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Chapter 14 Kinetics

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  1. Chapter 10 provided an introduction to kinetics and equilibrium. In this chapter we expand the quantitative treatment of chemical kinetics. Chapter 14Kinetics

  2. The Forces That Control a Chemical Reaction • A large negative value of ΔG° for a reaction means that the products are thermodynamically favored over the reactants. • It does not mean the reactants will convert to products.

  3. The Forces That Control a Chemical Reaction • Why would the reactants not convert to products if the products are more stable?

  4. The Forces That Control a Chemical Reaction • Why would the reactants not convert to products if the products are more stable? • The rate of conversion may be too slow to observe. • Calculating and measuring this rate is part of the field of chemical kinetics.

  5. Chemical Kinetics • What is the rate of a reaction? • What factors influence the rate? • What is the mechanism of the reaction?

  6. Chemical Kinetics • Sucrose(aq) + H3O+(aq) → glucose(aq) + fructose(aq) • Rate = k[sucrose] • As reaction proceeds, the rate decreases.

  7. Is the Rate of Reaction Constant? • In excess base, phenolphthalein turns pink. Over time the pink color disappears. • A solution is prepared which is initially 0.00500 M in phenolphthalein and 0.61 M in OH-(aq). • The slow decrease in phenolphthalein concentration is shown in the next three slides.

  8. Is the Rate of Reaction Constant? Table 14.1

  9. Is the Rate of Reaction Constant? Figure 14.2

  10. Instantaneous Rates of Reaction Figure 14.3

  11. Instantaneous Rates of Reaction • Instantaneous rate of reaction: • Rate = - dX/dt • Minus sign used for reactants so that rate > 0 • Initial instantaneous rate of reaction is measured at the moment of mixing

  12. Rate Laws and Rate Constants • In the phenolphthalein case, the rate is proportional to the current phenolphthalein concentration. • Rate = k[phenolphthalein] • k, the constant of proportionality, is called the rate constant. • The equation is called the rate law.

  13. The Rate Law Versus the Stoichiometry of a Reaction • The rate law for a reaction can’t be predicted from the stoichiometry of the reaction; it must be determined experimentally.

  14. The Rate Law Versus the Stoichiometry of a Reaction • CH3Br + OH-→ CH3OH + Br- • Rate = k[CH3Br][OH-] • (CH3)3CBr + OH-→ (CH3)3COH + Br- • Rate = k’[(CH3)3CBr ]

  15. The Rate Law Versus the Stoichiometry of a Reaction • The expression for the rate will depend on the stoichiometric coefficients and whether reactants or products are being considered. • For this reaction 2N2O5→ 4NO2 + O2 several equivalent expressions can be written.

  16. The Rate Law Versus the Stoichiometry of a Reaction 2N2O5→ 4NO2 + O2

  17. Order and Molecularity • Molecularity • Unimolecular: single molecule consumed • Bimolecular: two molecules consumed

  18. Order and Molecularity • ClNO2 + NO → ClNO + NO2 • Bimolecular • N2O5⇄ NO2 + NO3 • Forward reaction is unimolecular • Reverse reaction is bimolecular

  19. Order and Molecularity • Reactions are also classified by their order. • ClNO2 + NO → ClNO + NO2 • Rate = k[ClNO2][NO] • Overall second order reaction. First order in each reactant • N2O5⇄ NO2 + NO3 • Rate = k[N2O5] • First order reaction

  20. Order and Molecularity • Zero order? • Yes, reactions occurring on metal surfaces can be zero-order: Rate = k[N2O]0 = k’

  21. Order and Molecularity • Molecularity describes what happens at the molecular level. • The order of a reaction describes what happens at the macroscopic level. • We deduce the molecularity from the experimentally determined rate law.

  22. A Collision Theory of Chemical Reactions • Chemical reactions occur as a result of collisions between molecules. • The rate of a reaction depends on the frequency of the collisions. • Consider again ClNO2 + NO → ClNO + NO2

  23. A Collision Theory of Chemical Reactions Figure 14.4

  24. A Collision Theory of Chemical Reactions • If this picture is accurate, then the rate of the reaction should depend on the concentration of each reactant. • This is observed experimentally.

  25. A Collision Theory of Chemical Reactions • Now consider again (CH3)3CBr + OH-→ (CH3)3COH + Br- • Experimentally, the rate is determined to depend only on the (CH3)3CBr concentration. • No collisions?

  26. A Collision Theory of Chemical Reactions • A multistep reaction is proposed to account for the experimental observations. 1. (CH3)3CBr → (CH3)3C+ + Br- 2. (CH3)3C+ + H2O → (CH3)3COH2+ 3. (CH3)3COH2+ + OH- → (CH3)3COH + H2O • The first step is slowest and is the rate-limiting step. • The steps are the mechanism.

  27. The Mechanisms of Chemical Reactions • Main goal of chemical kinetics: determine a chemical reaction mechanism. • Proposed mechanisms lead to predicted rate laws. • These predicted laws are compared to the experimentally determined law. • Some mechanisms can be eliminated as possibilities.

  28. The Mechanisms of Chemical Reactions • Mechanisms often propose intermediates. • In this mechanism 1. (CH3)3CBr → (CH3)3C+ + Br- 2. (CH3)3C+ + H2O → (CH3)3COH2+ 3. (CH3)3COH2+ + OH- → (CH3)3COH + H2O (CH3)3C+ and (CH3)3COH2+ are proposed intermediates.

  29. The Mechanisms of Chemical Reactions • What intermediate is proposed in this mechanism? • What is the predicted rate law for this mechanism? The observed rate law is rate=k[NO]2[O2]. 2NO ⇄ N2O2 (fast) N2O2 + O2→ 2NO2 (slow)

  30. The Mechanisms of Chemical Reactions • Does the agreement of the predicted and experimental rate laws prove the mechanism is correct?

  31. The Mechanisms of Chemical Reactions • Does the agreement of the predicted and experimental rate laws prove the mechanism is correct? No, only that the mechanism is consistent with the observed rate law.

  32. Zero-Order Reactions • Zero-order behavior for a reactant implies a multi-step mechanism. • What about zero-order in all reactants?

  33. Zero-Order Reactions • Rate = k • Rate is zero order in all reactants as long as there is excess NO. • Rate is determined by the availability of sites on the Pt surface.

  34. Determining the Order of a Reaction From Rates of Reaction • Consider the decomposition of HI 2HI → H2 + I2 • Record the initial instantaneous rate of reaction for a series of initial concentrations. • From such a data set, the order of individual reactants can be determined.

  35. Determining the Order of a Reaction From Rates of Reaction Table 14.2 2HI → H2 + I2

  36. The Integrated Form of Zero-, First-, and Second-Order Rate Laws • Zero-Order • Rate = -d(X)/dt = k is the differential rate law. It contains a derivative. • The integrated rate law is found by integrating the differential rate law. • X(t) –X(0) = kt is the integrated rate law for a zero-order reaction.

  37. The Integrated Form of Zero-, First-, and Second-Order Rate Laws • First-order • -d(X)/dt = k(X) • Integrated form is ln(X(t)) – ln(X(0)) = -kt

  38. The Integrated Form of Zero-, First-, and Second-Order Rate Laws • Second-order in one reagent • -d(X)/dt = k(X)2 • Integrated form is 1/X(t) – 1/X(0) = kt

  39. The Integrated Form of Zero-, First-, and Second-Order Rate Laws • Consider radioactive decay (more in next chapter) • It is a first-order process. • Rate=k(amount of radioactive material) • After a period of time, t1/2, only half of the radioactive material remains. • This time, t1/2, is called the half-life of the radioactive material.

  40. The Integrated Form of Zero-, First-, and Second-Order Rate Laws • Using the integrated rate law, the half-life for a first order reaction can be expressed as

  41. The Integrated Form of Zero-, First-, and Second-Order Rate Laws • Each radioactive isotope has a characteristic half-life. • The half-life for 14C is 5730 years.

  42. The Integrated Form of Zero-, First-, and Second-Order Rate Laws Table 14.3

  43. Determining the Order of a Reaction with the Integrated Form of Rate Laws • The order of a reaction can be determined by finding the functional form of concentration vs. time. • For zero-order, X(t) = -kt + X(0) • For first-order, ln(X(t)) = -kt + ln(X(0)) • For second-order, 1/X(t) = kt + 1/X(0)

  44. Determining the Order of a Reaction with the Integrated Form of Rate Laws Figure 14.7

  45. Determining the Order of a Reaction with the Integrated Form of Rate Laws Figure 14.8

  46. Determining the Order of a Reaction with the Integrated Form of Rate Laws Figure 14.9

  47. Reactions That Are First-Order in Two Reactants • We have already seen ClNO2 + NO → ClNO + NO2 with rate = k[ClNO2][NO]. • None of these are appropriate: X(t) = -kt + X(0) ln(X(t)) = -kt + ln(X(0)) 1/X(t) = kt + 1/X(0).

  48. Reactions That Are First-Order in Two Reactants • Make the reaction into a pseudo-first-order reaction. • If [ClNO2] >>[NO], [ClNO2] will not change much during the reaction: it will be essentially constant. • Now, rate = k’[NO], where k’=k[ClNO2]. • A pseudo-first-order reaction • ln[NO(t)] = -k’t + ln[NO(0)]

  49. The Activation Energy of Chemical Reactions • Not every molecular collision results in the conversion of reactants to products. • The molecules must collide with the proper orientation and with enough kinetic energy to overcome the activation energy, Ea.

  50. The Activation Energy of Chemical Reactions Figure 14.15