1. Chapter 14 Chemical Kinetics Dr. Nick Blake Ventura Community College Ventura, California

2. 2 Kinetics is the study of the factors that affect the speed of a reaction and the mechanism by which a reaction proceeds Experimentally it is shown that there are 4 factors that influence the speed of a reaction:  nature of the reactants,  temperature,  catalysts,  concentration Kinetics

3. 3 Defining Rate rate is how much a quantity changes in a given period of time the speed you drive your car is a rate – the distance your car travels (miles) in a given period of time (1 hour)  so the rate of your car has units of mi/hr (mph)

4. 4 Defining Reaction Rate the rate of a chemical reaction is measured as the change of concentration of a reactant (or product) in a given period of time interval To make the rate > 0, for reactants, a negative sign is placed in front of the definition

5. 5 Reaction Rate: Changes Over Time as time goes on, the rate of a reaction generally slows down  because the concentration of the reactants decreases at some time the reaction stops, either because the reactants run out or because the system has reached equilibrium.

6. 6 at t = 0 [A] = 8 [B] = 8 [C] = 0 at t = 0 [X] = 8 [Y] = 8 [Z] = 0 at t = 16 [A] = 4 [B] = 4 [C] = 4 at t = 16 [X] = 7 [Y] = 7 [Z] = 1

7. 7 at t = 16 [A] = 4 [B] = 4 [C] = 4 at t = 16 [X] = 7 [Y] = 7 [Z] = 1 at t = 32 [A] = 2 [B] = 2 [C] = 6 at t = 32 [X] = 6 [Y] = 6 [Z] = 2

8. 8 at t = 32 [A] = 2 [B] = 2 [C] = 6 at t = 32 [X] = 6 [Y] = 6 [Z] = 2 at t = 48 [A] = 0 [B] = 0 [C] = 8 at t = 48 [X] = 5 [Y] = 5 [Z] = 3

9. 9 Hypothetical Reaction Red  Blue Time (sec) Number Red Number Blue 01000 58416 107129 155941 2050 254258 303565 353070 402575 452179 501882 In this reaction, one molecule of Red turns into one molecule of Blue The number of molecules will always total 100 The rate of the reaction can be measured as the speed of loss of Red molecules over time, or the speed of gain of Blue molecules over time

10. Tro, Chemistry: A Molecular Approach10 Hypothetical Reaction: Red  Blue

11. Tro, Chemistry: A Molecular Approach11 Hypothetical Reaction Red  Blue

12. 12 Reaction Rate and Stoichiometry in most reactions, the coefficients of the balanced equation are not all the same H 2 (g) + I 2 (g)  2 HI (g) for these reactions, the change in the number of molecules of one substance is a multiple of the change in the number of molecules of another  for the above reaction, for every 1 mole of H 2 used, 1 mole of I 2 will also be used and 2 moles of HI made  therefore the rate of change will be different in order to be consistent, the change in the concentration of each substance is multiplied by 1/coefficient

13. 13 Average Rate the average rate is the change in measured concentrations in any particular time period linear approximation of a curve the larger the time interval, the more the average rate deviates from the instantaneous rate

14. 14 Hypothetical Reaction Red  Blue Avg. Rate Time (sec) Number Red Number Blue (5 sec intervals) (10 sec intervals) (25 sec intervals) 01000 584163.2 1071292.62.9 1559412.4 2050 1.82.1 2542581.6 2.3 3035651.41.5 3530701 40257511 4521790.8 5018820.60.71

15. 15 H2H2 I2I2 HI Avg. Rate, M/s t (s)[H 2 ] t, M[HI] t, M-Δ[H 2 ]/Δt½ Δ[HI]/Δt 0.0001.000 10.0000.819 20.0000.670 30.0000.549 40.0000.449 50.0000.368 60.0000.301 70.0000.247 80.0000.202 90.0000.165 100.0000.135 Avg. Rate, M/s t (s)[H 2 ] t, M[HI] t, M-Δ[H 2 ]/Δt½ Δ[HI]/Δt 0.0001.0000.000 10.0000.8190.362 20.0000.6700.660 30.0000.5490.902 40.0000.4491.102 50.0000.3681.264 60.0000.3011.398 70.0000.2471.506 80.0000.2021.596 90.0000.1651.670 100.0000.1351.730 Avg. Rate, M/s t (s)[H 2 ] t, M[HI] t, M-Δ[H 2 ]/Δt 0.0001.0000.000 10.0000.8190.3620.0181 20.0000.6700.6600.0149 30.0000.5490.9020.0121 40.0000.4491.1020.0100 50.0000.3681.2640.0081 60.0000.3011.3980.0067 70.0000.2471.5060.0054 80.0000.2021.5960.0045 90.0000.1651.6700.0037 100.0000.1351.7300.0030 Avg. Rate, M/s t (s)[H 2 ] t, M[HI] t, M-Δ[H 2 ]/Δt½ Δ[HI]/Δt 0.0001.0000.000 10.0000.8190.3620.0181 20.0000.6700.6600.0149 30.0000.5490.9020.0121 40.0000.4491.1020.0100 50.0000.3681.2640.0081 60.0000.3011.3980.0067 70.0000.2471.5060.0054 80.0000.2021.5960.0045 90.0000.1651.6700.0037 100.0000.1351.7300.0030 HI

16. Tro, Chemistry: A Molecular Approach16 average rate = - slope of the line connecting the [H 2 ] points; = ½ slope of the line for [HI] the average rate for the first 10 s is 0.0181 M/s the average rate for the first 40 s is 0.0150 M/s the average rate for the first 80 s is 0.0108 M/s

17. 17 Instantaneous Rate the instantaneous rate is the change in concentration at any one particular time slope at one point of a curve determined by taking the slope of a line tangent to the curve at that particular point first derivative of the function

18. 18 H 2 (g) + I 2 (g)  2 HI (g) Using [H 2 ], the instantaneous rate at 50 s is: Using [HI], the instantaneous rate at 50 s is:

19. For the reaction given, the [I - ] changes from 1.000 M to 0.868 M in the first 10 s. Calculate the average rate in the first 10 s and the Δ[H + ]. H 2 O 2 (aq) + 3 I - (aq) + 2 H + (aq)  I 3 - (aq) + 2 H 2 O (l) Solve the equation for the Rate (in terms of the change in concentration of the Given quantity) Solve the equation of the Rate (in terms of the change in the concentration for the quantity to Find) for the unknown value

20. 20 Measuring Reaction Rate In order to measure the reaction rate you need to be able to measure the concentration of at least one component in the mixture at many points in time There are two ways of approaching this problem (1) for reactions that are complete in less than 1 hour, it is best to use continuous monitoring of the concentration, or (2) for reactions that happen over a very long time, sampling of the mixture at various times can be used when sampling is used, often the reaction in the sample is stopped by a quenching technique

21. 21 Continuous Monitoring polarimetry – measuring the change in the degree of rotation of plane-polarized light caused by one of the components over time spectrophotometry – measuring the amount of light of a particular wavelength absorbed by one component over time total pressure – the total pressure of a gas mixture is stoichiometrically related to partial pressures of the gases in the reaction

22. Tro, Chemistry: A Molecular Approach22 Sampling gas chromatography can measure the concentrations of various components in a mixture for samples that have volatile components separates mixture by adherence to a surface drawing off periodic aliquots from the mixture and doing quantitative analysis titration for one of the components gravimetric analysis

23. 23 Factors Affecting Reaction Rate Nature of the Reactants nature of the reactants means what kind of reactant molecules and what physical condition they are in.  small molecules tend to react faster than large molecules;  gases tend to react faster than liquids which react faster than solids;  powdered solids are more reactive than “blocks”  more surface area for contact with other reactants  certain types of chemicals are more reactive than others  e.g., the activity series of metals  ions react faster than molecules  no bonds need to be broken

24. 24 Increasing temperature increases reaction rate  chemist’s rule of thumb - for each 10°C rise in temperature, the speed of the reaction doubles  for many reactions there is a mathematical relationship between the absolute temperature and the speed of a reaction discovered by Svante Arrhenius which will be examined later Factors Affecting Reaction Rate Temperature

25. 25 catalysts are substances which affect the speed of a reaction without being consumed most catalysts are used to speed up a reaction, these are called positive catalysts  catalysts used to slow a reaction are called negative catalysts homogeneous = present in same phase heterogeneous = present in different phase how catalysts work will be examined later Factors Affecting Reaction Rate Catalysts

26. Tro, Chemistry: A Molecular Approach26 generally, the larger the concentration of reactant molecules, the faster the reaction i ncreases the frequency of reactant molecule contact concentration of gases depends on the partial pressure of the gas  higher pressure = higher concentration concentration of solutions depends on the solute to solution ratio (molarity) Factors Affecting Reaction Rate Reactant Concentration

27. 27 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  and homogeneous catalysts as well 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

28. 28 Reaction Order 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) 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

29. Tro, Chemistry: A Molecular Approach29 Sample Rate Laws The reaction is autocatalytic, because a product affects the rate. Hg 2+ is a negative catalyst, increasing its concentration slows the reaction.

30. 30 Reactant Concentration vs. Time A  Products

31. Tro, Chemistry: A Molecular Approach31 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

32. 32 Zero Order Reactions Rate = k[A] 0 = k  constant rate reactions [A] = -kt + [A] 0 graph of [A] vs. time is straight line with slope = -k and y-intercept = [A] 0 t ½ = [A 0 ]/2k when Rate = M/sec, k = M/sec [A] 0 [A] time slope = - k

33. 33 First Order Reactions Rate = k[A] ln[A] = -kt + ln[A] 0 graph ln[A] vs. time gives straight line with slope = -k and y-intercept = ln[A] 0  used to determine the rate constant t ½ = 0.693/k the half-life of a first order reaction is constant the when Rate = M/sec, k = sec -1

34. 34 ln[A] 0 ln[A] time slope = −k

35. 35 Half-Life of a First-Order Reaction Is Constant

36. 36 Rate Data for C 4 H 9 Cl + H 2 O  C 4 H 9 OH + HCl Time (sec)[C 4 H 9 Cl], M 0.00.1000 50.00.0905 100.00.0820 150.00.0741 200.00.0671 300.00.0549 400.00.0448 500.00.0368 800.00.0200 10000.00.0000

37. 37 C 4 H 9 Cl + H 2 O  C 4 H 9 OH + 2 HCl

38. 38 C 4 H 9 Cl + H 2 O  C 4 H 9 OH + 2 HCl

39. 39 C 4 H 9 Cl + H 2 O  C 4 H 9 OH + 2 HCl slope = -2.01 x 10 -3 k = 2.01 x 10 -3 s -1