1. Measuring Reaction Rates Continuous monitoring polarimetry spectrophotometry total pressure Taking aliquots gas chromatography titration for one of the components gravimetric analysis

2. The Rate Law The Rate Law of a reaction is the mathematical relationship between the rate of the reaction and the concentrations of the reactants The rate of a reaction is directly proportional to the concentration of each reactant raised to a power For the reaction aA + bB  products the rate law would have the form given below n and m are called the orders for each reactant k is called the rate constant

3. The exponent on each reactant in the rate law is called the order with respect to that reactant The sum of the exponents on the reactants is called the order of the reaction The rate law for the reaction: 2 NO(g) + O 2 (g)  2 NO 2 (g) is Rate = k[NO] 2 [O 2 ] The reaction is second order with respect to [NO], first order with respect to [O 2 ], and third order overall. Reaction Order

4. Sample Rate Laws Important: The rate laws can only be determined by experiment. The stoichiometry of the reaction does not tell us what the rate law is. ReactionRate Law CH 3 CN  CH 3 NC Rate = k[CH 3 CN] CH 3 CHO  CH 4 + CO Rate = k[CH 3 CHO] 3/2 2 N 2 O 5  4 NO 2 + O 2 Rate = k[N 2 O 5 ] H 2 + I 2  2 HI Rate = k[H 2 ][I 2 ] Tl +3 + Hg 2 +2  Tl +1 + 2 Hg +2 Rate = k[Tl +3 ][Hg 2 +2 ][Hg +2 ] -1

5. Why is the Rate Law Important? The concentrations of reactants and products can be predicted for any time throughout the reaction It can be used to propose reaction mechanisms that give insights into what is happening in the reaction on the molecular level.

6. Determining the Rate Law: Method of Initial Rates Most common method Rates are measured at the beginning of the reaction when products don’t interfere Several experiments are done, varying the concentration of one reactant at a time and measuring the initial rate each time.

7. For the following reaction run at 800˚C H 2 (g) + 2NO (g) --> N 2 O (g) +H 2 O (g) initial rates are measured as the concentration of the reactants are varied: Exp[H 2 ] (mol/L)[NO] (mol/L)initial rate (mol/L-sec) 10.100.100.12 20.200.100.24 30.200.200.96 What is the rate law for this reaction? Calculate the rate constant for the reaction at 800˚C.

8. For the following reaction -- BrO 3 - (aq) + 5 Br - (aq) + 6 H + (aq) --> 3 Br 2 (l) + 3H 2 O (l) initial rates are measured as the concentration of the reactants are varied: Exp[BrO 3 - ] (mol/L)[ Br - ] (mol/L)[ H + ] (mol/L) initial rate (mol/L-sec) 10.100.100.108.0 x 10 -4 20.200.100.10 1.6 x 10 -3 30.200.200.10 3.2 x 10 -3 40.100.100.203.2 x 10 -3 What is the rate law for this reaction? Calculate the rate constant for the reaction.

9. Integrated Rate Laws: Predicting Concentrations as a Function of Time We are going to discuss integrated rate laws for reactions that are zero, first and second order in one reactant only. Rate = k[A] 0 “zeroth” order Rate = k[A]first order Rate = k[A] 2 second order Other rate laws are too complicated mathematically

10. Reactant Concentration vs. Time A  Products

11. ln[A] 0 ln[A] time slope = −k First Order Reaction

12. The decomposition of N 2 O 5 is first order in [N 2 O 5 ] at 65˚, at which temperature the rate constant is 5.2 x 10 -3 s -1. If the initial concentration of N 2 O 5 is 4.0 x 10 -3 M, what is the concentration of N 2 O 5 600s after the reaction begins?

13. Half-Life The half-life, t 1/2, of a reaction is the length of time it takes for the concentration of the reactants to fall to ½ its initial value. The half-life of the reaction depends on the order of the reaction

14. Half-Life of a First-Order Reaction Is Constant

15. Half-life for a First Order Reaction

16. In the N 2 O 5 decomposition, after what time will half of the reactants decompose at 65˚C?

17. A certain first order reaction has a half life of 20.0 minutes. 1.Calculate the rate constant for this reaction. 2.How much time is required for this reaction to be 75% complete?

18. Summary: First Order Reactions Rate law: rate = k[A] Integrated rate law: ln[A] = -kt + ln[A] 0 Graph: ln[A] vs. time gives straight line slope = -k and y-intercept = ln[A] 0 used to determine the rate constant Half-life t ½ = 0.693/k The half-life of a first order reaction is constant Units for k: sec -1

19. Second Order Reaction

20. l/[A] 0 1/[A] time slope = k

21. The reaction HI (g) --> 1/2 I 2 (g) + 1/2 H 2 (g) Is second order with respect to HI. At 700˚C, the rate constant is 1.8 x 10 -3 M -1 s -1. If the initial concentration of HI is 1.0 M, what will be the concentration after 5.0 x 10 3 s.

22. The half-life of a second order reaction depends on the concentration of the reactant or reactants.

23. Summary: Second Order Reactions Rate law: rate = k[A] 2 Integrated rate law: 1/[A] = kt + 1/[A] 0 oooo 1/[A] vs. time gives straight line slope = k and y-intercept = 1/[A] 0 used to determine the rate constant Half life: t ½ = 1/(k[A 0 ]) Units for k: k = M -1 ∙ sec -1

24. Zero Order Reactions Rate law: rate = k[A] 0 = k constant rate reactions Integrated rate law: [A] = -kt + [A] 0 Graph: [A] vs. time is straight line with slope = -k and y-intercept = [A] 0 t ½ = [A 0 ]/2k Units: if Rate = M/sec, k = M/sec [A] 0 [A] time slope = - k