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Chemical Kinetics

Chemical Kinetics. Chapter 14. Introduction: Chemical Kinetics. Chemical Kinetics is the study of how fast chemical reactions occur. There are 3 important factors which affect rates of reactions: reactant concentration, temperature, catalysts

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Chemical Kinetics

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  1. Chemical Kinetics Chapter 14

  2. Introduction: Chemical Kinetics • Chemical Kinetics is the study of how fast chemical reactions occur. • There are 3 important factors which affect rates of reactions: • reactant concentration, • temperature, • catalysts • Goal: to understand how the rates of chemical reactions are determined.

  3. 1. Reaction Rates

  4. 2.Reaction Rates For reaction A  B A reaction from  t = 0 to  t = 60 min. Note that the rate between  t = 0 and  t = 5 min is greater than the rate between  t = 45 min and  t = 50 min.

  5. 1. Reaction Rates Define the average rate of reaction as the change in moles of B (or A) per unit time. For the time interval between 0 and 20 minutes, the average rate is: Or, equivalently:

  6. 1. Reaction Rates Table 14.1 gives the average rate for each ten-second interval for the reaction A  B.

  7. 1. Reaction Rates The rate of appearance of B is equal to the rate of disappearance of A because they have a one-to-one stoichiometric relationship. In general for aA + bB cC + dD Reaction rates are expressed in concentration per second: M/s (Ms–1),

  8. 1. Reaction Rates Consider the reaction C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) Using concentrations only

  9. 1. Reaction Rates We start with a 0.1000 M aqueous solution of C4H9Cl and monitor the concentration as the reaction proceeds over the time.

  10. 1. Reaction Rates The instantaneous rate of a reaction at a particular time is usually useful. The instantaneous rate is equal to the slope of the tangent to the curve at any given time.

  11. 2. The Dependence on Concentration Most chemical reactions slow down as they progress.To study the effect, we vary the concentrations of reactants and measure the initial rates. For the reaction: NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)

  12. 2. The Dependence on Concentration The data indicate that the rate of this reaction appears to be proportional to each of the concentrations. If it is proportional to each reactant's concentration, then it is proportional to the product of their concentrations. The constant k is the rate constant. The equation relating rate to reactant concentrations is called the rate law.

  13. 2. The Dependence on Concentration Using any of the experiments listed in the table 14.3, we can determine the value of the rate constant. Using the data from experiment 2, we have

  14. 2. The Dependence on Concentration • In general, reactions have the rate law: • The exponents  m and  n must be determined experimentally. • The reaction order with respect to a reactant = the exponent to the reactant's concentration, m or n. • The overall reaction order is the sum of the exponents in the rate law, m+n.

  15. 2. The Dependence on Concentration For the reaction: NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l) Since We say that the reaction is  first order in ammonium ion and first order in nitrite ion, the second order overall in the ammonium and nitrite reaction.

  16. 2. The Dependence on Concentration Units of thereaction rate constant depend on the overall order of the reaction because the reaction rate must be in units of Ms–1.

  17. 2. The Dependence on Concentration The rate law for a reaction can be determined using the method of initial rates. Suppose for the reaction A + B → C, the following data were collected.

  18. 3. The Change of Concentration with Time Two different ways to express the rate of the reaction A → B when the reaction is a first-order process. We can set these two different expressions equal to each other. We have: This relates the concentration of A at any time to the concentration of A at the start of the reaction.

  19. 3. The Change of Concentration with Time First-Order Reactions: the logarithm of concentration decrease linearly.

  20. 3. The Change of Concentration with Time Half-life • Half-life is the time taken for the concentration of a reactant to drop to half its original value. • That is, half life, t1/2 is the time taken for [A]0 to reach ½[A]0. • Mathematically,

  21. 3. The Change of Concentration with Time A second-order reaction has the rate law: rate = k[A]2 or rate = k[A][B]. For the rate = k[A]2 case,

  22. 3. The Change of Concentration with Time The plot using ln[A] is not linear, 1/[A] is linear. => Second Order

  23. Rate laws are empirical - measured from experimental data - It can be zero order

  24. Can be related to products, can be in fractional order

  25. 4. Temperature and Rate Most reactions speed up as temperature increases. (E.g. food spoils when not refrigerated.)

  26. By measuring rate constants Arrhenius found: The Arrhenius equation: • k is the rate constant, Eais the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K. • A is called the frequency factor. • Both A and Ea are specific to a given reaction.

  27. The Collision Theory • In order for molecules to react they must collide. • The greater the number of collisions the faster the rate. • More collisions will occur at higher reactant concentrations. • The higher temperature, the more collisions there will be per unit time • Higher temperature also contributes to more forceful collisions because molecules are moving faster.

  28. The Collision Theory • Activation Energy • Activation energy is the minimum energy required to initiate a chemical reaction. • The colliding molecules must have a total kinetic energy equal to or greater than the activation energy

  29. The Collision Theory EffectiveCollision • Only a very small percentage of the collisions result in a reaction. • In order for a collision to result in a reaction, it must be an effectivecollision. The molecules must be moving fast enough and oriented properly so that a reaction can occur.

  30. The Collision Theory Quantitatively, for gas, elementary reaction A+B

  31. The Collision Theory Considering steric effect

  32. The Transition State Theory • More general, applicable to solutions and any condensed phases • Molecules move randomly, at instance, two may meet each other, due to interactions with all surrounding molecules • Some meet do not react, some do.

  33. The Transition State Theory • There is an activated complex – the transition state • In transition state, original bond are lengthened, new bonds are partially formed. • The activation energy is measured as the energy difference between transition state and reactants. • Only molecules with sufficient kinetic energy can roll over the energy barrier.

  34. The Transition State Theory Potential Energy Surface Energy as function of atom positions The landscape indicate how elementary reaction occurs For example, in radical reaction:

  35. 4. Temperature and Rate Activation Energy The difference between the energy of the original molecule and the highest point in the reaction pathway is called the activation energy. At the point of greatest energy, the species present is called the transition state. It is also referred to as an activated complex.

  36. 5. Reaction Mechanisms 2NO(g) + Br2(g)  2NOBr(g) Rate = k[NO]2[Br2] • Exactly how a reaction occurs? • Some reactions occur in a single (elementary) step. • Most chemical reactions take place in a series of elementary steps.

  37. 5. Reaction Mechanisms • Elementary Steps • Elementary step: any process that occurs in a single step. • Molecularity: the number of molecules present in an elementary step. • Unimolecular: one molecule in the elementary step, • Bimolecular: two molecules in the elementary step, and • Termolecular: three molecules in the elementary step. • It is not common to see termolecular processes (statistically improbable).

  38. 5. Reaction Mechanisms • Rate Laws of Elementary Steps • The rate law of an elementary step is determined by its molecularity: • Q: What is the rate law for the elementary process • 2A + B → C? • rate = k [A][B]   rate = k [A]2  rate = k [A]2[B]   rate = k [A]

  39. 5. Reaction Mechanisms • Reaction Mechanism • For any multi-step process, there is one step that limits the overall rate of the process because it is so much slower than the others. We call this the rate-determining step. • Intermediate - a species that is first generated in one of the steps and then consumed in another. • Catalyst - a species is first consumed in one of the steps, and then regenerated by another.

  40. 5. Reaction Mechanisms Q: What is the intermediate in the reaction mechanism below? And catalyst?  (step 1) A + E → C + D(step 2) B + C → E + F C

  41. 5. Reaction Mechanisms In order for a reaction mechanism to be plausible, it must meet two criteria. • The steps must add to give the equation of interest. • The rate law predicted by the mechanism must be the same as the experimentally determined. Note that because a reaction mechanism meets these two criteria does not mean that it is the correct mechanism. It simply means that it is possibly correct.

  42. 5. Reaction Mechanisms Q: Which mechanism is plausible for the reaction A + 2B  C + 2D, which has an experimentally determined rate law of: rate = k [A][B]?   A (step 1) A + B C + D     (slow)         (step 2) C + B D            (fast)   B (step 1) A + B  D + E     (slow)         (step 2) E + B  C + D     (fast)   C (step 1) A + 2B  E + F    (slow)        (step 2) E + F  B + D      (fast)        (step 3) D   2C                 (fast)   D (step 1) B + B  C + E      (slow)         (step 2) E + A  D            (fast) B

  43. 5. Reaction Mechanisms Example: 2N2O(g)  2N2(g) +O2 (g) A plausible mechanism

  44. 5. Reaction Mechanisms Example: The experimentally determined rate law for: 2NO(g) + Br2(g)  2NOBr(g) is: Rate = k[NO]2[Br2] Because termolecular process is very unlikely. We propose another reaction mechanism. 1. Consider the following mechanism

  45. Reaction Mechanisms 2. Based on step two the rate law is: Rate = k2[NOBr2][NO] 3. NOBr2 is an intermediate. Its concentration is unknown. Because it is fast reaction in both directions, we assume the rates on both directions are the same (reach equilibrium): k-1[NOBr2] = k1[NO][Br2] Then: [NOBr2] = k1[NO][Br2] /k-1

  46. 5. Reaction Mechanisms Therefore, the overall rate law becomes It is consistent with the experimentally observed rate law.

  47. 6. Catalysis • A catalyst changes the rate of a chemical reaction. • Types of catalyst: • Homogeneous • Heterogeneous • Enzymes

  48. 6. Catalysis • Homogeneous Catalysis • The catalyst and reaction is in one phase. • Hydrogen peroxide decomposes very slowly: • 2H2O2(aq)  2H2O(l) + O2(g). • In the presence of the bromide ion, the decomposition occurs rapidly: • 2Br-(aq) + H2O2(aq) + 2H+(aq)  Br2(aq) + 2H2O(l). • Br2(aq) + H2O2(aq)  2Br-(aq) + 2H+(aq) + O2(g). • Br-is a catalyst because it can be recovered at the end of the reaction.

  49. 6. Catalysis A catalyst speeds up a reaction by lowering the activation energy. It does this by providing a different mechanism by which the reaction can occur.

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