Kinetics-chemical
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Chemical Kinetics The area of chemistry that concerns reaction rates.
Reaction Rate Change in concentration (conc) of a reactant or product per unit time. conc of A at time t2 − conc of A at time t1 Rate = t2 − t1 ∆A = ∆t
12_291
0.0100
NO 2
Concentrations (mol/L)
0.0075
0.0026
∆[NO 2 ] 0.0006 70s
∆t 110 s
0.005
NO
0.0003 70s
0.0025 O2
50
100
150
200
Time (s)
250
300
350
400
12_1575
Time
(a)
Time
(b)
(c)
Rate Laws Rate = k[NO2]n k = rate constant n = rate order
Types of Rate Laws Differential Rate Law: expresses how rate depends on concentration. Integrated Rate Law: expresses how concentration depends on time.
C4H9Cl + H2O → C4H9OH + HCl
Method of Initial Rates Initial Rate: the “instantaneous rate” just after the reaction begins. The initial rate is determined in several experiments using different initial concentrations.
NH4+(aq) + NO2-(aq) → N2(g) 2H2O(l)
Overall Reaction Order Sum of the order of each component in the rate law. rate = k[H2SeO3][H+]2[I−]3 The overall reaction order is 1 + 2 + 3 = 6.
2ClO2 + 2OH- → ClO3- + ClO2- + H2O Experiment [ClO2] M
[OH-] M
Rate, M s-1
1 2 3
0.030 0.030 0.090
0.0248 0.00276 0.00828
0.060 0.020 0.020
1. Determine the rate law for the reaction. 2. Calculate the rate constant. 3. What is the overall reaction order?
ICA
First-Order Rate Law For aA → Products in a 1st-order reaction, −∆ A Rate = =k A ∆t Integrated first-order rate law is ln[A] = −kt + ln[A]o
CH3NC → CH3CN Conversion of methyl isonitrile to acetonitrile
Half-Life of a First-Order Reaction t1/2
0.693 = k
t1/2 = half-life of the reaction k = rate constant For a first-order reaction, the half-life does not depend on concentration.
Half-Life of a First Order Rx 12_294
[N2O5]0
0.1000 0.0900
[N2O5] (mol/L)
0.0800 0.0700 0.0600
[N2O5]0 2
[N2O5]0 4
[N2O5]0 8
0.0500 0.0400 0.0300 0.0200 0.0100 50 t1/2
100
150
200
t1/2
250 t1/2
Time (s)
300
350
400
O (g) + NO2 (g) → NO (g) + O2 (g) P se u d o -F irst O rd e r R ate L aw s
ln [O]
y = -1 0 0 .1 5 x + 2 2 .3 4 5 2 3 .0 0 2 2 .0 0 2 1 .0 0 2 0 .0 0 1 9 .0 0 0
0 .0 1
0 .0 2 tim e (s )
0 .0 3
0 .0 4
Types of Radioactive Decay alpha production (α ): helium nucleus42 He 238 4 92 U → 2 He
+
234 90Th
beta production (β ):−10 e 234 234 90Th → 91Pa
+
0 −1e
Types of Radioactive Decay gamma ray production (γ ): 238 4 92 U → 2 He
+
234 90Th
High energy photon
0 + 20 γ
Decay Series A radioactive nucleus reaches a stable state by a series of steps. series of decays 208 232 → 82 Pb 90Th
21_475
202 80
120
Unstable region (too many neutrons; spontaneous beta production) e
80
St zo able ne n of ucli s t a de bil s in i ty t h
Number of neutrons (A–Z)
100
60
40
1 1:
n ro t u ne
n to o pr -to
tio a r
Cd (1.29:1 ratio) 110 48
Unstable region (too many protons; spontaneous positron production)
20 6 3
0
Hg (1.53:1 ratio)
0
20
Li (1:1 ratio) 40 60 80 Number of protons (Z)
100
21_476
U
238 236
Th
234
Pa
U
232 Th
230 Mass number (A)
228 Ra
226 224 Rn
222 220 Po
218 216
Pb Bi Po
214 212 210
Pb
Bi
Po
208 206 204
Pb 0
82 83 84 85 86 87 88 89 90 91 92 93 Atomic number (Z)
Rate of Decay rate = kN The rate of decay is proportional to the number of nuclides. This represents a firstorder process.
Decay of Strontium-90 21_477
10.0
1 halflife
6.0
90
Mass of38 Sr (g)
8.0
4.0
2 halflives 3 halflives
2.0
0
20 t1/ 2 = 2 8.8
40
60
t1/2 = 2 8.8
80
t 1/2 = 2 8.8
Time (yr)
4 halflives 100
t 1/ 2 = 2 8.8
120
Radioactive Decay
Second-Order Rate Law For aA → products in a second-order reaction, −∆ A Rate = =k A 2 ∆t Integrated rate law is 1 1 = kt + A Ao
Half-Life of a Second-Order Reaction t1/2
1 = kA
o
t1/2 = half-life of the reaction k = rate constant Ao = initial concentration of A
The half-life is dependent upon the initial concentration.
Zero Order Rate Laws Rate = k [A]0 Integrated Form [A] = -kt + [A]o
A Summary 1. Simplification: Conditions are set such that only forward reaction is important. 2. Two types: differential rate law integrated rate law 3. Which type? Depends on the type of data collected - differential and integrated forms can be interconverted.
A Summary (continued)
4. Most common: method of initial rates. 5. Concentration v. time: used to determine integrated rate law, often graphically. 6. For several reactants: choose conditions under which only one reactant varies significantly (pseudo n-order conditions).
12_06T
Table 12.6 Summary of the Kinetics for Reactions of the Type aA → Products That Are Zero, First, or Second Order in [A] Order Zero
First
Second
Rate = k
Rate = k[A]
[A] = -kt + [A]0
ln[A] = -kt + ln[A]0
Plot needed to give a straight line
[A] versus t
ln[A] versus t
Relationship of rate constant to the slope of straight line
Rate = k[A]2 1 1 = kt + [A] [A]0 1 versus t [A]
Slope = -k
Slope = -k
Rate law Integrated rate law
Half-life
t1/2 =
[A]0 2k
t1/2 =
0.693 k
Slope = k t1/2 =
1 k[A]0
Reaction Mechanism - The series of steps by which a chemical reaction occurs. - A chemical equation does not tell us how reactants become products - it is a summary of the overall process.
Reaction Mechanism (continued)
-
The reaction
O3 + O → 2O2 has several steps in the reaction mechanism.
Often Used Terms Intermediate: formed in one step and used up in a subsequent step and so is never seen as a product. Molecularity: the number of species that must collide to produce the reaction indicated by that step. Elementary Step: A reaction whose rate law can be written from its molecularity. uni, bi and termolecular
Rate-Determining Step In a multistep reaction, it is the slowest step. It therefore determines the rate of reaction.
Collision Model Key Idea: Molecules must collide to react. However, only a small fraction of collisions produces a reaction. Why? Arrhenius: An activation energy must be overcome.
Arrhenius Equation -
Collisions must have enough energy to produce the reaction (must equal or exceed the activation energy).
-
Orientation of reactants must allow formation of new bonds.
Temperature and Ea 12_300
T1 T2 > T 1 T2
0
0 Energy
Ea
Arrhenius Equation (continued)
k = Ae k = rate constant A = frequency factor Ea = activation energy T = temperature R = gas constant
− Ea / RT
Catalysis Catalyst: A substance that speeds up a reaction without being consumed Enzyme: A large molecule (usually a protein) that catalyzes biological reactions. Homogeneous catalyst: Present in the same phase as the reacting molecules. Heterogeneous catalyst: Present in a different phase than the reacting molecules.
Lower Ea for Catalyzed Rx 12_303
Energy
Uncatalyzed pathway Catalyzed pathway Products ∆E Reactants Reaction progress
Heterogeneous Catalysis Steps: 1. Adsorption and activation of the reactants. 2. Migration of the adsorbed reactants on the surface. 3. Reaction of the adsorbed substances. 4. Escape, or desorption, of the products.
END
Reaction Rate Change in concentration (conc) of a reactant or product per unit time. conc of A at time t2 − conc of A at time t1 Rate = t2 − t1 ∆A = ∆t
12_291
0.0100
NO 2
Concentrations (mol/L)
0.0075
0.0026
∆[NO 2 ] 0.0006 70s
∆t 110 s
0.005
NO
0.0003 70s
0.0025 O2
50
100
150
200
Time (s)
250
300
350
400
12_1575
Time
(a)
Time
(b)
(c)
Rate Laws Rate = k[NO2]n k = rate constant n = rate order
Types of Rate Laws Differential Rate Law: expresses how rate depends on concentration. Integrated Rate Law: expresses how concentration depends on time.
C4H9Cl + H2O → C4H9OH + HCl
Method of Initial Rates Initial Rate: the “instantaneous rate” just after the reaction begins. The initial rate is determined in several experiments using different initial concentrations.
NH4+(aq) + NO2-(aq) → N2(g) 2H2O(l)
Overall Reaction Order Sum of the order of each component in the rate law. rate = k[H2SeO3][H+]2[I−]3 The overall reaction order is 1 + 2 + 3 = 6.
2ClO2 + 2OH- → ClO3- + ClO2- + H2O Experiment [ClO2] M
[OH-] M
Rate, M s-1
1 2 3
0.030 0.030 0.090
0.0248 0.00276 0.00828
0.060 0.020 0.020
1. Determine the rate law for the reaction. 2. Calculate the rate constant. 3. What is the overall reaction order?
ICA
First-Order Rate Law For aA → Products in a 1st-order reaction, −∆ A Rate = =k A ∆t Integrated first-order rate law is ln[A] = −kt + ln[A]o
CH3NC → CH3CN Conversion of methyl isonitrile to acetonitrile
Half-Life of a First-Order Reaction t1/2
0.693 = k
t1/2 = half-life of the reaction k = rate constant For a first-order reaction, the half-life does not depend on concentration.
Half-Life of a First Order Rx 12_294
[N2O5]0
0.1000 0.0900
[N2O5] (mol/L)
0.0800 0.0700 0.0600
[N2O5]0 2
[N2O5]0 4
[N2O5]0 8
0.0500 0.0400 0.0300 0.0200 0.0100 50 t1/2
100
150
200
t1/2
250 t1/2
Time (s)
300
350
400
O (g) + NO2 (g) → NO (g) + O2 (g) P se u d o -F irst O rd e r R ate L aw s
ln [O]
y = -1 0 0 .1 5 x + 2 2 .3 4 5 2 3 .0 0 2 2 .0 0 2 1 .0 0 2 0 .0 0 1 9 .0 0 0
0 .0 1
0 .0 2 tim e (s )
0 .0 3
0 .0 4
Types of Radioactive Decay alpha production (α ): helium nucleus42 He 238 4 92 U → 2 He
+
234 90Th
beta production (β ):−10 e 234 234 90Th → 91Pa
+
0 −1e
Types of Radioactive Decay gamma ray production (γ ): 238 4 92 U → 2 He
+
234 90Th
High energy photon
0 + 20 γ
Decay Series A radioactive nucleus reaches a stable state by a series of steps. series of decays 208 232 → 82 Pb 90Th
21_475
202 80
120
Unstable region (too many neutrons; spontaneous beta production) e
80
St zo able ne n of ucli s t a de bil s in i ty t h
Number of neutrons (A–Z)
100
60
40
1 1:
n ro t u ne
n to o pr -to
tio a r
Cd (1.29:1 ratio) 110 48
Unstable region (too many protons; spontaneous positron production)
20 6 3
0
Hg (1.53:1 ratio)
0
20
Li (1:1 ratio) 40 60 80 Number of protons (Z)
100
21_476
U
238 236
Th
234
Pa
U
232 Th
230 Mass number (A)
228 Ra
226 224 Rn
222 220 Po
218 216
Pb Bi Po
214 212 210
Pb
Bi
Po
208 206 204
Pb 0
82 83 84 85 86 87 88 89 90 91 92 93 Atomic number (Z)
Rate of Decay rate = kN The rate of decay is proportional to the number of nuclides. This represents a firstorder process.
Decay of Strontium-90 21_477
10.0
1 halflife
6.0
90
Mass of38 Sr (g)
8.0
4.0
2 halflives 3 halflives
2.0
0
20 t1/ 2 = 2 8.8
40
60
t1/2 = 2 8.8
80
t 1/2 = 2 8.8
Time (yr)
4 halflives 100
t 1/ 2 = 2 8.8
120
Radioactive Decay
Second-Order Rate Law For aA → products in a second-order reaction, −∆ A Rate = =k A 2 ∆t Integrated rate law is 1 1 = kt + A Ao
Half-Life of a Second-Order Reaction t1/2
1 = kA
o
t1/2 = half-life of the reaction k = rate constant Ao = initial concentration of A
The half-life is dependent upon the initial concentration.
Zero Order Rate Laws Rate = k [A]0 Integrated Form [A] = -kt + [A]o
A Summary 1. Simplification: Conditions are set such that only forward reaction is important. 2. Two types: differential rate law integrated rate law 3. Which type? Depends on the type of data collected - differential and integrated forms can be interconverted.
A Summary (continued)
4. Most common: method of initial rates. 5. Concentration v. time: used to determine integrated rate law, often graphically. 6. For several reactants: choose conditions under which only one reactant varies significantly (pseudo n-order conditions).
12_06T
Table 12.6 Summary of the Kinetics for Reactions of the Type aA → Products That Are Zero, First, or Second Order in [A] Order Zero
First
Second
Rate = k
Rate = k[A]
[A] = -kt + [A]0
ln[A] = -kt + ln[A]0
Plot needed to give a straight line
[A] versus t
ln[A] versus t
Relationship of rate constant to the slope of straight line
Rate = k[A]2 1 1 = kt + [A] [A]0 1 versus t [A]
Slope = -k
Slope = -k
Rate law Integrated rate law
Half-life
t1/2 =
[A]0 2k
t1/2 =
0.693 k
Slope = k t1/2 =
1 k[A]0
Reaction Mechanism - The series of steps by which a chemical reaction occurs. - A chemical equation does not tell us how reactants become products - it is a summary of the overall process.
Reaction Mechanism (continued)
-
The reaction
O3 + O → 2O2 has several steps in the reaction mechanism.
Often Used Terms Intermediate: formed in one step and used up in a subsequent step and so is never seen as a product. Molecularity: the number of species that must collide to produce the reaction indicated by that step. Elementary Step: A reaction whose rate law can be written from its molecularity. uni, bi and termolecular
Rate-Determining Step In a multistep reaction, it is the slowest step. It therefore determines the rate of reaction.
Collision Model Key Idea: Molecules must collide to react. However, only a small fraction of collisions produces a reaction. Why? Arrhenius: An activation energy must be overcome.
Arrhenius Equation -
Collisions must have enough energy to produce the reaction (must equal or exceed the activation energy).
-
Orientation of reactants must allow formation of new bonds.
Temperature and Ea 12_300
T1 T2 > T 1 T2
0
0 Energy
Ea
Arrhenius Equation (continued)
k = Ae k = rate constant A = frequency factor Ea = activation energy T = temperature R = gas constant
− Ea / RT
Catalysis Catalyst: A substance that speeds up a reaction without being consumed Enzyme: A large molecule (usually a protein) that catalyzes biological reactions. Homogeneous catalyst: Present in the same phase as the reacting molecules. Heterogeneous catalyst: Present in a different phase than the reacting molecules.
Lower Ea for Catalyzed Rx 12_303
Energy
Uncatalyzed pathway Catalyzed pathway Products ∆E Reactants Reaction progress
Heterogeneous Catalysis Steps: 1. Adsorption and activation of the reactants. 2. Migration of the adsorbed reactants on the surface. 3. Reaction of the adsorbed substances. 4. Escape, or desorption, of the products.
END
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