Chapter 15: Kinetics

1. Chapter 15: Kinetics • The speed with which the reactants disappear and the products form is called the rate of the reaction • A study of the rate of reaction can give detailed information about how reactants change into products • The series of individual steps that add up to the overall observed reaction is called the reaction mechanism

2. There are five principle factors that influence reaction rates: • Chemical nature of the reactants • Ability of the reactants to come in contact with each other • Concentration of the reactants • Temperature • Availability of of rate-accelerating agents called catalysts

3. The progress of the reaction A  B. The number of A molecules (in red) decreases with time while the number of B molecules (in blue) increases. The steeper the concentration versus time curve, the faster the reaction rate. The film strip represents the relative number of A and B molecules at each time.

4. Chemical nature of the reactants • Bonds break and form during reactions • The most fundamental difference in reaction rates lie in the reactants themselves • Some reactions are fast by nature and others slow • Ability of the reactants to meet • Most reactions require that particles (atoms, molecules, or ions) collide before the reaction can occur • This depends on the phase of the reactants

5. In a homogeneous reaction the reactants are in the same phase • For example both reactants in the gas (vapor) phase • In a heterogeneous reaction the reactants are in different phases • For example one reactant in the liquid and the second in the solid phase • In heterogeneous reactions the reactants meet only at the intersection between the phases • Thus the area of contact between the phases determines the rate of the reaction

6. Effect of crushing a solid. When a single solid is subdivided into much smaller pieces, the total surface area on all of the pieces becomes very large.

7. Concentration of the reactants • Both homogeneous and heterogeneous reaction rates are affected by reactant concentration • For example, red hot steel wool bursts into flames in the presence of pure oxygen • Temperature of the system • The rates for almost all chemical reactions increase as the temperature is increased • Cold-blooded creatures, such as insects and reptiles, become sluggish at lower temperatures as their metabolism slows down

8. Presence of a catalyst • A catalysts is a substance that increases the rate of a chemical reaction without being consumed • Enzymes are biological catalysts that direct our body chemistry • A rate is always expressed as a ratio • One way to describe a reaction rate is to select one component of the reaction and describe the change in concentration per unit of time

9. Molarity (mol/L) is normally the concentration unit and the second (s) is the most often used unit of time • Typically, the reaction rate has the units

10. By convention, reaction rates are reported as a positive number even when the monitored species concentration decreases with time • If the rate is known with respect to one species, the coefficients of the balanced chemical equation can be used to find the rates with respect to the other species • Consider the combustion of propane:

11. Compared to the rate with respect to propane: • Rate with respect to oxygen is five times faster • Rate with respect to carbon dioxide is three times faster • Rate with respect to water is four times faster • Since the rates are all related any may be monitored to determine the reaction rate

12. A reaction rate is generally not constant throughout the reaction • Since most reactions depend on the concentration of reactants, the rate changes as they are used up • The rate at any particular moment is called the instantaneous rate • It can be calculated from a concentration versus time plot

13. A plot of the concentration of HI versus time for the reaction: 2HI(g)  H2(g) + I2(g). The slope is negative because we are measuring the disappearance of HI. When used to express the rate it is used as a positive number.

14. The rate of a homogeneous reaction at any instant is proportional to the product of the molar concentrations of the reactants raised to a power determined from experiment

15. Consider the following reaction: • From experiment, the rate law (determined from initial rates) is • At 0oC, k equals 5.0 x 105 L5 mol-5 s-1 • Thus, at 0oC

16. The exponents in the rate law are generally unrelated to the chemical equation’s coefficients • Never simply assume the exponents and coefficients are the same • The exponents must be determined from the results of experiments • The exponent in a rate law is called the order of reaction with respect to the corresponding reactant

17. For the rate law: • We can say • The reaction is first order with respect to H2SeO3 • The reaction is third order with respect to I- • The reaction is second order with respect to H+ • The reaction order is sixth order overall • Exponents in a rate law can be fractional, negative, and even zero

18. Looking for patterns in experimental data provide way to determine the exponents in a rate law • One of the easiest ways to reveal patterns in data is to form ratios of results using different sets of conditions • This technique is generally applicable • Again consider the hypothetical reaction

19. Suppose the experimental concentration-rate data for five experiments is:

20. For experiments 1, 2, and 3 [B] is held constant, so any change in rate must be due to changes in [A] • The rate law says that at constant [B] the rate is proportional to [A]m Thus m=1

21. This means that the reactions is first order with respect to reactant A • For experiments 3, 4, and 5 [A] is held constant, so any change must be due to changes in [B] • The rate law says that at constant [A] the rate is proportional to [B]n • Using the results from experiment 3 and 4:

22. The reaction is second order in B and rate=k[A][B]2 Thus n=2

23. The rate constant (k) can be determined using data from any experiment • Using experiment 1: • Using data from a different experiment might give a slightly different value

24. The relationship between concentration and time can be derived from the rate law and calculus • Integration of the rate laws gives the integrated rate laws • Integrate laws give concentration as a function of time • Integrated laws can get very complicated, so only a few simple forms will be considered

25. First order reactions • Rate law is: rate = k [A] • The integrate rate law can be expressed as: • [A]0 is [A] at t (time) = 0 • [A]t is [A] at t = t • e = base of natural logarithms = 2.71828…

26. Graphical methods can be used to determine the first-order rate constant, note

27. A plot of ln[A]t versus t gives a straight line with a slope of -k The decomposition of N2O5. (a) A graph of concentration versus time for the decomposition at 45oC. (b) A straight line is obtained from a logarithm versus time plot. The slope is negative the rate constant.

28. The simplest second-order rate law has the form • The integrated form of this equation is

29. Graphical methods can also be applied to second-order reactions • A plot of 1/[B]t versus t gives a straight line with a slope of k Second-order kinetics. A plot of 1/[HI] versus time (using the data in Table 15.1).

30. The amount of time required for half of a reactant to disappear is called the half-life, t1/2 • The half-life of a first-order reaction is not affected by the initial concentration

31. First-order radioactive decay of iodine-131. The initial concentration is represented by [I]0.

32. The half-life of a second-order reactions does depend on the initial concentration

33. One of the simplest models to explain reactions rates is collision theory • According to collision theory, the rate of reaction is proportional to the effective number of collisions per second among the reacting molecules • An effective collision is one that actually gives product molecules • The number of all types of collisions increase with concentration, including effective collisions

34. There are a number of reasons why only a small fraction of all the collisions leads to the formation of product: • Only a small fraction of the collisions are energetic enough to lead to products • Molecular orientation is important because a collision on the “wrong side” of a reacting species cannot produce any product • This becomes more important as the complexity of the reactants increases

35. The key step in the decomposition of NO2Cl to NO2 and Cl2 is the collision of a Cl atom with a NO2Cl molecules. (a) A poorly orientated collision. (b) An effectively orientated collision.

36. The minimum energy kinetic energy the colliding particles must have is called the activation energy, Ea • In a successful collision, the activation energy changes to potential energy as the bonds rearrange to for products • Activation energies can be large, so only a small fraction of the well-orientated, colliding molecules have it • Temperature increases increase the average kinetic energy of the reacting particles

37. Kinetic energy distribution for a reaction at two different temperatures. At the higher temperature, a larger fraction of the collisions have sufficient energy for reaction to occur. The shaded area under the curves represent the reacting fraction of the collisions.

38. Transition state theory explains what happens when reactant particles come together • Potential-energy diagrams are used to help visualize the relationship between the activation energy and the development of total potential energy • The potential energy is plotted against reaction coordinate or reaction progress

39. The potential-energy diagram for an exothermic reaction. The extent of reaction is represented as the reaction coordinate.

40. A successful (a) and unsuccessful (b) collision for an exothermic reaction.

41. Activation energies and heats of reactions can be determined from potential-energy diagrams Potential-energy diagram for an endothermic reaction. The heat of reaction and activation energy are labeled.

42. Reactions generally have different activation energies in the forward and reverse direction Activation energy barrier for the forward and reverse reactions.

43. The brief moment during a successful collision that the reactant bonds are partially broken and the product bonds are partially formed is called the transition state • The potential energy of the transition state is a maximum of the potential-energy diagram • The unstable chemical species that “exists” momentarily is called the activated complex

44. Formation of the activated complex in the reaction between NO2Cl and Cl. NO2Cl+ClNO2+Cl2

45. The activation energy is related to the rate constant by the Arrhenius equation k = rate constant Ea = activation energy e = base of the natural logarithm R = gas constant = 8.314 J mol-1 K-1 T = Kelvin temperature A = frequency factor or pre-exponential factor

46. The Arrhenius equation can be put in standard slope-intercept form by taking the natural logarithm • A plot of ln k versus (1/T) gives a straight line with slope = -Ea/RT

47. The activation energy can be related to the rate constant at two temperatures • The reaction’s mechanism is the series of simple reactions called elementary processes • The rate law of an elementary process can be written from its chemical equation

48. The overall rate law determined for the mechanism must agree with the observed rate law • The exponents in the rate law for an elementary process are equal to the coefficients of the reactants in chemical equation

49. Multistep reactions are common • The sum of the element processes must give the overall reaction • The slow set in a multistep reaction limits how fast the final products can form and is called the rate-determining or rate-limiting step • Simultaneous collisions between three or more particles is extremely rate

50. A reaction that depended a three-body collision would be extremely slow • Thus, reaction mechanism seldom include elementary process that involve more than two-body or bimolecular collisions • Consider the reaction • The mechanism is thought to be