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## Chemical Kinetics

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**Chemical Kinetics**Chapter 12**Reaction Rates 01**• Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). • change in concentration divided by the change in time Reactant Products A B 2 HI(g) H2(g) + I2(g) Chapter 12**1**2 [HI] t Rate = − = [I2] t Reaction Rates and Stoichiometry • What is the general rate of the following reaction ? 2 HI(g) H2(g) + I2(g) Chapter 12**aA + bB**cC + dD = = Rate* = − = − 1 d 1 c 1 a 1 b [C] t [D] t [A] t [B] t Reaction Rates and Stoichiometry • To generalize, for the reaction *: General rate of reaction Chapter 12**Which of the expressions below, corresponding to the**reaction of bromine with formic acid, is incorrect?**Which of the expressions below, corresponding to the**reaction of bromine with formic acid, is incorrect?**How Do we study Rate of a reaction?**• Consider the decomposition of N2O5 to give NO2 and O2: 2 N2O5(g) 4 NO2(g) + O2(g) Brown Colorless Chapter 12**2 N2O5(g) 4 NO2(g) + O2(g)**Reaction Rates: concentration versus time curve 03 Average Rate = Rate between two points in time The slope of each triangle Between two points Chapter 12**2N2O5(g)**4NO2(g) + O2(g) Reaction Rates**Rate for specific instance in time**Instantaneous rate: Slope of the tangent to a concentration versus time curve Initial Rate Chapter 12**Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g)**time Br2(aq) 393 nm 393 nm Detector light D[Br2] aDAbsorption Chapter 12**Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g)**slope of tangent slope of tangent slope of tangent [Br2]final – [Br2]initial D[Br2] average rate = - = - Dt tfinal - tinitial instantaneous rate = rate for specific instance in time The slope of a line tangent to the curve at any point is the instantaneous rate at that time Chapter 12**slope of**tangent slope of tangent Chapter 12**rate**k = [Br2] rate a [Br2] rate = k [Br2] = rate constant The Rate Law; rate = 3.50 x 10-3 s-1 [Br2] Chapter 12**k = 3.50 x 10-3 s-1**Chapter 12**aA + bB cC + dD**The Rate Law and Reaction Order The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers. Rate = k [A]x[B]y reaction is xth order in A reaction is yth order in B reaction is (x +y)th order overall Chapter 12**The Rate Law and Reaction Order are Experimentally**Determined Chapter 12**Determine the reaction order for:**F2(g) + 2ClO2(g) 2FClO2(g) ---- rate = k [F2]x[ClO2]y 1 vs 3 Double [F2] with [ClO2] constant Rate doubles x = 1 1 vs 2 rate = k [F2][ClO2] Quadruple [ClO2] with [F2] constant Rate quadruples y = 1 The instantaneous rate at the beginning of a reaction is called initial rate Chapter 12**F2(g) + 2ClO2(g) 2FClO2(g)**1 Rate Laws • Rate laws are always determined experimentally. • Reaction order is always defined in terms of reactant (not product) concentrations. • The order of a reactant is not related to the stoichiometric coefficient of the reactant in the balanced chemical equation. rate = k [F2][ClO2] Chapter 12**Determine the rate law and calculate the rate constant for**the following reaction from the following data: S2O82-(aq) + 3I-(aq) 2SO42-(aq) + I3-(aq) rate k = 2.2 x 10-4 M/s = [S2O82-][I-] (0.08 M)(0.034 M) rate = k [S2O82-]x[I-]y y = 1 x = 1 rate = k [S2O82-][I-] Double [I-], rate doubles (experiment 1 & 2) Double [S2O82-], rate doubles (experiment 2 & 3) = 0.08/M•s Chapter 12**N2(g) + 2 H2O(l)**NH4+(aq) + NO2−(aq) Determine the Rate Law and Reaction Order Comparing Experiments 1 and 2, when [NH4+] doubles, the initial rate doubles. Chapter 12**N2(g) + 2 H2O(l)**NH4+(aq) + NO2−(aq) Likewise, comparing Experiments 5 and 6, when [NO2−] doubles, the initial rate doubles. Chapter 12**This means**Rate [NH4+] Rate [NO2−] Rate [NH+] [NO2−] or Rate = k [NH4+] [NO2−] • This equation is called the rate law, and k is the rate constant. Chapter 12**Rate Laws**• The exponents tell the order of the reaction with respect to each reactant. • This reaction is First-order in [NH4+] First-order in [NO2−] Chapter 12**E**x p e ri m e n t [ NO ] [ H ] I n iti a l Ra t e (M/ s ) 2 – 3 – 3 – 5 1 5 . 0 x 1 0 2 . 0 x 1 0 1 . 3 x 1 0 – 3 – 3 – 5 2 1 0 . 0 x 1 0 2 . 0 x 1 0 5 . 0 x 1 0 – 3 – 3 – 5 3 1 0 . 0 x 1 0 4 . 0 x 1 0 1 0 . 0 x 1 0 Rate Law & Reaction Order • The reaction of nitric oxide with hydrogen at 1280°C is: 2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g) • From the following data determine the rate law and rate constant. Second order in NO, First order in H2 k = 1/3(250+250+260) = 250 M-2.s-1 Chapter 12**A product**D[A] - = k [A] Dt First-Order ReactionsConcentration and Time Equation 01 • First Order: Reaction rate depends on the reactant concentration raised to first power. Rate = k[A] Chapter 12**D[A]**- = K Δt rate = [A] M/s M [A] = [A]0exp(-kt) ln = k t [A]0 [A] Concentration and Time Equation For A First-Order Reactions -(ln[A] -ln[A]0) = kt [A] ln[A] = ln[A]0 - kt See next slide for proof of the formula [A] = [A]0exp(-kt) [A] is the concentration of A at any time t [A]0 is the concentration of A at time t = 0 = 1/s or s-1 k = Chapter 12**Integration:**Chapter 12**ln[A] = ln[A]0 - kt**ln = k t [A]0 [A] First-Order Reactions ln[A] = ln[A]0 - kt [A] is the concentration of A at any time t [A]0 is the concentration of A at time t = 0 Chapter 12**0.88 M**ln The reaction 2A B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ? 0.14 M = 2.8 x 10-2 s-1 ln ln = k t k [A]0 [A]0 [A] [A] [A]0 = 0.88 M [A] = 0.14 M t = ? = 66 s t = Chapter 12**[A]0**ln t½ [A]0/2 0.693 = = = k k ln ln2 = k t k [A]0 [A] What is Half- Life ? The half-life, t½, is the time required for the concentration of a reactant to decrease to half of its initial concentration. t½ = t when [A] = [A]0/2 Half Life For the First Order Reaction Chapter 12**Reaction Orders**Zeroth Order Reaction: Rate = K [A]0 = K Units of Rate Constants vs Reaction Orders Chapter 12**What is the order of decomposition of N2O5if it decomposes**with a rate constant of 5.7 x 10-4s-1? What is the half life of decomposition of N2O5 ? = t½ ln2 0.693 = k 5.7 x 10-4 s-1 2N2O5(g) 4NO2(g) + O2(g) units of k (s-1) Therefore, decomposition is first order? = 1200 s = 20 minutes Chapter 12**Half life of a First Order Reaction**Chapter 12**A product**# of half-lives [A] [A] = [A]0 x(1/2)n First-order reaction 1 ½ [A]0 2 1/4 [A]0 3 1/8 [A]0 4 1/16 [A]0 Chapter 12**First-Order Reaction**2N2O5(g) 4NO2(g) + O2(g) • Show that the decomposition of N2O5 is first order and calculate the rate constant and Half life. t1/2 = 408 S k = 1.7 x 10-3 s-1 Chapter 12**A product**rate = [A]2 M/s D[A] 1 1 - M2 = k [A]2 = + kt Dt [A] [A]0 D[A] rate = - Dt Second-Order Reactions rate = k [A]2 What is Unit of k ? = 1/M•s or M-1 s-1 k = What is Conc. Vs time equation? [A] is the concentration of A at any time t [A]0 is the concentration of A at time t = 0 Chapter 12**[A]0**= [A] t1/2 2 Second-Order Reactions So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line, and the slope of that line is k. t = t1/2 Drive the formula for half life of a second order reaction Chapter 12**= kt1/2 +**= kt + 2 1 1 1 t1/2 = [A]0 [A]0 [A]0 [A]t [A]0 1 = [A] t1/2 k[A]0 2 Half-life for a second-order reaction t = t1/2 Chapter 12**t1/2**= 1 k[A]0 Second-Order Reactions For a second-order reaction, the half-life is dependent on the initial concentration. Each successive half-life is twice as long as the preceding one. Chapter 12**Is the following reaction first or second order ?**• What is the value of k? Example: 2 NO2(g) 2NO(g) + O2(g) Chapter 12**k = 0.54 M-1 . S-1**Second-Order Reactions Chapter 12**Zero Order Reaction:**Rate = k Example of Zeroth Order Reaction: Decomposition of N2O on hot platinum surface: N2O → N2 + 1/2 O2 Rate [N2O]0 = k[N2O]0 = k d[N2 O]/dt = k Chapter 12**Reaction Mechanisms 01**• A reaction mechanism is a sequence of molecular events, or reaction steps, that defines the pathway from reactants to products. Chapter 12**Reaction Mechanisms 02**• Single steps in a mechanism are called elementary steps (reactions). • An elementary step describes the behavior of individual molecules. • An overall reaction describes the reaction stoichiometry. Chapter 12**Reaction Mechanisms NO2(g) + CO(g) NO(g) + CO2(g)**• NO2(g) + NO2(g) NO(g) + NO3(g) Elementary • NO3(g) + CO(g) NO2(g) + CO2(g) Elementary • NO2(g) + CO(g) NO(g) + CO2(g) Overall • The chemical equation for an elementary reaction is a description of an individual molecular event that involves the breaking and/or making of chemical bonds. NO3(g) is called reaction intermediate. Chapter 12**Reaction Mechanisms 04**• Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation. • Unimolecular: Single reactant molecule. Chapter 12**Reaction Mechanisms 05**• Bimolecular: Two reactant molecules. • Termolecular: Three reactant molecules. Chapter 12