UMass Boston, Chem 116©H. Sevian 1CHEM 116Collision Theory andReaction MechanismsLecture 13Prof. SevianNote: If there is anything we do not finish about reaction mechanisms today, that is where we will start on Tuesday with Lecture 14.Today’s agendaKinetics: the study of the rates of chemical reactionsz Using data that can be experimentally obtained to determine rate lawsz Finish example of a table of initial reaction rates to determine the order of reaction for different species involved in a reaction, and the value and units for rate constant (k)z The special case of first-order rate lawsz Modeling kinetics at the particle levelz Collision theory for explaining/predicting why different factors(e.g., concentration, temperature) affect ratez Arrhenius equation for explaining/predicting temperature dependence of rate constant (k)z Reaction mechanismsUMass Boston, Chem 116©H. Sevian 2Method 2: Determining rate law by measuring initial rate at various concentrationsExampleGiven the following measurements of initial rate of reaction under various conditions of initial concentrations of reactants, determine:z the rate lawz the value of the rate law constant, kz the units of k0.0140.0200.01050.2270.0200.04040.1140.0400.02030.0570.0200.02020.0280.0100.0201(M/s)[O2][NO]ExperimentInitial rateConcentration (M)InitialA clicker question about material we covered at the last lectureThe rate of appearance of C is 6.2 × 10-2mol/L·s in the chemical reaction below. A (g) → 2 C (g)What is the rate of disappearance of A?(A) -6.2 × 10-2mol/L·s(B) -1.2 × 10-1mol/L·s(C) -3.1 × 10-2mol/L·s(D) There is not enough information to tell.UMass Boston, Chem 116©H. Sevian 3Half-lifeMathematical definitionNeed to find time at which concentration of the reactant is equal to half the initial concentrationGraphical representationThe amount of time it takes for half of the reactant to react (disappear)[][][] [][][]00A21A when of value theis life-HalfAlnAlnbygiven A order,-firstFor offunction a is A=−=ttttttktConcentration vs. time00.511.522.500.5 11.5 22.5time (min)concentration, [A] (mol/L)What does t1/2equal in this example?General equation for half-lifeIf the reaction is first-order, meaning and if you know the value of the rate law constant k,then you can determine the half-life algebraically[][][] []tkktt−==ΔΔ=0AlnAlnAARatedifferential rate lawintegrated rate law[] [][][][] [][][]()()kttktktktlifehalflifehalftttt2ln2ln:gone isreactant thehalf where timeat the SoAAln g,RearranginAlnAln2AAor ,A21A when of for value Looking0000===⎟⎟⎠⎞⎜⎜⎝⎛−===−−lifehalflifehalftkkt−−==693.0or693.0UMass Boston, Chem 116©H. Sevian 4Sometimes it is easier to work with the half-lifeExample: If a given reaction is first-order and the half-life is 2.5 minutes, how much reactant remains after 5.0 minutes have passed if the initial amount of reactant is 100. grams? Amount of reactant # of half-livesAll (100%) 0Half (50%) 1One-fourth (25%) 2One-eighth (12.5%) 3[] []0lives-half #A21A:remainingreactant ofAmount of⎟⎠⎞⎜⎝⎛=Example of working with the half-lifeExample: If a given reaction is first-order and the half-life is 2.5 minutes, how much reactant remains after 4.0 minutes have passed if the initial amount of reactant is 100. grams? Amount of reactant # of half-livesAll (100%) 0Half (50%) 1One-fourth (25%) 2[] [][] []()ggttimeoflifehalfof33.1003299.0A21A6.1min 2.5min 4.0lives-half #A21A06.10lives-half #==⎟⎠⎞⎜⎝⎛====⎟⎠⎞⎜⎝⎛=−UMass Boston, Chem 116©H. Sevian 5All nuclear decay processes are first-orderExampleRadioactive iodine-125, which is used for studies of thyroid functioning, has a rate constant for decay of 0.011 day-1. If you begin a treatment with iodine-125, and start with 1.6×1015atoms, how many atoms remain after 2.0 days?Reaction rates: what’s happening at the particle level?Figure Ratio of NO:O3# of collisions per sec(a) 1/16 2(b) 2/16 4(c) 1/32 4For a nice review of these concepts, along with animations, see http://www.sciencepages.co.uk/keystage4/GCSEChemistry/m3ratesofreaction.phpFrom Chemistry & Chemical Reactivity 5thedition by Kotz / Treichel. C 2003. Reprinted with permission of Brooks/Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215.[][]3223ONO)(O)(NO)(O)(NO kRategggg=+→+UMass Boston, Chem 116©H. Sevian 6Why isn’t collision frequency the only factor affecting reaction rate?Why is (a) effective and (b) is ineffective?Cl + NOCl → NO + Cl2What affects the reaction rate?Macroscopic levelEvidence: use experimental measurements to determine orders and value of k in rate law1. When you increase reactant concentrations, rate of reaction increases2. When you increase temperature, rate of reaction increases3. Some reactions have very slow rates and some very fast rates –what differs is the value of kParticle levelWhat we believe is happening at the particle level that explains why reaction rates have the mathematical form they do1. When there are more reactant particles, they collide more often2. When the average speeds of reactant particles increases, they collide more often3. There must be some reason for this at the particle level…Assumption: in order for molecules to react with each other, they must collideAssumption: Rate laws always have the mathematical formRate = k [A]n[B]mUMass Boston, Chem 116©H. Sevian 7What is the theoretical basis for the form of the rate law? Must be based on how particles behave.Rate = k [A]n[B]m1. Numbers of particles: reflected in concentration2. Temperature: must be part of k3. There must be something else that is part of k that explains why two reactions at the same T can have different values of kForward: NO2+ CO → NO + CO2Activation energy: 132 kJ/molHeat of reaction is exothermicReverse: NO + CO2→ NO2+ COActivation energy: 358 kJ/molHeat of reaction is endothermicEnergy considerations: Activation barrierForward: NO + O3→ NO2+ O2Activation energy: 10 kJ/molHeat of reaction is exothermicReverse: NO2+ O2→ NO + O3Activation energy: 210 kJ/molHeat of reaction is endothermicFrom Chemistry & Chemical Reactivity 5thedition by Kotz / Treichel. C 2003. Reprinted with permission of Brooks/Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215.Transition state orActivated complexUMass Boston, Chem 116©H. Sevian 8What does the rate constant depend on?RTEaeAk−=Rate constant that appears in the rate law:Rate = k [A]n[B]mA constant