1. TOPIC C: REACTION MECHANISMS

2. Mechanism - the sequence of elementary steps that make up a chemical reaction Each step will be relatively fast or relatively slow The overall rate of the chemical reaction is dependent upon the slowest elementary step. For this reason, the slowest step is known as the rate determining step or RDS.

3. To study reaction rates we need to express changing concentrations of reactants in some quantitative form We use a rate equation or rate law. General form, Rate = k [A] x [B] y [C] z k is the rate constant x, y and z are the orders with respect to the concentrations of reactants A, B and C. The order with respect to a given reactant is the power to which the concentration of that reactant is raised to in the rate equation. The overall order of the chemical reaction is the sum of the individual orders.

4. The reactants in the rate-determining step are ones that affect the rate Only these reactants appear in the overall rate equation Often the RDS rate law will match the overall rate law

5. Important Points: 1. You cannot determine the order of a reaction from the balanced equation Orders must be determined experimentally It is possible to determine the overall order of a reaction from the slowest elementary step [ the coefficient in the slow step is the power that the concentration of that substance is raised to in the rate equation ]

6. 2. Units and magnitude of the rate constant are important. They vary a great deal (since reaction rates vary widely), and have often been the subject of AP questions. 3. A reactant that has no effect on the rate has an order equal to zero. It has no effect on the rate Any number raised to the power of zero is equal to 1, so it can be omitted from the rate equation.

7. 4. Orders can be fractional, e.g., ½. 5. In valid mechanisms the sum of the elementary steps must add up to the overall chemical reaction. 6. Intermediates are formed in one elementary step during the overall reaction, but are then used up in a subsequent elementary step. 7. If a substance is present at the beginning of a reaction and present in the same form at the end of the reaction, it can be identified as a catalyst.

8. The overall reaction is shown. This allows the cancellation of I-, since it is present both at the beginning and the end of the reaction (considered a catalyst). (Note, IO- also cancels out, but not because it is a catalyst, rather it is an intermediate). Step 1: H 2 O 2 + I -  H 2 O + IO - Step 2: IO - + H 2 O 2  H 2 O + I - + O 2 _______________________________ Overall: 2H 2 O 2  2H 2 O + O 2

9. Practice: Identify the catalyst and the intermediate in the mechanism below. Step 1: SO 2 + V 2 O 5  SO 3 + V 2 O 4 Step 2: V 2 O 4 + ½O 2  V 2 O 5

10. Determining rate law by inspection Example #1 – see handout Example #2 – see handout Example #3 – see handout Practice Problems (handout)

11. Reaction Rate (additional background) Rate = [A] at time t 2 - [A] at time t 1 t 2 – t 1 Rate =  [A] Dt Reaction Rate – is a change in concentration of a reactant or product per unit time For this reaction: 2NO 2 (g) → 2NO (g) + O 2 (g)

12. 2NO 2 (g)  2NO(g) + O 2 (g) Reaction Rates: 2. Can measure appearance of products 1. Can measure disappearance of reactants 3. Are proportional stoichiometrically

13. 2NO 2 (g)  2NO(g) + O 2 (g) Reaction Rates: 4. Are equal to the slope tangent to that point  [NO 2 ] tt 5. Change as the reaction proceeds, if the rate is dependent upon concentration

14. We can define rate in terms of the disappearance of the reactant or in terms of the rate of appearance of the product. In our exampleN 2 + 3H 2 2NH 3 -  [N 2 ] or -3  [H 2 ] or 2  [NH 3 ]  t  t  t Defining Rate of a Reaction

15. Rate Laws Reactions are reversible. As products accumulate they can begin to turn back into reactants. Early on the rate will depend on only the amount of reactants present. We want to measure the reactants as soon as they are mixed. This is called the Initial rate method.

16. Two key points 1. The concentration of the products do not appear in the rate law because this is an initial rate. 2. The order must be determined experimentally, it cannot be obtained from the equation. Rate Laws

17. Rate will only depend on the concentration of the reactants. Products have not built up yet. To define rate in terms of NO 2 : Rate = k[NO 2 ] n This is called a rate law expression. k is called the rate constant. n is the order of the reactant - usually a positive integer. (must be determined by experiment) 2 NO 2(g) → 2 NO (g) + O 2(g)

18. Types of Rate Laws Differential Rate law - describes how rate depends on concentration. (Typically just called Rate Law) Integrated Rate Law - Describes how concentration depends on time. For each type of differential rate law there is an integrated rate law and vice versa. Rate laws can help us better understand reaction mechanisms.

19. Determining Rate Laws The first step is to determine the form of the rate law (especially its order). Must be determined from experimental data. For this reaction in CCl 4 soln. 2 N 2 O 5 (aq) → 4NO 2 (aq) + O 2 (g) Oxygen escapes the solution and therefore there is no reverse reaction

20. [N 2 O 5 ] (mol/L) Time (s) 1.000 0.88200 0.78400 0.69600 0.61800 0.541000 0.481200 0.431400 0.381600 0.341800 0.302000 Now graph the data

21. To find rate we have to find the slope at two points We will use the tangent method.

22. At.90 M the rate is - 5.4 x 10 -4

23. At.45 M the rate is - 2.7 x 10 -4

24. As the [ ] doubles the rate of reaction doubles. (Twice as fast) Rate = -D[N 2 O 5 ] = k[N 2 O 5 ] 1 = k[N 2 O 5 ] Dt We say this reaction is first order in N 2 O 5.90 = -5.4 x 10 -4.45 -2.7 x 10 -4 ∆ [ ]RateOrder of Reaction 2x2x 2 Rate Doubles1 st Order (x = 1) 2x2x 4 Rate Quadruples2 nd Order (x = 2) 2x2x 8 3 rd Order (x = 3)

25. Mathematically (Initial rates method) It is also possible to use the initial rates method to find the orders We use the ratio of the rate equations.

26. The method of Initial Rates This method requires that a reaction be run several times. The initial concentrations of the reactants are varied. The reaction rate is measured just after the reactants are mixed. Eliminates the effect of the reverse reaction.

27. An example For the reaction BrO 3 - + 5 Br - + 6H + 3Br 2 + 3 H 2 O The general form of the Rate Law is Rate = k[BrO 3 - ] n [Br-] m [H + ] p We use experimental data to determine the values of n,m,and p

28. Initial concentrations (M) Rate (M/s) BrO 3 - Br - H+H+H+H+ 0.100.100.108.0 x 10 -4 0.100.100.108.0 x 10 -4 0.200.100.101.6 x 10 -3 0.200.100.101.6 x 10 -3 0.200.200.103.2 x 10 -3 0.200.200.103.2 x 10 -3 0.100.100.203.2 x 10 -3 0.100.100.203.2 x 10 -3 Now we have to see how the rate changes with concentration