Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 14 Chemical Kinetics John D. Bookstaver St. Charles Community College Cottleville, MO Chemical Kinetics 2009, Prentice-Hall, Inc. Kinetics

In kinetics we study the rate at which a chemical process occurs. Besides information about the speed at which reactions occur, kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs). Chemical Kinetics 2009, Prentice-Hall, Inc. Factors That Affect Reaction Rates Physical State of the Reactants In order to react, molecules must come in contact with each other. The more homogeneous the mixture of reactants, the faster the molecules can

react. Chemical Kinetics 2009, Prentice-Hall, Inc. Factors That Affect Reaction Rates Concentration of Reactants As the concentration of reactants increases, so does the likelihood that reactant molecules will collide. Chemical Kinetics 2009, Prentice-Hall, Inc.

Factors That Affect Reaction Rates Temperature At higher temperatures, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy. Chemical Kinetics 2009, Prentice-Hall, Inc. Factors That Affect Reaction Rates Presence of a Catalyst Catalysts speed up reactions by changing the mechanism of the reaction.

Catalysts are not consumed during the course of the reaction. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Rates Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time. Chemical Kinetics 2009, Prentice-Hall, Inc.

Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) In this reaction, the concentration of butyl chloride, C4H9Cl, was measured at various times. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

The average rate of the reaction over each interval is the change in concentration divided by the change in time: [CC4H9Cl] Average rate = t Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Rates

C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) Note that the average rate decreases as the reaction proceeds. This is because as the reaction goes forward, there are fewer collisions between reactant molecules. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

A plot of [CC4H9Cl] vs. time for this reaction yields a curve like this. The slope of a line tangent to the curve at any point is the instantaneous rate at that time. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Rates C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) All reactions slow down

over time. Therefore, the best indicator of the rate of a reaction is the instantaneous rate near the beginning of the reaction. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Rates and Stoichiometry C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq) In this reaction, the ratio of C4H9Cl to C4H9OH is

1:1. Thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH. Rate = -[CC4H9Cl] t = [CC4H9OH] t

Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Rates and Stoichiometry What if the ratio is not 1:1? 2 HI(g) H2(g) + I2(g) In such a case, 1 [CHI] [CI2] Rate = = 2 t t Chemical

Kinetics 2009, Prentice-Hall, Inc. Reaction Rates and Stoichiometry To generalize, then, for the reaction aA + bB cC + dD 1 [CA] 1 [CB] 1 [CC] 1 [CD] = = =

Rate = a b t c t d t t Chemical Kinetics 2009, Prentice-Hall, Inc. Concentration and Rate One can gain information about the rate of a reaction by seeing how the rate changes with changes in concentration. Chemical

Kinetics 2009, Prentice-Hall, Inc. Concentration and Rate NH4+(aq) + NO2(aq) N2(g) + 2 H2O(l) If we compare Experiments 1 and 2, we see that when [CNH4+] doubles, the initial rate doubles. Chemical Kinetics 2009, Prentice-Hall, Inc.

Concentration and Rate NH4+(aq) + NO2(aq) N2(g) + 2 H2O(l) Likewise, when we compare Experiments 5 and 6, we see that when [CNO2] doubles, the Chemical initial rate doubles. Kinetics 2009, Prentice-Hall, Inc. Concentration and Rate This means Rate [CNH4+]

Therefore, Rate [CNO2 ] Rate [CNH4+] [CNO2] which, when written as an equation, becomes Rate = k [CNH4+] [CNO2] This equation is called the rate law, and k isChemical the Kinetics rate constant. 2009, Prentice-Hall, Inc. Rate Laws

A rate law shows the relationship between the reaction rate and the concentrations of reactants. The exponents tell the order of the reaction with respect to each reactant. Since the rate law is Rate = k [CNH ] [CNO2 ] the reaction is First-order in [CNH4+] and + 4 First-order in [CNO2].

Chemical Kinetics 2009, Prentice-Hall, Inc. Rate Laws Rate = k [CNH4+] [CNO2] The overall reaction order can be found by adding the exponents on the reactants in the rate law. This reaction is second-order overall. Chemical Kinetics 2009, Prentice-Hall, Inc. Integrated Rate Laws Using calculus to integrate the rate law

for a first-order process gives us Where [CA]t ln = kt [CA]0 [CA]0 is the initial concentration of A, and [CA]t is the concentration of A at some time, t, Chemical during the course of the reaction. Kinetics 2009, Prentice-Hall, Inc.

Integrated Rate Laws Manipulating this equation produces [CA]t ln [CA]0 = kt ln [CA]t ln [CA]0 = kt ln [CA]t = kt

which is in the form y + ln [CA]0 = mx + b Chemical Kinetics 2009, Prentice-Hall, Inc. First-Order Processes ln [CA]t = -kt + ln [CA]0 Therefore, if a reaction is first-order, a plot of ln [CA] vs. t will yield a straight

line, and the slope of the line will be -k. Chemical Kinetics 2009, Prentice-Hall, Inc. First-Order Processes Consider the process in which methyl isonitrile is converted to acetonitrile. CH3NC CH3CN Chemical

Kinetics 2009, Prentice-Hall, Inc. First-Order Processes CH3NC CH3CN This data was collected for this reaction at 198.9 C. Chemical Kinetics 2009, Prentice-Hall, Inc.

First-Order Processes When ln P is plotted as a function of time, a straight line results. Therefore, The process is first-order. k is the negative of the slope: 5.1 10-5 s1. Chemical Kinetics 2009, Prentice-Hall, Inc. Second-Order Processes Similarly, integrating the rate law for a process that is second-order in reactant A, we get

1 1 = kt + [CA]t [CA]0 y = mx + b also in the form Chemical Kinetics 2009, Prentice-Hall, Inc. Second-Order Processes 1 1 = kt +

[CA]t [CA]0 So if a process is second-order in A, a 1 plot of [A] vs. t will yield a straight line, and the slope of that line is k. Chemical Kinetics 2009, Prentice-Hall, Inc. Second-Order Processes The decomposition of NO2 at 300C is described by the equation 1 NO2 (g)

NO (g) + 2 O2 (g) and yields data comparable to this: Time (s) [CNO2], M 0.0 0.01000 50.0 0.00787 100.0

0.00649 200.0 0.00481 300.0 0.00380 Chemical Kinetics 2009, Prentice-Hall, Inc. Second-Order Processes Plotting ln [CNO2] vs. t yields the graph at the right.

The plot is not a straight line, so the process is not first-order in [CA]. Time (s) [CNO2], M ln [CNO2] 0.0 0.01000 4.610 50.0

0.00787 4.845 100.0 0.00649 5.038 200.0 0.00481 5.337

300.0 0.00380 5.573 Chemical Kinetics 2009, Prentice-Hall, Inc. Second-Order Processes 1 Graphing ln [NO ] vs. t, however,

gives this plot. 2 Time (s) [CNO2], M 1/[CNO2] 0.0 0.01000 100 50.0

0.00787 127 100.0 0.00649 154 200.0 0.00481 208

300.0 0.00380 263 Because this is a straight line, the process is secondorder in [CA]. Chemical Kinetics 2009, Prentice-Hall, Inc. Half-Life

Half-life is defined as the time required for one-half of a reactant to react. Because [CA] at t1/2 is one-half of the original [CA], [CA]t = 0.5 [CA]0. Chemical Kinetics 2009, Prentice-Hall, Inc. Half-Life For a first-order process, this becomes ln

0.5 [CA]0 = kt1/2 [CA]0 ln 0.5 = kt1/2 0.693 = kt1/2 NOTE: For a first-order process, then, the half-life does not depend on [CA]0. 0.693 = t1/2 k Chemical Kinetics 2009, Prentice-Hall, Inc.

Half-Life For a second-order process, 1 0.5 [CA]0 1 = kt1/2 + [CA]0 2 [CA]0 1 = kt1/2 + [CA]0

2 1 = 1 = kt 1/2 [CA] [CA]0 0 1 = t1/2 k[CA]0 Chemical Kinetics 2009, Prentice-Hall, Inc. Temperature and Rate Generally, as temperature

increases, so does the reaction rate. This is because k is temperature dependent. Chemical Kinetics 2009, Prentice-Hall, Inc. The Collision Model In a chemical reaction, bonds are broken and new bonds are formed. Molecules can only react if they collide with each other. Chemical

Kinetics 2009, Prentice-Hall, Inc. The Collision Model Furthermore, molecules must collide with the correct orientation and with enough energy to cause bond breakage and formation. Chemical Kinetics 2009, Prentice-Hall, Inc. Activation Energy In other words, there is a minimum amount of energy required for reaction: the activation energy, Ea. Just as a ball cannot get over a hill if it does not roll

up the hill with enough energy, a reaction cannot occur unless the molecules possess sufficient energy to get over the activation energy barrier. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Coordinate Diagrams It is helpful to visualize energy changes throughout a process on a reaction coordinate diagram like this

one for the rearrangement of methyl isonitrile. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Coordinate Diagrams The diagram shows the energy of the reactants and products (and, therefore, E). The high point on the diagram is the transition state. The species present at the transition state is

called the activated complex. The energy gap between the reactants and the activated complex is the activation energy barrier. Chemical Kinetics 2009, Prentice-Hall, Inc. MaxwellBoltzmann Distributions Temperature is defined as a measure of the average kinetic energy of the molecules in a

sample. At any temperature there is a wide distribution of kinetic energies. Chemical Kinetics 2009, Prentice-Hall, Inc. MaxwellBoltzmann Distributions As the temperature increases, the curve flattens and broadens. Thus at higher temperatures, a larger population of

molecules has higher energy. Chemical Kinetics 2009, Prentice-Hall, Inc. MaxwellBoltzmann Distributions If the dotted line represents the activation energy, then as the temperature increases, so does the fraction of molecules that can overcome the activation energy barrier. As a result, the reaction rate increases. Chemical

Kinetics 2009, Prentice-Hall, Inc. MaxwellBoltzmann Distributions This fraction of molecules can be found through the expression -E a f = e RT where R is the gas constant and T is the Kelvin temperature. Chemical Kinetics 2009, Prentice-Hall, Inc. Arrhenius Equation

Svante Arrhenius developed a mathematical relationship between k and Ea: -E a k = A e RT where A is the frequency factor, a number that represents the likelihood that collisions would occur with the proper orientation for reaction. Chemical Kinetics 2009, Prentice-Hall, Inc. Arrhenius Equation Taking the natural logarithm of both

sides, the equation becomes Ea 1 ln k = ( T ) + ln A R y = m x + b Therefore, if k is determined experimentally at several temperatures, Ea can be calculated

1 from the slope of a plot of ln k vs. T . Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Mechanisms The sequence of events that describes the actual process by which reactants become products is called the reaction mechanism. Chemical Kinetics

2009, Prentice-Hall, Inc. Reaction Mechanisms Reactions may occur all at once or through several discrete steps. Each of these processes is known as an elementary reaction or elementary process. Chemical Kinetics 2009, Prentice-Hall, Inc. Reaction Mechanisms The molecularity of a process tells how many

molecules are involved in the process. Chemical Kinetics 2009, Prentice-Hall, Inc. Multistep Mechanisms In a multistep process, one of the steps will be slower than all others. The overall reaction cannot occur faster than this slowest, rate-determining step. Chemical Kinetics 2009, Prentice-Hall, Inc.

Slow Initial Step NO2 (g) + CO (g) NO (g) + CO2 (g) The rate law for this reaction is found experimentally to be Rate = k [CNO2]2 CO is necessary for this reaction to occur, but the rate of the reaction does not depend on its concentration. This suggests the reaction occurs in two steps. Chemical Kinetics 2009, Prentice-Hall, Inc. Slow Initial Step A proposed mechanism for this reaction is Step 1: NO2 + NO2 NO3 + NO (slow)

Step 2: NO3 + CO NO2 + CO2 (fast) The NO3 intermediate is consumed in the second step. As CO is not involved in the slow, rate-determining step, it does not appear in the rate law. Chemical Kinetics 2009, Prentice-Hall, Inc. Fast Initial Step 2 NO (g) + Br2 (g) 2 NOBr (g) The rate law for this reaction is found to be Rate = k [CNO]2 [CBr2] Because termolecular processes are

rare, this rate law suggests a two-step mechanism. Chemical Kinetics 2009, Prentice-Hall, Inc. Fast Initial Step A proposed mechanism is Step 1: NO + Br2 NOBr2 (fast) Step 2: NOBr2 + NO 2 NOBr

(slow) Step 1 includes the forward and reverse reactions. Chemical Kinetics 2009, Prentice-Hall, Inc. Fast Initial Step The rate of the overall reaction depends upon the rate of the slow step. The rate law for that step would be Rate = k2 [CNOBr2] [CNO] But how can we find [CNOBr2]? Chemical

Kinetics 2009, Prentice-Hall, Inc. Fast Initial Step NOBr2 can react two ways: With NO to form NOBr By decomposition to reform NO and Br2 The reactants and products of the first step are in equilibrium with each other. Therefore, Ratef = Rater Chemical Kinetics 2009, Prentice-Hall, Inc.

Fast Initial Step Because Ratef = Rater , k1 [CNO] [CBr2] = k1 [CNOBr2] Solving for [CNOBr2] gives us k1 [CNO] [CBr2] = [CNOBr2] k1 Chemical Kinetics 2009, Prentice-Hall, Inc. Fast Initial Step Substituting this expression for [CNOBr2] in the rate law for the rate-determining step gives Rate =

k2k1 [CNO] [CBr2] [CNO] k1 = k [CNO]2 [CBr2] Chemical Kinetics 2009, Prentice-Hall, Inc. Catalysts Catalysts increase the rate of a reaction by decreasing the activation energy of the reaction. Catalysts change the mechanism by which the process occurs.

Chemical Kinetics 2009, Prentice-Hall, Inc. Catalysts One way a catalyst can speed up a reaction is by holding the reactants together and helping bonds to break. Chemical Kinetics

2009, Prentice-Hall, Inc. Enzymes Enzymes are catalysts in biological systems. The substrate fits into the active site of the enzyme much like a key fits into a lock. Chemical Kinetics 2009, Prentice-Hall, Inc.