1. Chapter 15: Chemical Kinetics

2. Rate of a reaction Reaction rate – how fast a reaction occurs
𝑅𝑎𝑡𝑒= ∆[𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛] ∆𝑡𝑖𝑚𝑒
Rate can be related to reactants or products
Actual reaction rates must be determined experimentally

3. Writing out reaction rates
For general reaction, aA + bB  cC + dD
𝑅𝑎𝑡𝑒=− 1 𝑎 ∆[𝐴] ∆𝑡 =− 1 𝑏 ∆[𝐵] ∆𝑡 =+ 1 𝑐 ∆[𝐶] ∆𝑡 =+ 1 𝑑 ∆[𝐷] ∆𝑡
𝑅𝑎𝑡𝑒=− 1 1 ∆[ 𝐻 2 ] ∆𝑡 =− 1 1 ∆[ 𝐼 2 ] ∆𝑡 = ∆[𝐻𝐼] ∆𝑡

4. Calculating average rates

5. Calculating instantaneous rates
As concentration changes, the rate at a given point in time changes
To calculate the instantaneous rate of a reaction, use the slope of the tangent curve of a concentrations vs time graph

6. What is the instantaneous rate for the reaction at 50 seconds?
𝑅𝑎𝑡𝑒=− ∆ 𝐻 2 ∆𝑡
−(−0.28𝑀) 40𝑠 =0.007 𝑀 𝑠
𝑅𝑎𝑡𝑒= ∆[𝐻𝐼] ∆𝑡
1 2 (0.56𝑀) 40𝑠 =0.007 𝑀 𝑠

7. Practice
Define the rate of the reaction with respect to H2?
If the initial H2 concentration is M, and the final concentration is M after 10 seconds, what is the average rate of the reaction in this time frame?
3H2 + N2  2NH3

8. The rate law General simple reaction, A products 𝑅𝑎𝑡𝑒 𝐿𝑎𝑤=𝑘 [𝐴] 𝑛
k = rate constant
n = reaction order
Depending on the reaction order, the rate depends on the concentration differently

9. Reaction orders
If n = 0 (zero order), rate is independent of concentration A
If n = 1 (first order), rate is directly proportional to concentration A
If n = 2 (second order), rate is proportional to the square of concentration A

11. Determining reaction order
Method of initial rates – observe initial rates at different concentrations, then assign order of reaction based on concentration dependence of the initial rate values

12. Reaction order for multiple reactants
General Reaction aA + bB  cC + dD
Rate law = k[A]m[B]n
Assign reaction order for each reactant based on exponent
Overall reaction order determined by the sum of the exponents(orders) of each reactant
Example Rate = k[Cl2]3[H2]2
[Cl2] = third order
[H2] = second order
Overall = fifth order

13. Practice NO2(g) + CO(g)  NO(g) + CO2(g)
What is the rate order for NO2?
What is the rate order for CO?
Write the rate law for the reaction
What is the overall order of the reaction?

14. The integrated rate law relates the concentration of the reactants with respect to time based on the reaction order
A straight fit line can help determine reaction order based off integrated rate law
Integrated Rate Law

15. Straight line fit for zero order
Chapter 13, Figure 13.10
Zero-Order Integrated Rate Law

16. Straight line fit for first order
Chapter 13, Figure 13.8
First-Order Integrated Rate Law

17. Straight line fit for second order
Chapter 13, Figure 13.8
First-Order Integrated Rate Law

18. Using the straight line fit to find reaction order

19. Concentration versus time – zero order???

20. ln[Concentration] versus time – first order??
Chapter 13, Unnumbered Figure 1, Page 577

21. 1/[Concentration] versus time – second order??
Chapter 13, Unnumbered Figure 1, Page 577

22. Practice
Determine the reaction order from the following data Which graph represent the correct order of the reaction?

23. Half-Life of a Reaction
Half-life (t1/2) the required time it takes for the concentration of a reactant to be half of its initial value
Derived from integrated rate law equations
k = rate constant
A0 = initial concentration

24. Derivation of the half-life equation: First order
𝑙𝑛 [𝐴] 𝑡 =−𝑘𝑡+𝑙𝑛 𝐴 0
𝑙𝑛 [𝐴] 𝑡 −𝑙𝑛 𝐴 0 =−𝑘𝑡
𝑙𝑛 [𝐴] 𝑡 [𝐴] 0 =−𝑘𝑡 [𝐴] 𝑡 [𝐴] 0 =50%= 1 2
𝑙𝑛 1 2 =−𝑘 𝑡 1/2 𝑙𝑛 1 2 =−0.693
−0.693=−𝑘 𝑡 1/2
𝟎.𝟔𝟗𝟑 𝒌 = 𝒕 𝟏/𝟐
Derivation of the half-life equation: First order

25. Chapter 13, Figure 13.11
Half-Life: Concentration versus Time for a First-Order Reaction

27. How long will it take to get 17.89% of the original concentration?
How long will it take for the initial concentration to decrease to 25% of the original concentration?
For a first order reaction with a half life of 17.8s, what is the rate constant?
Practice

28. The Arrhenius Equation
Reactions rates are dependant on temperature. This is expressed through the rate constant “k” which is constant at a given temperature
Arrhenius Equation
R = J/mol·K Universal gas constant
k = rate constant
A = frequency factor
Ea = Activation energy or Activation barrier
= exponential factor

29. Ea or the activation energy/barrier
Energy that must be overcome to transform reactants into products
At top of hill, reactants are in a transition state or activated complex
Chapter 13, Figure 13.12
The Activation Energy Barrier

30. Chapter 13, Unnumbered Figure, Page 582

31. Chapter 13, Unnumbered Figure 1, Page 583

32. Chapter 13, Figure 13.13
The Activated Complex

33. A or Frequency factor
Relates to the number of approaches to the activation barrier
Higher frequency factor = more approaches to activation barrier
Chapter 13, Unnumbered Figure 2, Page 583

34. The exponential factor
The fraction of molecules that can successfully overcome the activation energy and transform into product
Dependence on Ea and T
Lower Ea and higher T = higher ex factor
Higher Ea and lower T = lower ex factor
Chapter 13, Figure 13.14
Thermal Energy Distribution

35. Arrhenius Plots

36. Chapter 13, Unnumbered Table, Page 584

37. Chapter 13, Unnumbered Figure, Page 584

38. Two-point form Arrhenius equation
If you have the rate constants at two different temperatures (Kelvin), you can relate it to the activation energy of the reaction
𝑙𝑛 𝑘 2 𝑘 1 = 𝐸 𝑎 𝑅 1 𝑇 1 − 1 𝑇 2

39. The activation energy of a reaction is 56
The activation energy of a reaction is kJ/mol and the frequency factor is 1.5 x 1011 (1/s). What is the rate constant of the reaction at 25 °C?
y = -1.12x104(x)
Using the equation from the graph from the previous slide, solve for the frequency factor and the activation energy of the reaction
Practice

40. Collision Theory Reaction needs Reactants colliding
Correct orientation
Sufficient energy
Chapter 13, Figure 13.15
The Collision Model

41. Chapter 13, Unnumbered Figure 1, Page 587

42. Chapter 13, Unnumbered Figure 2, Page 587

43. Reaction Mechanisms
General chemical equation usually represents the overall reaction and no the individual steps by which a reaction occurs
H2 + 2ICl  2HCl + I2
The reaction mechanism is the individual or elementary steps that leads to the overall reaction
Step 1 H2 + ICl  HI + HCl
Step 2 HI + ICl  HCl + I2
Overall H2 + 2ICl  2HCl + I2

44. Rate Laws for Elementary Steps

45. Chapter 13, Unnumbered Figure, Page 590

46. Rate Determining Step and Overall Reaction Rate Laws
Step 1 H2 + ICl  HI + HCl slow
Step 2 HI + ICl  HCl + I fast
The slow step determines the rate law
For a valid mechanism
the predicted rate law must match the experimental rate law
The elementary steps must sum to the overall reaction
A valid mechanism is only a possibility but not the guaranteed reaction route

47. Chapter 13, Figure 13.16
Energy Diagram for a Two-Step Mechanism

48. Catalysts!!!
Speed up reactions by lowering the activation energy by incorporating lower energy transition states to a reaction
It makes the reaction faster without being consumed
Chapter 13, Figure 13.18
Homogeneous and Heterogeneous Catalysis

49. Chapter 13, Figure 13.17
Catalyzed and Uncatalyzed Decomposition of Ozone

50. Chapter 13, Figure 13.20
Catalytic Hydrogenation of Ethene

51. Chapter 13, Figure 13.21
Enzyme–Substrate Binding

52. Chapter 13, Unnumbered Figure, Page 597

53. Chapter 13, Figure 13.22
An Enzyme-Catalyzed Reaction

54. Reaction rates!!! – calculating average and instantaneous rates
Rate laws – zero, first, and second order reactions
Intergrated rate law – straight line fit plots
Half-life – the initial concentration decreases to 50% of initial value
Arrhenius equations and plots – reactions dependant on temperature
Collision Theory - what a reaction needs to occur
Reaction Mechanisms – elementary steps of a reaction
Catalysts – speed up reaction through lower energy transition states
Chapter 15 Summary