1. Case two for second-order would occur for a reaction involving two reactants: A + B P 241

2. Case two for second-order would occur for a reaction involving two reactants: A + B P 242

3. Case two for second-order would occur for a reaction involving two reactants: A + B P The integrated rate law becomes 243

4. Case two for second-order would occur for a reaction involving two reactants: A + B P The integrated rate law becomes For this more complicated case it is necessary to keep track of two different concentrations. 244

5. Half-Lives 245

6. Half-Lives Half-life: The time required for the concentration of a reactant to decrease to half of its initial concentration. 246

7. Half-Lives Half-life: The time required for the concentration of a reactant to decrease to half of its initial concentration. Zero-order reaction: put in the expression leads to the result: 247

8. First-order reaction: put in the expression 248

9. First-order reaction: put in the expression leads to the result: 249

10. Decomposition of N 2 O 5 (first-order kinetics). 250

11. Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. 251

12. Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. A common example of the use of the half-life concept is the decay of radioactive isotopes. 252

13. Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. A common example of the use of the half-life concept is the decay of radioactive isotopes. Example: 253

14. Measuring the half-life of a reaction is one way to determine the rate constant of a first-order reaction. A common example of the use of the half-life concept is the decay of radioactive isotopes. Example: This is a beta-decay where denotes an electron. 131 is the mass number = number of protons + number of neutrons; 53 is the atomic number. 254

15. 255 Radioisotope usage to image the thyroid gland. The thyroid gland absorbs ions, which undergo beta decay that exposes a photographic film.

16. 256

17. 257

18. Theory of Chemical Reaction Rates 258

19. Theory of Chemical Reaction Rates The effect of temperature 259

20. Theory of Chemical Reaction Rates The effect of temperature The Arrhenius Equation 260

21. Theory of Chemical Reaction Rates The effect of temperature The Arrhenius Equation Nearly all reactions proceed faster at higher temperatures. 261

22. Theory of Chemical Reaction Rates The effect of temperature The Arrhenius Equation Nearly all reactions proceed faster at higher temperatures. As a rough rule – the reaction rate doubles when the temperature is increased by 10 o C. 262

23. How do reactions get started? 263

24. How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. 264

25. How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. According to the collision theory of chemical kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions. 265

26. How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. According to the collision theory of chemical kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions. 266

27. How do reactions get started? Many chemical reactions get started as a result of collisions among reacting molecules. According to the collision theory of chemical kinetics, we would expect the rate of reaction to be directly proportional to the frequency or rate of molecular collisions. This relation explains the dependence of rate on concentration. 267

28. The preceding proportionality is oversimplified in one important respect. 268

29. The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules. 269

30. The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules. Any molecule in motion possesses kinetic energy. When molecules collide, part of their kinetic energy is converted to vibrational energy. 270

31. The preceding proportionality is oversimplified in one important respect. A chemical reaction does not occur simply on encounter of two reactant molecules. Any molecule in motion possesses kinetic energy. When molecules collide, part of their kinetic energy is converted to vibrational energy. If the kinetic energies are large, then the molecules will vibrate so strongly that some chemical bonds will break – which is the first step towards the formation of products. 271

32. If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen. 272

33. If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen. In order to react, the colliding molecules must have a certain minimum kinetic energy – called the activation energy E a. 273

34. If the kinetic energies are small, the molecules will merely bounce off each other and nothing will happen. In order to react, the colliding molecules must have a certain minimum kinetic energy – called the activation energy E a. Activation energy: The minimum energy with which molecules must collide to react. 274

35. 275 NO + O 3 NO 2 + O 2

36. 276 NO + O 3 NO 2 + O 2

37. We can think of the activation energy as the barrier that prevents less energetic molecules from reacting. 277

38. We can think of the activation energy as the barrier that prevents less energetic molecules from reacting. In a normal reaction in the gas phase, there is a tremendous spread in the kinetic energies of the molecules. 278

39. We can think of the activation energy as the barrier that prevents less energetic molecules from reacting. In a normal reaction in the gas phase, there is a tremendous spread in the kinetic energies of the molecules. Normally, only a small fraction of these molecules – the very fast moving ones – can take part in a reaction. 279

40. 280 The speeds of the molecules follow the Maxwell-Boltzmann distribution. Maxwell-Boltzmann distribution.

41. Energy level diagram for a chemical reaction. 281

42. Energy level diagram for a chemical reaction showing fraction of gas phase molecules that have the required energy to reach products. 282

43. Since a higher temperature gives rise to a greater number of energetic molecules – the rate of product formation is greater. 283

44. Arrhenius Equation 284

45. Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as 285

46. Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant 286

47. Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy 287

48. Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy R is the gas constant (8.314 JK -1 mol -1 ) 288

49. Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy R is the gas constant (8.314 JK -1 mol -1 ) T is the temperature (Kelvin scale) 289

50. Arrhenius Equation Arrhenius showed that the rate constant of a reaction can be written as where k is the rate constant E a is the activation energy R is the gas constant (8.314 JK -1 mol -1 ) T is the temperature (Kelvin scale) A is related to the collision frequency and is called the frequency factor (pre-exponent factor) 290

51. A second form of the Arrhenius equation, which is useful for the determination of E a, is obtained by taking the natural log of both sides of the Arrhenius equation. 291

52. Math Aside: Review of log properties. 292

53. Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 293

54. Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 294

55. Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 295

56. Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 296

57. Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 297

58. Math Aside: Review of log properties. Some useful properties of logs that occur frequently. 298

59. From the Arrhenius equation we have: 299

60. From the Arrhenius equation we have: 300