1. 1 Chemical Kinetics Chapter 13

2. 2 Chemical Kinetics Kinetics is the study of how fast chemical reactions occur and how they occur. There are 4 important factors which affect rates of reactions: –reactant concentration –temperature –catalyst –surface area Goal: to understand chemical reactions at the molecular level.

3. 3 Reaction Rates Speed of a reaction (rxn) is measured by the change in concentration with time. For a rxn A → B Suppose A reacts to form B. Let us begin with 1.00 mol A (and no B).

4. 4 Reaction Rates –At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present. –At t = 20 min, there is 0.54 mol A and 0.46 mol B. –At t = 40 min, there is 0.30 mol A and 0.70 mol B. –Eventually, there will be no more A left, and only B will be present.

5. 5 Reaction Rates

6. 6

7. 7 We can use this data to find the average rate:

8. 8 Chemical Kinetics Reaction Rates For the rxn A →B there are two ways of measuring rate: –the speed at which the products appear (i.e. change in moles of B per unit time), or –the speed at which the reactants disappear (i.e. the change in moles of A per unit time). –Note the minus sign! This reminds us that the rate is being expressed as the disappearance of a reactant.

9. 9 Rates in Terms of Concentrations Most of the time, we will determine the rate of a rxn by monitoring a change in concentration of a reactant or product. Molarity is the most useful unit for rxn rates although pressure is used for gases. Since volume is usually constant, molarity (or pressure) and moles are directly proportional.

10. 10 Rates in Terms of Concentrations Consider: C 4 H 9 Cl(aq) + H 2 O(l) →C 4 H 9 OH(aq) + HCl(aq) We can calculate the average rate in terms of the disappearance of C 4 H 9 Cl. The units for average rate are mol/Ls or M/s. The average rate decreases with time as C 4 H 9 Cl disappears.

11. 11 Rates in Terms of Concentrations C 4 H 9 Cl(aq) + H 2 O(l) → C 4 H 9 OH(aq) + HCl(aq)

12. 12 Rates in Terms of Concentrations We now plot [C 4 H 9 Cl] versus time. The rate at any instant in time is called the instantaneous rate. The instantaneous rate is the slope of the straight line tangent to the curve at that instant. Instantaneous rate is different from average rate. Note: The instantaneous rate is usually just called the rate, unless otherwise specified.

13. 13 Rates in Terms of Concentrations

14. 14 Reaction Rates and Stoichiometry For the rxn C 4 H 9 Cl(aq) + H 2 O(l) → C 4 H 9 OH(aq) + HCl(aq) we know What if the stoichiometric relationships aren’t 1:1? 2HI(g) → H 2 (g) + I 2 (g) The HI:H 2 ratio and the HI:I 2 ratio are both 2:1!

15. 15 Reaction Rates and Stoichiometry 2HI(g) →H 2 (g) + I 2 (g) It should be clear that as HI is consumed (or disappears), only half as much H 2 (and I 2 ) is produced or appears. So the rate of disappearance of HI is twice the rate of appearance of H 2 (and I 2 ). rate HI = 2rate H2 OR rate H2 = 0.5rate HI

16. 16 Reaction Rates and Stoichiometry We now have 2 different rates for the same rxn. These rates are related by the balanced equation stoichiometry. We commonly talk in terms of the rxn rate, or the rate of the rxn, not just in terms of the rate of appearance of a product or the rate of disappearance of a product.

17. 17 Reaction Rates and Stoichiometry The rxn rate, or called just the rate, may be expressed as: Or we can write it more generally as: rate rxn = rate H2 = rate I2 = 0.5rate HI

18. 18 Reaction Rates and Stoichiometry In general for the rxn: aA + bB → cC + dD The overall rxn rate may be expressed as: Or in nonmathematical terms:

19. 19 Reaction Rates and Stoichiometry Be careful! Experiments are conducted in terms of the rates of appearance/disappearance of a product/reactant. These rates may then be converted to rxn rates using the balanced equation. Read problems carefully so you know what you are given! If it is not specified, it is by default a rxn rate.

20. 20 The Dependence of Rate on Concentration In general, rates: –Increase when reactant [ ] are increased. –Decrease when product [ ] are increased. We often examine the effects of concentration on a rxn rate by measuring how the rxn rate at the beginning of a rxn depends on concentration. The instantaneous rxn rate at the start of a rxn is called the initial rate.

21. 21 The Dependence of Rate on Concentration Let’s look at the following rxn: NH 4 + (aq) + NO 2 - (aq) →N 2 (g) + 2H 2 O(l) The initial rate is the instantaneous rate at t = 0. (You get the initial rate from a graph.) We find the initial rate for various initial concentrations of each reactant; for this rxn, NH 4 + and NO 2 -.

22. 22 Finding Initial Rate

23. 23 The Dependence of Rate on Concentration

24. 24 The Dependence of Rate on Concentration As [NH 4 + ] doubles, with [NO 2 - ] constant, the rate doubles. So the rate is proportional to [NH 4 + ] As [NO 2 - ] doubles, with [NH 4 + ] constant, the rate doubles. So the rate is proportional to [NO 2 - ] We conclude that the rate ∝ [NH 4 + ] and to [NO 2 - ].

25. 25 The Dependence of Rate on Concentration The overall concentration dependence of the rxn rate is given in a rate law or rate expression. For this example, the rate law is: Rate = k[NH 4 + ][ NO 2 - ] k is the rate constant and is constant except for a change in temperature.

26. 26 The Dependence of Rate on Concentration So what is a rate law? It is a mathematical description of how the concentration of a reactant affects the rate of the rxn. After we determine the rate law and k for a rxn, we can then use this info to calculate initial rates or concentrations for any initial reactant concentrations.

27. 27 Reaction Order For a general reaction with rate law Rate = k[reactant 1] m [reactant 2] n, we say the reaction is mth order in reactant 1 and nth order in reactant 2. The overall rxn order is m + n + …. The rxn orders (values of the exponents) must be determined experimentally. They are not necessarily related to stoichiometry. Rxn orders of 0, 1, and 2 are common (0 th, 1 st, and 2 nd orders). But negative and fractional rxn orders are possible.

28. 28 Reaction Order For the rxn: NH 4 + (aq) + NO 2 - (aq) → N 2 (g) + 2H 2 O(l) The rxn has been experimentally found to be 1 st order in NH 4 + and 1 st in NO 2 -. The overall rxn order is 2. So, the rate law is: Rate = k[NH 4 + ][ NO 2 - ].

29. 29 Units of k, the Rate Constant The units of the rate constant, k, depend on the overall rxn order. For example, for a rxn with a rxn order of 2, the k units are: Units of rate = (units of rate constant)(units of concentration )2 Or:

30. 30 Using Initial Rates to Determine Rate Laws To determine the rate law, we observe the effect of changing initial concentrations. For the general rxn: aA + bB → cC + dD The rate law is: Rate = k[A] m [B] n

31. 31 Using Initial Rates to Determine Rate Laws Mathematically, we compare the rates of 2 or more experiments, which are conducted at different reactant concentrations. Solving this gives us the exponents, which gives us the rxn order. Once the exponents are known, k may be calculated. We then know the complete rate law!

32. 32 Using Initial Rates to Determine Rate Laws A rxn is zero order in a reactant if the change in concentration of that reactant produces no effect. A rxn is first order if doubling the concentration causes the rate to double. A rxn is second order if doubling the concentration results in a 2 2 increase in rate. A rxn is nth order if doubling the concentration causes an 2 n increase in rate. Note that the rate, not the rate constant, depends on concentration.

33. 33 Example for rxn A + B → C: Exp #[A][B]Initial rate (M/s) 10.100 4.0x10 -5 20.1000.2004.0x10 -5 30.2000.10016.0x10 -5 40.400 50.1002.0x10 -5 Find a) rate law; b) k; and c) fill in the blanks.