Chapter 14 Chemical Kinetics

1. Chapter 14Chemical Kinetics

2. 14.1 Factors that Affect Reaction Rates

3. Chemical Kinetics In chemical kinetics we study the rate (or speed) at which a chemical process occurs. Besides information about the speed at which reactions occur, kinetics also sheds light on the reaction mechanism, a molecular-level view of the path from reactants to products.

4. Factors that Affect Reaction Rates • Physical state of the reactants • Reactant concentrations • Reaction temperature • Presence of a catalyst

5. Physical State of the Reactants • The more readily the reactants collide, the more rapidly they react. • Homogeneous reactions are often faster. • Heterogeneous reactions that involve solids are faster if the surface area is increased; i.e., a fine powder reacts faster than a pellet or tablet.

6. Reactant Concentrations • Increasing reactant concentration generally increases reaction rate. • Since there are more molecules, more collisions occur.

7. If a heated steel nail were placed in pure O2, would you expect it to burn as readily as the steel wool does? Yes, the nail and steel wool should have the same composition. Yes, the O2 is the major contributor to the reaction. No, the surface area of the nail is not as great as that of the wool.

8. Temperature • Reaction rate generally increases with increased temperature. • Kinetic energy of molecules is related to temperature. • At higher temperatures, molecules move more quickly, increasing numbers of collisions and the energy the molecules possess during the collisions.

9. Presence of a Catalyst • Catalysts affect rate without being in the overall balanced equation. • Catalysts affect the kinds of collisions, changing the mechanism (individual reactions that are part of the pathway from reactants to products). • Catalysts are critical in many biological reactions.

10. In a reaction involving reactants in the gas state, how does increasing the partial pressures of the gases affect the reaction rate? The effect of increasing the partial pressures of the reactive components of a gaseous mixture depends on which side of the chemical equation has the most gas molecules. Increasing the partial pressures of the reactive components of a gaseous mixture has no effect on the rate of reaction if each reactant pressure is increased by the same amount. Increasing the partial pressures of the reactive components of a gaseous mixture increases the rate of reaction. Increasing the partial pressures of the reactive components of a gaseous mixture decreases the rate of reaction.

11. 14.2 Reaction Rates

12. Reaction Rate • Rate is a change in concentration over a time period: Δ[ ]/Δt. • Δ means “change in.” • [ ] means molar concentration. • t represents time. • Types of rate measured: • average rate • instantaneous rate • initial rate

13. Estimate the number of moles of A in the mixture after 30 s. ~0.6 mol A ~0.4 mol A < 0.4 mol A > 0.3 mol A and < 0.4 mol A

14. Sample Exercise 14.1Calculating an Average Rate of Reaction From the data given in the caption of Figure 14.3, calculate the average rate at whichA disappears over the time interval from 20 s to 40 s.

15. Practice Exercise 1 If the experiment in Figure 14.3 is run for 60 s, 0.16 mol A remain. Which of the following statements is or are true? (i) After 60 s there are 0.84 mol B in the flask. (ii) The decrease in the number of moles of A from t1 = 0 s to t2 = 20 s is greater than that from t1 = 40 to t2 = 60 s. (iii) The average rate for the reaction from t1 = 40 s to t2 = 60 s is 7.0 × 10–3M/s. (a) Only one of the statements is true. (b) Statements (i) and (ii) are true. (c) Statements (i) and (iii) are true. (d) Statements (ii) and (iii) are true. (e) All three statements are true.

16. Practice Exercise 2 Use the data in Figure 14.3 to calculate the average rate of appearance of B over the time interval from 0 s to 40 s.

17. Following Reaction Rates Rate of a reaction is measured using the concentration of a reactant or a product over time. In this example, [C4H9Cl] is followed.

18. Following Reaction Rates The average rate is calculated by the –(change in [C4H9Cl]) ÷ (change in time). The table shows the average rate for a variety of time intervals.

19. Plotting Rate Data • A plot of the data gives more information about rate. • The slope of the curve at one point in time gives the instantaneous rate. • The instantaneous rate at time zero is called the initial rate; this is often the rate of interest to chemists. • This figure shows instantaneous and initial rate of the earlier example. Note: Reactions typically slow down over time!

20. How does the instantaneous rate of reaction change as the reaction proceeds? No change Increases Decreases

21. Sample Exercise 14.2 Using Figure 14.4, calculate the instantaneous rate of disappearance of C4H9Cl at t = 0 (the initial rate).

22. Practice Exercise 2 Using Figure 14.4, determine the instantaneous rate of disappearance of C4H9Cl at t = 300 s.

23. In Figure 14.4, order the rates from fastest to slowest: (i) The average rate of the reaction between 0 s and 600 s, (ii) the instantaneous rate at t= 0 s, and (iii) the instantaneous rate at t = 600 s. You should not have to do any calculations. i > ii > iii iii > ii > i ii > i > iii iii > i > ii

24. Relative Rates • As was said, rates are followed using a reactant or a product. Does this give the same rate for each reactant and product? • Rate is dependent on stoichiometry. • If we followed use of C4H9Cl and compared it to production of C4H9OH, the values would be the same. Note that the change would have opposite signs—one goes down in value, the other goes up.

25. Relative Rates and Stoichiometry What if the equation is not 1:1? What will the relative rates be for: 2 O3 (g) → 3 O2 (g)

26. Sample Exercise 14.3 a) How is the rate at which ozone disappears related to the rate at which oxygen appears in the reaction 2 O3(g) → 3O2(g)? (b) If the rate at which O2 appears, Δ[O2]/Δt, is 6.0 × 10–5M/s at a particular instant, at what rate is O3 disappearing at this same time, –Δ[O3]/Δt?

27. Practice Exercise 1 At a certain time in a reaction, substance A is disappearing at a rate of 4.0 × 10–2M/s, substance B is appearing at a rate of 2.0 × 10–2M/s, and substance C is appearing at a rate of 6.0 × 10–2M/s. Which of the following could be the stoichiometry for the reaction being studied? (a) 2A + B → 3C (b) A → 2B + 3C (c) 2A → B + 3C (d) 4A → 2B + 3C (e) A + 2B → 3C

28. Practice Exercise 2 If the rate of decomposition of N2O5 in the reaction 2 N2O5(g) → 4 NO2(g) + O2(g) at a particular instant is 4.2 × 10–7M/s, what is the rate of appearance of (a) NO2 and (b) O2 at that instant?

29. 14.3 Concentration and Rate laws

30. Determining Concentration Effect on Rate How do we determine what effect the concentration of each reactant has on the rate of the reaction? We keep every concentration constant except for one reactant and see what happens to the rate. Then, we change a different reactant. We do this until we have seen how each reactant has affected the rate.

31. An Example of How Concentration Affects Rate • Experiments 1–3 show how [NH4+] affects rate. • Experiments 4–6 show how [NO2−] affects rate. • Result: The rate law, which shows the relationship between rate and concentration for all reactants: Rate = k [NH4+] [NO2−]

32. More about Rate Law The exponents tell the order of the reaction with respect to each reactant. In our example from the last slide: Rate = k [NH4+] [NO2−] The order with respect to each reactant is 1. (It is first order in NH4+and NO2−.) The reaction is second order (1 + 1 = 2; we just add up all of the reactants’ orders to get the reaction’s order). What is k? It is the rate constant. It is a temperature-dependent quantity.

33. How do reaction rate, rate law, and rate constant differ? • Reaction rate is experimentally measured as a reaction proceeds. • Rate constant is calculated from a rate law. • Rate law relates reaction rate to rate constant and concentrations. • Rate law describes the mechanism of a reaction. • Reaction rate depends on the stoichiometry of the reaction. (1), (2), (4) (2), (4), (4) (2), (3), (5) (1), (2), (3)

34. Does the rate constant have the same units as the rate? Yes, the rate is directly proportional to the rate constant in a rate law. Yes, only if the order of each concentration is one in the rate law. No, as the order of each concentration changes in a rate law, the units of the rate constant change, but those of the rate are always concentration/time. No, as the order of each concentration changes in a rate law, there are changes in the units of both.

35. The experimentally determined rate law for the reaction 2 NO(g)+ 2 H2(g) ⟶ N2(g) + 2 H2O(g) is rate = k[NO]2[H2]. What are the reaction orders in this rate law? 2nd order in NO, 1st order in H2, 2nd order overall 2nd order in NO, 1st order in H2, 3rd order overall 1st order in NO, 1st order in H2, 2nd order overall 1st order in NO, 2nd order in H2, 3rd order overall

36. The experimentally determined rate law for the reaction 2 NO(g) + 2 H2(g) ⟶ N2(g) + 2 H2O(g) is rate = k[NO]2[H2]. Would the reaction rate increase more if we doubled the concentration of NO or the concentration of H2? NO H2 Same effect from doubling NO or H2

37. Sample Exercise 14.4 Consider a reaction A + B → C for which rate = k[A][B]2. Each of the boxes represent a reaction mixture (A is red, B is purple). Rank these mixtures in order of increasing rate of reaction.

38. Practice Exercise 1 Suppose the rate law for the reaction in this Sample Exercise were rate = k[A]2[B]. What would be the ordering of the rates for the three mixtures shown above, from slowest to fastest? (a) 1 < 2 < 3 (b) 1 < 3 < 2 (c) 3 < 2 < 1 (d) 2 < 1 < 3 (e) 3 < 1 < 2

39. Practice exercise 2 Assuming the rate = k[A][B], rank the mixtures in order of increasing rate.

40. Units of Rate Constant • Units of rate = (units of rate constant)(units of concentration)x So, • Units of rate constant = units of rate / (units of concentration)x • Units of kMEMORIZE OR UNDERSTAND • Zero order: M/s • First order: s-1 • Second order: M-1s-1 • Third order: M-2s-1

41. Suppose the reactions A ⟶ B and X ⟶ Y have the same value of k. When [A] = [X], will the two reactions necessarily have the same rate? Yes, the rate constant governs the rate. No, the rate law can be different.

42. Sample Exercise 14.5 (a) What are the overall reaction orders for the reactions described in Equations 14.9 and 14.11? (b) What are the units of the rate constant for the rate law in Equation 14.9? 14.9 2 N2O5→ 4 NO2 + O2 Rate = k[N2O5] 14.11 CHCl3 + Cl2→ CCl4 + HCl Rate = k[CHCl3][Cl2]1/2

43. Practice Exercise 1 Which of the following are the units of the rate constant for Equation 14.11? (a)M –1/2 s–1 (b)M –1/2 s–1/2 (c)M 1/2 s–1 (d)M –3/2 s–1 (e)M –3/2s–1/2 14.11 CHCl3 + Cl2→ CCl4 + HCl Rate = k[CHCl3][Cl2]1/2

44. Practice Exercise 2 (a) What is the reaction order of the reactant H2 in Equation 14.10? (b) What are the units of the rate constant for Equation 14.10? 14.10 H2 + I2→ 2HI Rate = k[H2][I2]

45. Method of Initial Rates • Used to find the form of the rate law • Write the general form of the rate law, then determine order by doing the following. • Choose one reactant to start with • Find two experiments where the concentration of that reactant changes but all other reactants stay the same • Write the rate laws for both experiments • Divide the two rate laws • Use log rules to solve for the order • Follow the same technique for other reactants

46. Example • Choose one reactant to start with NH4+ • Find two experiments where the concentration of that reactant changes but all other reactants stay the same Exp 2 & 3

47. Example • BrO3- : Exp 1 & 2 Exp 1: Rate = 8.0x10-4 = k(0.10)x(0.10)y(0.10)z Exp 2: Rate = 1.6x10-3 = k(0.20)x(0.10)y(0.10)z 0.50 = 0.50x x = 1

48. Example • Br- : Exp 2 & 3 Exp 2: Rate = 1.6x10-3 = k(0.20)1(0.10)y(0.10)z Exp 3: Rate = 3.2x10-3 = k(0.20)1(0.20)y(0.10)z 0.50 = 0.50y y = 1

49. Example • H+ : Exp 1 & 4 Exp 1: Rate = 8.0x10-4 = k(0.10)1(0.10)1(0.10)z Exp 4: Rate = 3.2x10-3 = k(0.10)1(0.10)1(0.20)z 0.25 = 0.50z OR ¼ = (½)z z = 2

50. Example • So Rate = k[BrO3-]1[Br-]1[H+]2 • Overall order of reaction = 4 • Solve for rate constant, k