is:NO2(g)+NO2(g)NO3(g)+NO(g)(slow)NO3(g)+CO(g)NO2(g)+CO2(g)(fast)For this mechanism,the researcher has proposed that first step is slow compared to the second,and is the rate determining step.k1k2Reaction MechanismsThe proposed mechanism for the reaction is:NO2(g)+NO2(g)NO3(g)+NO(g)(slow)NO3(g)+CO(g)NO2(g)+CO2(g)(fast)The rate of the reaction will be the rate of the first step.Rate=k1NO22This is the derived rate law.k1k2Reaction MechanismsThe derived rate law is:Rate=k1NO22The observed rate law is:Rate=kNO22Since the rate laws match,the proposed mechanism may be the correct mechanism.Reaction MechanismsFurther experimentation and research into related reaction mechanisms would be needed to help confirm the proposed reaction mechanism.In general,reaction mechanisms cannot be proven absolutely.Mechanisms with a rapid pre-equilibrium2 NO +2 H2 N2+2 H2OObserved rate law:rate=k NO2H2Proposed Mechanism:2 NO N2O2(fast,k1 and k-1)N2O2+H2 N2O+H2O(slow,k2)N2O+H2 N2+H2O(fast,k3)Mechanisms with a rapid pre-equilibrium2 NO +2 H2 N2+2 H2OObserved rate law:rate=k NO2H2Proposed Mechanism:2 NO N2O2(fast,k1 and k-1)N2O2+H2 N2O+H2O(slow,k2)N2O+H2 N2+H2O(fast,k3)2 NO +2 H2 N2+2 H2OCatalystsA catalyst is a substance which provides a lower energy pathway for the reaction.Catalysts alter the reaction mechanism of the reaction.Catalysts allow the reaction to proceed more rapidly at lower temperatures.CatalysisThe reaction will go faster with a catalyst,or proceed at a comparable rate at lower temperatures.CatalysisThe reaction goes faster because a greater percentage of molecules have sufficient energy to form products when the activation energy is lower.CatalystsCatalysts are present at the beginning of the reaction.Although they are involved in the reaction,they are regenerated.The net result is that the catalyst speeds up the reaction without being consumed.Biological catalysts are called enzymes.Enzymes allow many complex chemical reactions to occur at body temperature(37oC).CatalysisCatalysis and the Ozone LayerFreons,or chloroflurocarbons,have been linked to destruction of the ozone layer of the earth.Freons,when exposed to high energy light in the upper atmosphere,form highly reactive chorine atoms.These chlorine atoms convert ozone to oxygen and are regenerated in the process.Catalysis and the Ozone LayerCFCl3+h CFCl2+ClCl+O3 ClO+O2ClO+O Cl +O2_O3+O 2 O2Ozone is depleted,and the chlorine radical is regenerated.Heterogeneous CatalysisHeterogeneous catalysis usually involves gaseous reactants that react on the surface of a solid catalyst.An example is the reaction of ethylene with hydrogen.H2C=CH2(g)+H2(g)H3CCH3(g)Heterogeneous CatalysisH2C=CH2(g)+H2(g)H3CCH3(g)The reaction proceeds slowly due to the strength of the bond in hydrogen.The gaseous reactants are collected on the surface of catalysts such as platinum,palladium or nickel,where the reaction occurs.Heterogeneous CatalysisThe metal catalyst The metal catalyst interacts with the interacts with the hydrogen molecules hydrogen molecules and weakens the H-H and weakens the H-H bond.bond.Heterogeneous Catalysis
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