11.1: Meaning of Reaction Rates 1 Define Reaction Rates How to Express Reaction Rates Can You Write an Expression Rate Concentration vs. Time Curve Determining Instantaneous Rates for a Reaction

Reaction Rate Defined 2 Reaction rate : changes in a concentration of a product or a reactant per unit time.  [ ] concentration Reaction rate = ——  t change

Expressing Reaction Rates 3 aA + bB cC + dD

Expressing reaction rates 4 For a chemical reaction, there are many ways to express the reaction rate. The relationships among expressions depend on the equation. 2 NO(g) + O 2 (g) 2 NO 2 (g)  [O 2 ] 1  [NO] 1  [NO 2 ] Reaction rate = – ——— = – — ———— = — ———  t 2  t 2  t Make sure you can write expressions for any reaction and figure out the relationships. For example, give the reaction rate expressions for 2 N 2 O 5 4 NO 2 + O 2

5  [N 2 O 5 ]  [O 2 ]  [NO 2 ] Reaction rate = – ——— = ———— = ———— 2  t  t 4  t

Change in Concentration with Time 6

Determining Instantaneous Rate 7

11.2: Reaction Rate and Concentration 8 Rate Constants and Rate Expression Order of Reaction Involving Single Reactant Order of Reaction Involving More Than One Reactant

9 2 N 2 O 5 4 NO 2 + O 2 Let’s look at our previous example : If we look at the plot below which plots rate versus concentration of dinitrogen pentoxide, we see it is a straight line:

10 2 N 2 O 5 4 NO 2 + O 2 Since it is a straight line we can say that the rate only depends on the concentration of dinitrogen pentoxide. Therefore …. Rate = k [N 2 O 5 ] This equation is the rate expression for the decomposition of dinitrogen pentoxide and tells us that the rate of the reaction depends only on concentration of reactant (N 2 O 5 ). The proportionality constant, k, is called the rate constant, and is independent of the other quantities in the equation.

Order of Reaction: Single Reactant 11 A Products The rate expression has the general form… Rate = k [A] m The power to which the concentration is raised (m) is known as the order of the reaction. Usually m = integers 0,1,2 etc., but they can be fractions “m” must be determined experimentally, it cannot be deduced from stoichiometric coefficients

Determining Order: Using Rates and Concentration 12 Simply choose 1 st two concentrations (0.2 and 0.3) and use following relationship that is derived in your textbook CH 3 CHO CH 4 + CO [CH 3 CHO]0.20 M0.30 M0.40 M0.50 M Rate (M/s)

Determining Order: Using Rates and Concentration 13 [CH 3 CHO]0.20 M0.30 M0.40 M0.50 M Rate (M/s) Rate = k [CH 3 CHO] 2 Now we can determine rate constant k using concentration and rate numbers

Order of Reaction with More Than One Reactant 14 Rate = k [A] m x [B] n m = order of reaction with respect to A n = order of reaction with respect to B Overall order of reaction = m + n aA + bB products

How Do We Figure Out n and m? 15 Rate 1 = k [A] 1 m x [B] n Rate 2 = k [A] 2 m x [B] n Hold B constant and change concentration of A. We can now solve for “m” and get order with respect to A To get order of B, keep concentration of A constant and solve for “n”.

11.3: Reaction Concentration and Time 16 First-Order Reactions Half-Life Zero-Order Reactions Second-Order Reactions

Why Time is Better Than Rate 17 Rate = k [N 2 O 5 ] This equation shows that the rate changes with dinitrogen pentoxide concentration, but in practice, it is probably more valuable to know how [N 2 O 5 ] changes with time. Why? How much [N 2 O 5 ] is left after 5 minutes or one hour is usually the information you are looking for.

First Order Reactions 18 Rate = k [A] A Products Using calculus reveals the following relationship between Concentration and time for this simple 1 st order reaction …. Where [A] o is initial concentration,[A] is concentration at time t, and k is the first- order rate constant.

Graphing First Order Reactions 19 Solve for [A]

Graphing First Order Reactions 20

First-Order Problem 21 For the first-order decomposition of N 2 O 5 at 67 o C, the rate constant was determined to be 0.35/min. a) The concentration after eight minutes, starting at M

First-Order Problem 22 For the first-order decomposition of N 2 O 5 at 67 o C, the rate constant was determined to be 0.35/min. b) The time required for the concentration to drop to M

First-Order Problem: Half Life 23 For the first-order decomposition of N 2 O 5 at 67 o C, the rate constant was determined to be 0.35/min. c) When half of the sample has decomposed

Half-Life 24 The time required for one half of a reactant to decompose via a first-order reaction has a fixed value, independent of concentration = half-life For a first-order reaction

Most Important 1 st -Order Rxn 25 Radioactive decay- When an unstable nucleus decomposes Letting X be the amount of a radioactive isotope at time t, then rate = kX

Most Important 1 st -Order Rxn 26 Radioactive decay- When an unstable nucleus decomposes Letting X be the amount of a radioactive isotope at time t, then rate = kX

Radioactive decay problem 27 Plutonium-240 is a byproduct of the nuclear reaction that takes place in a reactor. It takes one thousand years for 10% of a 4.60 gram sample to decay. What is the half-life of Pu-240? x 4.60 = g Thus, X o = 4.60 g and X = 4.14g ln X o – ln X = kt ln 4.60 – ln 4.14 =k(1000 yr) k = 1.05 x yr -1 Then plug into half-life equation t 1/2 = 0.693/k t 1/2 = 0.693/ 1.05 x yr -1 t 1/2 = 6.60 x 10 3 yr

Zero-Order Reactions 29 A Products Rate = k [A] 0 = k Independent of Concentration – Pretty rare, but many heterogeneous catalysis reactions are zero- order

Second-Order Reactions 30 A Products Rate = k [A] 2 Resorting to calculus gives us the concentration-time relationship

Summary of Reaction Order 31