Chemical Kinetics

21 downloads 16674 Views 954KB Size Report
Chemistry, The Central Science, 11th edition. Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten. Chemical. Kinetics. © 2009, Prentice-Hall, Inc.
aa 2013-14

Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten

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.

1

aa 2013-14

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.

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.

2

aa 2013-14

Reaction Rates C4H9Cl(aq) + H2O(l) ⎯⎯→ C4H9OH(aq) + HCl(aq) •  A plot of [C4H9Cl] 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 •  To generalize, then, for the reaction aA + bB

cC + dD

1 Δ[B] 1 Δ[D] 1 Δ[A] 1 Δ[C] =− Rate = − a b Δt = c Δt = d Δt Δt

Chemical Kinetics © 2009, Prentice-Hall, Inc.

3

aa 2013-14

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 [NH4+] 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 [NO2−] doubles, the initial rate doubles. Chemical Kinetics © 2009, Prentice-Hall, Inc.

4

aa 2013-14

Concentration and Rate •  This means Rate ∝ [NH4+] Rate ∝ [NO2−] Therefore, Rate ∝ [NH4+] [NO2−] which, when written as an equation, becomes Rate = k [NH4+] [NO2−] •  This equation is called the rate law, and k is the rate constant. Chemical Kinetics © 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 [NH4+] [NO2−] the reaction is First-order in [NH4+] and Chemical First-order in [NO2−]. Kinetics © 2009, Prentice-Hall, Inc.

Rate Laws Rate = k [NH4+] [NO2−] •  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.

5

aa 2013-14

Integrated Rate Laws Using calculus to integrate the rate law for a first-order process gives us ln

[A]t = −kt [A]0

Where [A]0 is the initial concentration of A, and [A]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… ln

[A]t = −kt [A]0

ln [A]t − ln [A]0 =

− kt

ln [A]t =

− kt

…which is in the form

y

+ ln [A]0

= mx + b Chemical Kinetics © 2009, Prentice-Hall, Inc.

First-Order Processes ln [A]t = -kt + ln [A]0

Therefore, if a reaction is first-order, a plot of ln [A] vs. t will yield a straight line, and the slope of the line will be -k.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

6

aa 2013-14

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 s−1.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

7

aa 2013-14

Second-Order Processes Similarly, integrating the rate law for a process that is second-order in reactant A, we get 1 1 = kt + [A]t [A]0

also in the form

y = mx + b Chemical Kinetics © 2009, Prentice-Hall, Inc.

Second-Order Processes 1 1 = kt + [A]t [A]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.

Half-Life •  Half-life is defined as the time required for one-half of a reactant to react. •  Because [A] at t1/2 is one-half of the original [A], [A]t = 0.5 [A]0. Chemical Kinetics © 2009, Prentice-Hall, Inc.

8

aa 2013-14

Half-Life For a first-order process, this becomes ln

0.5 [A]0 = −kt1/2 [A]0 ln 0.5 = −kt1/2 −0.693 = −kt1/2

NOTE: For a first-order process, then, the half-life does not depend on [A]0.

0.693 = t1/2 k Chemical Kinetics © 2009, Prentice-Hall, Inc.

Half-Life For a second-order process, 1 1 = kt1/2 + [A]0 0.5 [A]0 1 2 = kt1/2 + [A]0 [A]0 2 − 1 = 1 = kt 1/2 [A]0 [A]0 1 = t1/2 k[A]0

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.

9

aa 2013-14

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.

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.

10

aa 2013-14

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, ΔE). •  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.

11

aa 2013-14

Maxwell–Boltzmann 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.

Maxwell–Boltzmann 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.

Maxwell–Boltzmann 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.

12

aa 2013-14

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.

13

aa 2013-14

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.

14

aa 2013-14

Chemistry, The Central Science, 11th edition Theodore L. Brown, H. Eugene LeMay, Jr., and Bruce E. Bursten

Chemical Equilibrium

John D. Bookstaver St. Charles Community College Cottleville, MO

Chemical Kinetics © 2009, Prentice-Hall, Inc.

The Concept of Equilibrium

Chemical equilibrium occurs when a reaction and its reverse reaction proceed at the same rate.

Chemical Kinetics

© 2009, Prentice-Hall, Inc.

The Concept of Equilibrium •  As a system approaches equilibrium, both the forward and reverse reactions are occurring. •  At equilibrium, the forward and reverse reactions are proceeding at the same rate. Chemical Kinetics © 2009, Prentice-Hall, Inc.

15

aa 2013-14

A System at Equilibrium Once equilibrium is achieved, the amount of each reactant and product remains constant.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

Depicting Equilibrium Since, in a system at equilibrium, both the forward and reverse reactions are being carried out, we write its equation with a double arrow. N2O4 (g)

2 NO2 (g)

Chemical Kinetics © 2009, Prentice-Hall, Inc.

The Equilibrium Constant Chemical Kinetics © 2009, Prentice-Hall, Inc.

16

aa 2013-14

The Equilibrium Constant •  Forward reaction: N2O4 (g) ⎯⎯→ 2 NO2 (g)

•  Rate Law: Rate = kf [N2O4]

Chemical Kinetics © 2009, Prentice-Hall, Inc.

The Equilibrium Constant •  Reverse reaction: 2 NO2 (g) ⎯⎯→ N2O4 (g)

•  Rate Law: Rate = kr [NO2]2

Chemical Kinetics © 2009, Prentice-Hall, Inc.

The Equilibrium Constant •  Therefore, at equilibrium Ratef = Rater kf [N2O4] = kr [NO2]2 •  Rewriting this, it becomes

kf [NO2]2 = kr [N2O4] Chemical Kinetics © 2009, Prentice-Hall, Inc.

17

aa 2013-14

The Equilibrium Constant The ratio of the rate constants is a constant at that temperature, and the expression becomes

Keq =

kf kr

=

[NO2]2 [N2O4] Chemical Kinetics © 2009, Prentice-Hall, Inc.

The Equilibrium Constant •  Consider the generalized reaction aA + bB

cC + dD

•  The equilibrium expression for this reaction would be

Kc =

[C]c[D]d [A]a[B]b

Chemical Kinetics © 2009, Prentice-Hall, Inc.

The Equilibrium Constant Since pressure is proportional to concentration for gases in a closed system, the equilibrium expression can also be written

Kp =

(PCc) (PDd) (PAa) (PBb) Chemical Kinetics © 2009, Prentice-Hall, Inc.

18

aa 2013-14

Relationship Between Kc and Kp •  From the Ideal Gas Law we know that

PV = nRT •  Rearranging it, we get

P=

n RT V Chemical Kinetics © 2009, Prentice-Hall, Inc.

Relationship Between Kc and Kp Plugging this into the expression for Kp for each substance, the relationship between Kc and Kp becomes

Kp = Kc (RT)Δn where Δn = (moles of gaseous product) - (moles of gaseous reactant) Chemical Kinetics © 2009, Prentice-Hall, Inc.

Equilibrium Can Be Reached from Either Direction

As you can see, the ratio of [NO2]2 to [N2O4] remains constant at this temperature no matter what the initial concentrations of NO2 and N2O4 are.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

19

aa 2013-14

Equilibrium Can Be Reached from Either Direction This is the data from the last two trials from the table on the previous slide.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

Equilibrium Can Be Reached from Either Direction

It doesn’t matter whether we start with N2 and H2 or whether we start with NH3: we will have the same proportions of all three substances at equilibrium. Chemical Kinetics © 2009, Prentice-Hall, Inc.

What Does the Value of K Mean? •  If K>>1, the reaction is product-favored; product predominates at equilibrium.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

20

aa 2013-14

What Does the Value of K Mean? •  If K>>1, the reaction is product-favored; product predominates at equilibrium.

•  If K 0 Chemical Kinetics © 2009, Prentice-Hall, Inc.

28

aa 2013-14

Second Law of Thermodynamics These last truths mean that as a result of all spontaneous processes the entropy of the universe increases.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

Entropy Changes •  In general, entropy increases when –  Gases are formed from liquids and solids; –  Liquids or solutions are formed from solids; –  The number of gas molecules increases; –  The number of moles increases.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

Third Law of Thermodynamics The entropy of a pure crystalline substance at absolute zero is 0.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

29

aa 2013-14

Standard Entropies •  These are molar entropy values of substances in their standard states. •  Standard entropies tend to increase with increasing molar mass. Chemical Kinetics © 2009, Prentice-Hall, Inc.

Free Energy Changes At temperatures other than 25°C, ΔG° = ΔH° - TΔS° How does ΔG° change with temperature?

Chemical Kinetics © 2009, Prentice-Hall, Inc.

Gibbs Free Energy 1.  If ΔG < 0, the forward reaction is spontaneous. 2.  If ΔG=0 , the system is at equilibrium. 3.  If ΔG >0, the reaction is spontaneous in the reverse direction. Chemical Kinetics © 2009, Prentice-Hall, Inc.

30

aa 2013-14

Standard Free Energy Changes Analogous to standard enthalpies of formation are standard free energies of formation, ΔG°. f ΔG° = ΣnΔG°f (products) - ΣmΔG° (reactants) f where n and m are the stoichiometric coefficients.

Chemical Kinetics © 2009, Prentice-Hall, Inc.

31