Chemical Kinetics

1. Chemical Kinetics Chapter 14 AP Chemistry

2. Chemical Kinetics • Kinetics – the area of chemistry concerned with the rate (or speed) of a reaction. • Kinetics vs. Thermodynamics • Applications: Medicine, Chemical Engineering

3. Reaction Rate Factors • Physical state of reactants • Surface area • Concentration • Rate increases with concentration increase • Temperature • Rate doubles every 10oC increase • Catalyst • Increase the reaction rate w/o being used up

4. Reaction Rates • Speed is the change in a particular quantity with respect to a change in time. • In chemistry, we define the reaction rate • The change in concentration of the reactants or products over time • Units are usually M/sec • Rate =

5. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)

6. C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) • A graph of concentration vs. time is often plotted. • Slope of the tangent line at any point along the curve is the instantaneous rate. • Rate decreases with time. • Reactants decrease with time

7. Average Rate • Because the rate of reaction changes with time, it is useful to consider an average rate. • Rate = • The average rate for a reaction is usually take as the early stages of a reaction.

8. Measuring Rates • To determine the progress of a reaction, we can measure two quantities: • Disappearance of the reactant • Formation of products • Reaction rate is a positive value. • Reaction rate is the same, no matter the method of measurement.

9. aA + bB cC + dD • The rate of reaction is given by the following equalities: • A: Rate = • B: Rate = • C: Rate = • D: Rate = • Rate =

10. H2O2(g)  H2(g) + O2(g) • Write the rate in terms of each species.

11. SO2(g) + O2(g)  SO3(g) • Write the rate in terms of each species.

12. H2(g) + O2(g)  H2O(g) • Hydrogen is burning at the rate of 0.85 M/sec. Rate of oxygen consumption? Rate of water vapor formation?

13. How? • How is it possible to measure the concentration of reactants or products? • There are a variety of methods. • One of the more common methods is spectroscopy. • Measures the ability to absorb/transmit light and converts the data to a concentration.

14. Spectrophotometer (Spec-20)

15. Beer-Lambert Law • There is a linear relationship between the concentration of a sample and its absorbance. • A = -logT • Beer’s Law: A = εbC • Standards to find slope • Convert T to A to C

16. NH3(g)  N2(g) + H2(g) • Nitrogen is forming at the rate of 0.264 M/sec. Rate of ammonia consumption? Rate of hydrogen formation?

17. Rate Law • General Equation: aA + bB cC + dD • Rate = • m is the order of A • n is the order of B • (m+n) is the overall reaction order • k is the rate constant • specific for a rxn, Temperature dependent

18. Rate = k[A]m[B]n • The rate law must be experimentally determined. • m and n are NOT the stoichiometric coefficient • Unit of rate constant k • M-p s-1 or 1/(Mp s) • p = (m+n) – 1 • Rate depends on reactant conc…k does not depend on reactant conc.

19. Rate = k[A][B] • What happens to the rate if we… • Double conc of A (everything else the same)? • Double conc of B (everything else the same)? • Triple conc of A and double conc of B? • Order of A? B? Overall?

20. Rate = k[A]2[B] • What happens to the rate if we… • Double conc of A (everything else the same)? • Double conc of B (everything else the same)? • Triple conc of A and double conc of B? • Order of A? B? Overall?

21. Rate = k[A]0[B]3 • What happens to the rate if we… • Double conc of A (everything else the same)? • Double conc of B (everything else the same)? • Triple conc of A and double conc of B? • Order of A? B? Overall?

22. Rate = k[A]m[B]n • Two ways to determine the rate law • Initial rate method • Can have many reactants • Graphical Method • Can only have one reactant • Solving a rate Law: • Need to determine the orders of the reactants • Need to determine the rate constant k

23. Determinethe rate law:

24. Determinethe rate law:

25. Determinethe rate law:

26. Change in Conc. with time • So far, we have considered rate based on the change in concentration and rate constants. • Using calculus, we can convert these same equations to more useful forms. • This is the graphing method to determining the order of a reaction. • Specific for only one reactant: [A]

27. Rate Laws • Differential Rate Law: • Expressed how rate depends on concentration. • Integrated Rate Law • Integrated form of the differential. Has specific variables.

28. Zero Order Reaction • Rate only depends on the rate constant…not on the concentration of A • Differential: • Integrated:

29. First Order Reaction • Rate only depends on the rate constant and on the concentration of A • Differential: • Integrated:

30. First Order Plot of [A] vs. t Plot of ln[A] vs. t

31. Second Order Reaction • Rate only depends on the rate constant and on the square concentration of A • Differential: • Integrated:

32. Second Order Plot of ln[A] vs. t Plot of 1/[A] vs. t

33. Usefulness of the Integrated Rate Laws [A]t = -kt + [A]0 • We can know the concentration at any time point for a given reaction. • We can determine the order of a reaction. • We can determine the half life of a reaction.

34. Determining the Order [A]t = -kt + [A]0 • This tells us that a plot of concentration of A vs time will yield a straight line. • Because this is the zero order rate equation, a plot of [A] vs. t will yield a straight line. y = mx + b

35. Determining the Order • First Order: ln[A]t = -kt + ln[A]0 • A plot of ln[A] vs. t will give a straight line. • Second Order: • A plot of 1/[A] vs. t will give a striaght line.

36. Half life, t1/2 • The time required for the concentration of a reactant to reach one-half its value: • [A]t1/2 = ½[A]0 • This is a convenient way to describe the rate of a reaction. • A fast reaction will have a short half life.

37. Derivation: t1/2 of First Order ln[A]t = -kt + ln[A]0

38. Summary ** Note: The half life of a first order says that it does NOT depend the concentration of the reactant A. So, the concentration decreases by ½ each regular time interval, t1/2.

39. A first order reaction has k = 6.7 x 10-4 s-1. • How long will it take for the conc to go from 0.25M to 0.15M? • If the initial conc is 0.25M, what is the conc after 8.8 min?

40. A first order reaction has [A] = 2.00M initially. After 126 min, [A] = 0.0250M. • What is the rate constant k? • What is the half life?

41. A second order reaction has k = 7.0 x 10-9 M-1s-1. • If the initial conc is 0.086M, what is the conc after 2.0 min?

42. A first order reaction has t1/2 = 35.0 sec. • What is the rate constant k? • How long would it take for 95% decomposition of the reactant?

43. A first order reaction has a half life of 19.8 min. What is the reaction rate when [A] = 0.750M?

44. Temperature

45. Collision Model • Based on Kinetic Molecular Theory • Molecules must collide to react • Greater the collisions, greater the rate • As concentration increases, rate increases • As temperature increases, rate increases

46. Orientation • Most collisions do not lead to reactions • Molecular orientation of collision is important

47. Still not enough • Usually, a collision in the correct orientation is still not enough to cause a reaction. • Kinetic energy of a collision must cause bonds to break. • For a reaction to occur, there must be enough kinetic energy to be greater than some energy. • Activation Energy, Ea, is the minimum energy required to initiate a reaction.

48. Activation Energy

49. Transition State • Transition state is also called the activated complex • High energy intermediate state • The activation energy represents the higher energy state of the transition state ‡ A A B B A A + B B A B + A B