Chemistry, The Central Science, 11th edition. Theodore L. Brown; H. Eugene
LeMay, Jr.; and Bruce E. Bursten. Chemical. Kinetics. © 2009, Prentice-Hall, Inc.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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