Chapter 14: Chemical Kinetics

1. Chapter 14:Chemical Kinetics AP/IB Chemistry

2. Reaction Rate • Reaction Rate: speed of a chemical reaction • Change in concentration of reactant or product in a given amount of time • Units: M/s

3. The Collision Theory • Collision theory explains that chemical reactions occur through collisions between molecules or atoms • Reactant molecules must collide to react • Things to think about… • Number of collisions, or collision frequency • Concentration of reactants • Temperature • Energy of collisions • Appropriate collision orientation

4. Factors that Affect Reaction Rates • There are 4 factors that affect reaction rates • Physical state of reactants • Concentration of reactants • Temperature • Presence or absence of catalysts • Catalysts: increase RR without being used up • Know: biological enzymes

5. Reaction Rates • For a reaction A  B • Aside: [B] means “molarity of B in mol/L”

6. Reaction Rates • At t = 0 there is 1.00 M A and no B • At t = 20 s, there is 0.54 M A and 0.46 M B • At t = 40 s, there is 0.30 M A and 0.70 M B

7. Reaction Rates For A  B there are 2 ways of measuring rate: • Speed at which products appear • Speed at which reactants disappear NOTE: rates always expressed as positive #’s

8. Change of Rate with Time • Calculate the average rate in terms of the disappearance of reactant over some time interval • Instantaneous rate: the RR at any given instant • Determined from the slope of the tangent to the rate curve (derivative) • Instantaneous rate is different from average rate! • We usually call the instantaneous rate the “reaction rate” • Initial rate: instantaneous rate at t=0

10. Reaction Rates and Stoichiomtery • In general, for the reaction: aA + bBcC + dD • a, b, c and d are the stoichiometric coefficients of the balanced chemical equation

11. Sample Problem The decomposition of dinitrogenpentoxide proceeds according to the following equation: 2 N2O5 (g) 4 NO2 (g) + O2 (g) If the rate of decomposition of N2O5 at a particular instant in a reaction vessel is 4.2 x 10-7M/s, what is the rate of appearance of NO2? Of O2?

12. Rate Laws • Rate Law:an expression that relates the reaction rate to the concentration of reactants • Example: if the rate law for the reaction, 2 N2O5 (g) 4 NO2 (g) + O2 (g) is: Rate = k [N2O5] • It tells you that reaction rate is directly proportional to concentration of N2O5 • If you double [N2O5], reaction rate doubles • k is the rate constant

13. Rate Laws • For the reaction: NH4+(aq) + NO2-(aq) N2(g) + 2H2O(l) we note that: • As [NH4+] doubles, with [NO2-] held constant, the rate doubles • As [NO2-] doubles, with [NH4+] constant, the rate doubles • Rate is directly proportional to concentration of both reactants • Rate law:

14. General Form of Rate Laws aA + bB cC + dD Rate = k[A]m[B]n • Exponents m and n are small whole numbers (0, 1, 2) called the kinetic orders • The reaction is mth-order in reactant 1 and nth-order in reactant 2 • The overall order of reaction is m + n + …. (sum of all exponents) • Values of the exponents (orders) have to be determined experimentally

15. General Forms of Rate Law • If exponent is 0, the order for that reactant is zero-order • Means that as the [reactant] changes, it produces no effect in RR • If the exponent is 1, the rate is first-order • Means that as the [reactant] doubles, the RR doubles, as [reactant] triples, RR triples, etc. • If the exponent is 2, the rate is second order • Means that as the [reactant] doubles, the RR quadruples, or as [reactant] triples, RR goes up by factor of 9

16. Take Home… • RR depends on concentration of reactants • Rate constant (k) is experimentally determined and depends on: • Temperature • Presence or absence of a catalyst

17. Sample Problem The following data were obtained for the reaction A + B  C Determine the rate law for the reaction.

18. Change in Concentration with Time • There is a relationship between concentration of reactants and time: • For a first order reaction: ln[A]t = –kt + ln[A]0 • k = rate constant • t = time • [A]0 = concentration at start of reaction • [A]t = concentration at time, t

19. First Order Reactions:Change in Concentration with Time ln[A]t = –kt + ln[A]0 y = mx + b

20. Change in Concentration with Time • There is a relationship between concentration of reactants and time: • For a second order reaction: Rate = k[A]2 y = mx + b

21. Half Life • Half-life: time it takes for the concentration of a reactant to drop to half its original value • For a first order process: • Half life, t½ is the time it takes for [A]0 to reach ½[A]0 • Radioactive decay is a type of half-life process

22. Sample Problem • The half-life of a first-order reaction is 6.00 x 10-2 s. What is the rate constant for the reaction?

23. Change in Rate with Temperature • RR increases w/ increasing temp • Why? • As temp increases, rate constant (k) increases

24. Change in Rate with Temperature • Arrhenius: molecules must posses a minimum amount of energy to react. Why? • To form products, bonds are broken in reactants • Bond breakage requires energy • Activation energy, Ea, is the minimum energy required to initiate a chemical reaction • Ea changes from reaction to reaction

26. Change in Rate with Temperature • Arrhenius discovered RR data obey the Arrhenius equation: • k = rate constant • Ea = activation energy • R = gas constant (8.314 J/K-mol) • T = temperature • A = frequency factor • Related to number of collisions • Both A and Ea are specific to a given reaction

27. Determining Ea • If there is a lot of data, determine Ea and A graphically by rearranging Arrhenius equation: y = mx + b

28. Reaction Mechanisms • Reaction Mechanisms: the process by which a chemical reaction occurs • Gives the path of a reaction • Remember: reactions take place as a result of collisions between the reactants

29. Elementary Reactions • Elementary Reactions: chemical rxns that occur in a single step • Molecules that collide must be correctly oriented and have enough energy to react

30. Multistep Mechanisms • Multistep Mechanism: consists of a sequence of elementary rxns • Net change = balanced chemical eqn NO2 + NO2 NO3 + NO NO3 + CO  NO2 + CO2 NO2 + CO  NO + CO2 • Chemical eqns for elementary rxns in a multistep mechanism must add up the give correct chemical eqn

31. Rate Laws for Multistep Mechanisms • Most rxns involve >2 elementary rxns • Each rxn has its own k and Ea • Rate-Determining Step: in a multistep rxn, one step is usually much slower than the others • The rate of the whole reaction can’t be faster than the rate of the slowest elementary step • The slowest step in a multistep rxn limits the overall rate

32. Mechanisms with Slow Initial Step • If step 1 is slow and step 2 is fast, step 1 is rate-limiting • Overall rate and rate law of rxn has to be equal to that of step 1

33. Sample Problem O3 reacts with NO2 to produce N2O5 and O2: The reaction is believed to occur in 2 steps: O3 + NO2 NO3 + O2 (slow) Rate = k[O3][NO2] NO3 + NO2 N2O5 (fast) Rate = k[NO3]2[NO2] What is the predicted rate law?

34. Catalysis • Catalyst: changes the rate of a chemical reaction without being used up • Generally, catalysts lower the Ea of a reaction • Two types of catalysts: • Homogeneous • Heterogeneous • Cl atoms are catalysts for the destruction of O3

35. Homogenous Catalysts • Homogenous Catalyst: catalyst present in same phase as the reactants • H2O2 decomposes very slowly 2H2O2 (aq) 2H2O (l) + O2 (g) • In the presence of bromide ion, decomposition occurs quickly: 2Br- (aq) + H2O2 (aq) + 2H+ (aq) Br2 (aq) + 2H2O (l) Br2 (aq) + H2O2 (aq) 2Br- (aq) + 2H+ (aq) + O2 (g) 2H2O2 (aq) 2H2O (l) + O2 (g) • Br- is a catalyst because it is recovered at the end of the reaction

36. Heterogenous Catalysts • Heterogenous Catalyst: catalyst present in a different phase as the reactants • Reaction occurs on the surface of solids • Example: decomposition of H2O2 by silver

37. Catalysts Lower Ea of Reaction