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Chemistry

CHEM 1AA3

Jeff Landry

Fall

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CHEM 1AA3: Intro. Chemistry II
Chapter 14:
Chemical Kinetics
Chem 1AA3Chem 1AA3
2
Preface
The 3 big questions in any chemical reaction:
(1) What are the products?
(2) What is the equilibrium position?
A
G
H
J
?
?
? Chem 1AA3Chem 1AA3
3
Preface
(3) How fast is the reaction?
Chem 1AA3Chem 1AA3
3
Preface
(3) How fast is the reaction?
Chem 1AA3Chem 1AA3
4
Preface
Why we measure rates:
(1) predict/control reactions:
-industrial syntheses-environmental reactions (e.g., smog formation, ozonelayer breakdown)
(2) monitor biological or chemical systems:
-clinical diagnostics (e.g., liver damage)
-polymerization (e.g. strength of plastics) Chem 1AA3Chem 1AA3
5
Preface
(3) understand reaction mechanisms:
-reaction order (e.g., SN1 vs SN2)
-structure/function relationships (e.g. rate vs. leaving
group ability in SN2)
(4) tell the temperature:
-count rate of crickets chirping:
T (°C) = 4
3
s25inchirps# +
Chem 1AA3Chem 1AA3
6
14-1. The rate of a chemical reaction
• rate = change in concentration of reactants and products
over time
•e.g.
A . (1)
• 1 min after starting reaction, [G] = 1 M
• What is the rate of the reaction over 1 min?
Chem 1AA3Chem 1AA3
5
Preface
(3) understand reaction mechanisms:
-reaction order (e.g., SN1 vs SN2) -structure/function relationships (e.g. rate vs. leaving
group ability in SN2)
(4) tell the temperature:
-count rate of crickets chirping:
T (°C) = 4
3
s25inchirps# +
Chem 1AA3Chem 1AA3
6
14-1. The rate of a chemical reaction
• rate = change in concentration of reactants and products
over time
•e.g.
A . (1)
• 1 min after starting reaction, [G] = 1 M
• What is the rate of the reaction over 1 min? Chem 1AA3Chem 1AA3
7
14-1. The rate of a chemical reaction
• average rate = 1 M / 1 min.
time (min)
0.0 0.5 1.0 1.5 2.0
[G]
(M)
0.0
0.5
1.0
1.5
2.0
.t = 1 min
.[G] = 1 M
A . G
Chem 1AA3Chem 1AA3
7
14-1. The rate of a chemical reaction
• average rate = 1 M / 1 min.
time (min)
0.0 0.5 1.0 1.5 2.0
[G]
(M)
0.0
0.5 1.0
1.5
2.0
.t = 1 min
.[G] = 1 M
A . G
Chem 1AA3Chem 1AA3
8
14-1. The rate of a chemical reaction
(2)
• rates are always positive
.put a negative sign in front of [A]:
(3)
• stoichiometry is important:
A . 2G (4)
(5)
.t
.[G]rateaverage =
.t
.[A]-rateaverage =
.t
.[G]
2
1
.t
.[A]-rateaverage == Chem 1AA3Chem 1AA3
9
14-1. The rate of a chemical reaction
• In general:
aA + bB .gG + hH (6, 14.5)
(7, 14.2)
• Key concepts:
-rate is change in concentration over time
-rates are always positive
-stoichiometry matters
t
[H]1
t
[G]1
t
[B]1 -
t
[A]1 -rateaverage
..=
..=
..=
..=
hgba
Chem 1AA3Chem 1AA3
9
14-1. The rate of a chemical reaction • In general:
aA + bB .gG + hH (6, 14.5)
(7, 14.2)
• Key concepts:
-rate is change in concentration over time
-rates are always positive
-stoichiometry matters
t
[H]1
t
[G]1
t
[B]1 -
t
[A]1 -rateaverage
..=
..=
..=
..=
hgba
Chem 1AA3Chem 1AA3
10
14-2. Measuring reaction rates
• The food colouring expt showed that rate can change
during a reaction.
• Many reactions could give an average rate of 1 M/min for 1 min.
time (min)
0.0 0.5 1.0 1.5 2.0
[G] (
M)
0.0
0.5
1.0
1.5
2.0
.t = 1 min
.[G] = 1 M 14-2. Measuring reaction rates
0.0 0.5 1.0 1.5 2.0
[G] (M)
0.0
0.5
1.0
1.5
2.0
14-2. Measuring reaction rates
0.0 0.5 1.0 1.5 2.0
[G] (M)
0.0
0.5
1.0
1.5
2.0
time (min)
• average rate = 1 M/min over 1 min for all 3 curves
• average rate provides limited information
Chem 1AA3Chem 1AA3
11
Chem 1AA3Chem 1AA3
12
• instantaneous rate (v):
– the exact reaction rate at a defined time • v = tangent to the line when plotting [G] vs. time.
14-2. Measuring reaction rates
time (min)
0.0 0.5 1.0 1.5 2.0
[G] (M)
0.0
0.5
1.0
1.5
2.0
v = 0.69 M/min
@ t = 1 min Chem 1AA3Chem 1AA3
13
14-2. Measuring reaction rates
• measuring .[A] or .[G] over a finite time interval, .t,
gives the average rate
• we want the instantaneous rate, v, the rate over an
infinitely short time interval
• taking an infinitely short time interval is the same as
differentiating an equation in calculus
(N.B. -"v" is an italicized letter vee (not the Greek letter nu). "v" comes from
velocity, the other common term for rate. The textbook just writes out "rate
of reaction" every time.)
Chem 1AA3Chem 1AA3
13
14-2. Measuring reaction rates
• measuring .[A] or .[G] over a finite time interval, .t,
gives the average rate
• we want the instantaneous rate, v, the rate over an
infinitely short time interval
• taking an infinitely short time interval is the same as
differentiating an equation in calculus
(N.B. -"v" is an italicized letter vee (not the Greek letter nu). "v" comes from
velocity, the other common term for rate. The textbook just writes out "rate
of reaction" every time.)
Chem 1AA3Chem 1AA3
14 14-2. Measuring reaction rates
(7, 14.2)
(8)
t
[G]1rateaverage
..=
g
dt
d[G]1
.t
.[G]1
0 ggt
lim
=
..=v Chem 1AA3Chem 1AA3
15
Average vs. instantaneous rate
• Experimental rates:
-always average rates
-we want instantaneous rates
• What can we do to ensure that experimentally observed
rates are as close as possible to instantaneous rates?
– measure .[A] over the shortest possible .t
– measure average rate as close as possible to t = 0
Chem 1AA3Chem 1AA3
15
Average vs. instantaneous rate
• Experimental rates:
-always average rates
-we want instantaneous rates
• What can we do to ensure that experimentally observed
rates are as close as possible to instantaneous rates?
– measure .[A] over the shortest possible .t
– measure average rate as close as possible to t = 0
Chem 1AA3Chem 1AA3
16
Average vs. instantaneous rate
• e.g., food colouring expt:
(Data from Berti section.)
time (s) 0 50 100 150 200
[red]
(mM)
0.0
0.2
0.4
0.6
0.8
1.0
time (s)
0 5 10 15 20 25
[red] (mM)
0.0
0.2
0.4
0.6
0.8
1.0 Chem 1AA3Chem 1AA3
17
Average vs. instantaneous rate
0.0280.4420
0.0320.6810
0.0400.922
0.0400.961
1.000
(mM/s)(mM)(s)
calculated
average rate
calc'd
[red]time
v0 = 0.041 mM/s
(Data from Berti section.)
Chem 1AA3Chem 1AA3
17
Average vs. instantaneous rate
0.0280.4420
0.0320.6810
0.0400.922
0.0400.961
1.000
(mM/s)(mM)(s)
calculated
average rate calc'd
[red]time
v0 = 0.041 mM/s
(Data from Berti section.)
Chem 1AA3Chem 1AA3
18
14-2. Measuring reaction rates
• initial rate is v0
– rate at t = 0
– when discussing enzymatic reactions, we use v0
almost exclusively:
• avoids complications from reactant depletion, product
inhibition, equilibrium effects, enzyme inactivation over
time. Chem 1AA3Chem 1AA3
19
14-2. Measuring reaction rates
Key concepts:
– want to know instantaneous rates
– experimental rates are average rates
– to approach instantaneous rates experimentally, use
short measurement times & measure rates near t = 0
– use initial rates for enzymatic reactions
Chem 1AA3Chem 1AA3
19
14-2. Measuring reaction rates
Key concepts:
– want to know instantaneous rates
– experimental rates are average rates
– to approach instantaneous rates experimentally, use
short measurement times & measure rates near t = 0
– use initial rates for enzymatic reactions
Chem 1AA3Chem 1AA3
20
PH
Formative iClicker Question #18
For the following reaction, which statement is correct?
(a) avg. rate = .O2/.t
(b) avg. rate = .H2O/.t
(c) avg. rate = -½ × .O2/.t (d) avg. rate = -2 × .O2/.t
CH4 + 2 O2 CO2 + 2 H2O Chem 1AA3Chem 1AA3
21
PB
Formative iClicker Question #18
For the following reaction, which statement is not correct?
(a) v = ½ × dO2/dt
(b) v = ½ × dH2O/dt
(c) v = -dCH4/dt
(d) v = dCO2/dt
CH4 + 2 O2 CO2 + 2 H2O
Chem 1AA3Chem 1AA3
21
PB
Formative iClicker Question #18
For the following reaction, which statement is not correct?
(a) v = ½ × dO2/dt
(b) v = ½ × dH2O/dt
(c) v = -dCH4/dt
(d) v = dCO2/dt
CH4 + 2 O2 CO2 + 2 H2O
Chem 1AA3Chem 1AA3
22
JV
Formative iClicker Question #18
For the following reaction, which statement is correct?
(a) v = dNH3/dt (b) v = ½ × dNH3/dt
(c) v = 2 × dNH3/dt
(d) v = dN2/dt
N2 + 3 H2 2 NH3 Chem 1AA3Chem 1AA3
23
HS
Formative iClicker Question #18
For the following reaction, which statement is not correct?
(a) avg. rate = .N2/.t
(b) avg. rate = -1/3 × .H2/.t
(c) avg. rate = ½ × .NH3/.t
(d) v = ½ × dNH3/dt
N2 + 3 H2 2 NH3
Chem 1AA3Chem 1AA3
23
HS
Formative iClicker Question #18
For the following reaction, which statement is not correct?
(a) avg. rate = .N2/.t
(b) avg. rate = -1/3 × .H2/.t
(c) avg. rate = ½ × .NH3/.t
(d) v = ½ × dNH3/dt
N2 + 3 H2 2 NH3
14-3. Effect of concentration on reaction
rates: The rate law
• in the food colouring experiment,
v0 .[A]:
0.0 0.5 1.0 1.5 2.0
v0 (M/min)
0.0
1.0
2.0
3.0
4.0
[A] (M)
Chem 1AA3Chem 1AA3
24 14-3. Effect of concentration on reaction rates: The rate law
• v0 = constant is also possible
4.0
v0
(M/min)
3.0
2.0
1.0
0.0
0.0 0.5 1.0 1.5 2.0
[A] (M)
Chem 1AA3Chem 1AA3
25
Chem 1AA3Chem 1AA3
26
14-3. Effect of concentration on reaction rates: The rate law
• v0 .[A]2
[A] (M) 0.0 0.5 1.0 1.5 2.0
v0
(M/min)
0.0
1.0
2.0
3.0
4.0 Chem 1AA3Chem 1AA3
27
14-3. Effect of concentration on reaction rates: The rate law
• dependence of v0 on [A] gives information about
mechanism
• relationship between concentration and rate is the rate law
or rate equation:
aA + bB .gG + hH (6, 14.5)
v0 = k[A]m[B]n (9, 14.6)
• m does not (necessarily) equal a
• n does not (necessarily) equal b
• a & b are determined by stoichiometry Chem 1AA3Chem 1AA3
27
14-3. Effect of concentration on reaction rates: The rate law
• dependence of v0 on [A] gives information about
mechanism
• relationship between concentration and rate is the rate law
or rate equation:
aA + bB .gG + hH (6, 14.5)
v0 = k[A]m[B]n (9, 14.6)
• m does not (necessarily) equal a
• n does not (necessarily) equal b
• a & b are determined by stoichiometry
Chem 1AA3Chem 1AA3
28
14-3. Effect of concentration on reaction rates: The rate law v0 = k[A]m[B]n (9, 14.6)
• m & n
– determined experimentally
– usually small, positive integers (0, 1 or 2)
•overall order of a reaction is (m + n)
– order w.r.t.* A is m
– order w.r.t. B is n
(* w.r.t. = with respect to) Chem 1AA3Chem 1AA3
29
14-3. Effect of concentration on reaction rates: The rate law
• Method of initial rates
• find m and n by measuring v0 at varying [A], [B]
Zero-order m = 0, no effect of [A]
First-order m = 1, v0 .[A]
Second-order (m + n) = 2, v0 .[A]2 or [A][B]
• once m & n are known, use v0 to derive the rate
constant, k• k is a fundamental property of the reaction, whereas v0
reflects [A], [B]
Chem 1AA3Chem 1AA3
29
14-3. Effect of concentration on reaction rates: The rate law
• Method of initial rates
• find m and n by measuring v0 at varying [A], [B]
Zero-order m = 0, no effect of [A]
First-order m = 1, v0 .[A]
Second-order (m + n) = 2, v0 .[A]2 or [A][B]
• once m & n are known, use v0 to derive the rate
constant, k• k is a fundamental property of the reaction, whereas v0
reflects [A], [B]
Chem 1AA3Chem 1AA3
30
14-3. Effect of concentration on reaction rates: The rate law
• order of the reaction tells us how many species are present in the rate-limiting step of the reaction
• Key concepts:
– order . stoichiometry
– order is determined experimentally
– order = number of species involved at transition state
of the rate-limiting step PH
Formative iClicker Question #19
Chem 1AA3Chem 1AA3
31
Which of the following rate equations is not third
order overall?
(a) v0 = k[A]3
(b) v0 = k[B]3[C][D]-1
(c) v0 = k[A]3[B]
(d) v0 = k[A][B]2
Chem 1AA3Chem 1AA3
32
PB
Formative iClicker Question #19
Which of the following rate equations is fourth order
overall?
(a) v0 = k[A]3[B]0
(b) v0 = k[B]3[C][D]-1
(c) v0 = k[A]3[B]
(d) v0 = k[A][B]2 JV
Formative iClicker Question #19
Chem 1AA3Chem 1AA3
33
Which of the following rate equations is not fourth
order overall?
(a) v0 = k[A]3[B][D]-1
(b) v0 = k[B]3[C]2[D]-1
(c) v0 = k[B]3[C]
(d) v0 = k[A]4
Chem 1AA3Chem 1AA3
34
HS
Formative iClicker Question #19
Which of the following rate equations is third order
overall?
(a) v0 = k[A]2
(b) v0 = k[B]2[C][D]-1
(c) v0 = k[A]3[B]
(d) v0 = k[A][B]2 Chem 1AA3Chem 1AA3
35
14-4. Zero-order reactions
• v0 is independent of [A]
v0 = k = constant (13)
• units for v are concentration/time (e.g., M/s) (always)
Concept check:
What are the units of k for a zero-order reaction?
• units for k are concentration/time, e.g., M•s-1
Chem 1AA3Chem 1AA3
35
14-4. Zero-order reactions
• v0 is independent of [A]
v0 = k = constant (13)
• units for v are concentration/time (e.g., M/s) (always)
Concept check:
What are the units of k for a zero-order reaction?
• units for k are concentration/time, e.g., M•s-1
Chem 1AA3Chem 1AA3
36
14-4. Zero-order reactions
• integrated rate law:
[A]t = [A]0 -kt (14, 14.10)
time (min)
0.0 0.5 1.0 1.5 2.0
[A] ( M)
0.00
0.25
0.50
0.75
1.00 Chem 1AA3Chem 1AA3
37
14-4. Zero-order reactions
• Zero-order processes:
– evaporation / sublimation with constant surface area
• Pseudo zero-order reactions:
– reactions where catalyst is saturated with reactants
(e.g., drug/alcohol metabolism)
Key concepts:
– rate = rate constant (k)
– true zero-order reactions are rare
Chem 1AA3Chem 1AA3
37
14-4. Zero-order reactions
• Zero-order processes:
– evaporation / sublimation with constant surface area
• Pseudo zero-order reactions:
– reactions where catalyst is saturated with reactants
(e.g., drug/alcohol metabolism)
Key concepts:
– rate = rate constant (k)
– true zero-order reactions are rare
Chem 1AA3Chem 1AA3
38
14-5. First-order reactions
• reaction of MeOH with tBu-Cl is SN1: Cl O + HClOH
MeOH tBu-Cl MTBE Chem 1AA3Chem 1AA3
39
14-5. First-order reactions
• reaction order w.r.t. tBu-Cl? 1st-order
MeOH? 0th-order
• overall reaction order? 1st-order
• rate equation? v= k[tBu-Cl]
= k[tBu-Cl]1[MeOH]0
[MeOH] (M)
v0
(M/min)
variable MeOH,
constant tBu-Cl
[tBu-Cl] (M)
v0
(
M/min)
variable tBu-Cl,
constant MeOH
Chem 1AA3Chem 1AA3
39
14-5. First-order reactions
• reaction order w.r.t. tBu-Cl? 1st-order
MeOH? 0th-order
• overall reaction order? 1st-order
• rate equation? v= k[tBu-Cl] = k[tBu-Cl]1[MeOH]0
[MeOH] (M)
v0
(M/min)
variable MeOH,
constant tBu-Cl
[tBu-Cl] (M)
v0
(
M/min)
variable tBu-Cl,
constant MeOH
Chem 1AA3Chem 1AA3
40
14-5. First-order reactions
Why first order?
• rate-limiting C-Cl bond cleavage
• MeOH attack is fast
.rate controlled by C-Cl bond cleavage
Cl
tBu-Cl
Cl-SLOW
O + H2O-CH3 + Cl-
MTBE
Cl-OH
fast MeOH
O
H fast
HO
++ Chem 1AA3Chem 1AA3
41
14-5. First-order reactions
• MeOH does not enter until after the rate-limiting step,
.no effect from [MeOH]
• one molecule in the rate-limiting step,
.1st-order
v0 = k[A] (10, 14.12)
Concept check:
What are the units of k for a first-order reaction?
– units for k are 1/time (e.g., s-1)
Chem 1AA3Chem 1AA3
41
14-5. First-order reactions
• MeOH does not enter until after the rate-limiting step,
.no effect from [MeOH]
• one molecule in the rate-limiting step,
.1st-order
v0 = k[A] (10, 14.12)
Concept check:
What are the units of k for a first-order reaction?
– units for k are 1/time (e.g., s-1)
Chem 1AA3Chem 1AA3
42
14-5. First-order reactions
• Characteristics of k: (1) constant regardless of concentration
(2) depends on the identity of the reactants, temperature,
catalyst, solvent Che
CheChe
m
mm
1AA3
1AA31AA3
43
14-5. First-order reactions
• Integrated rate law for first-order reactions
– rate equation gives v at every instant
– integrating v vs. time gives [A] consumed (or [G]
produced)
– integrate d[A]/dt with respect to time:
(11, 14.13)
• ln[A] is unitless, so kt is unitless
(integration is shown on p. 583 of the text)
0t
0
t ln[A]tln[A]ort
[A]
[A] -
+=-=
kkln
14-5. First-order reactions
• rearrange eq. 11: [A]t = [A]0•e-kt
• Half-life -t1/2
–1st-order reactions have constant t1/2
[A]t = ½•[A]0 at t1/2:
()
1/2
1/2
t
t
[A]
[A]
21
0
021
•
•
-=
-=
.
.
.
.
.
.
.
. k
k
ln
ln
(11a)
Che
CheChe
m
mm
1AA3
1AA31AA3
44 Chem 1AA3Chem 1AA3
45
14-5. First-order reactions
(12, 14.14)kk
6902
21
.lnt / ==
)ln 2lnthat(
recall 21 =
..
.
.
..
.
.
-=
k
21
1/2tln
Chem 1AA3Chem 1AA3
46
14-5. First-order reactions
• Reactions involving gases
– same as solution reactions, but use partial pressures
(PA) in place of molarity, e.g.:
(11b, 14.15)t )(
)(
0
t k-=
A
A
P
Pln Chem 1AA3Chem 1AA3
47
14-5. First-order reactions
• Examples of first-order reactions:
(1) radioactive decay
(2) SN1 nucleophilic substitutions
• Key Concepts:
– v0 .[A]
–t1/2 = constant
– rate and integrated equations
Chem 1AA3Chem 1AA3
47
14-5. First-order reactions
• Examples of first-order reactions:
(1) radioactive decay
(2) SN1 nucleophilic substitutions
• Key Concepts:
– v0 .[A]
–t1/2 = constant
– rate and integrated equations
Chem 1AA3Chem 1AA3
48
14-6. Second-order reactions
A second-order reaction:
•SN2 nucleophilic substitution
ClH3C O CH3 H3C
+ HClH3C
OH
MeOH Me-Cl Me2O Chem 1AA3Chem 1AA3
49
14-6. Second-order reactions
• reaction order w.r.t. Me-Cl? 1st-order
MeOH? 1st-order
• overall reaction order? 2nd-order
• rate equation? v= k[Me-Cl][MeOH]
= k[Me-Cl]1[MeOH]1
[MeOH] (M)
v0
(M/min)
variable MeOH,
constant Me-Cl
[Me-Cl] (M)
v0
(M/min)
variable Me-Cl,
constant MeOH
Chem 1AA3Chem 1AA3
49
14-6. Second-order reactions
• reaction order w.r.t. Me-Cl? 1st-order
MeOH? 1st-order
• overall reaction order? 2nd-order
• rate equation? v= k[Me-Cl][MeOH]
= k[Me-Cl]1[MeOH]1 [MeOH] (M)
v0
(M/min)
variable MeOH,
constant Me-Cl
[Me-Cl] (M)
v0
(M/min)
variable Me-Cl,
constant MeOH
Chem 1AA3Chem 1AA3
50
14-6. Second-order reactions
• Why second order?
– single concerted step with both reactants present at rate-
limiting step
• rate depends on the presence of both reactants
ClH3C O CH3
H3C
+ HClH3C
OH
MeOH Me-Cl Me2O
H
HH
O Cl
H3C H d+ dtransition
state Chem 1AA3Chem 1AA3
51
14-6. Second-order reactions
v0 = k[MeOH][Me-Cl] (15)
• units for v are concentration/time (e.g., M/s)
• units of [MeOH] and [Me-Cl] are concentration (e.g., M)
Concept check:
What are the units of k for a second-order reaction?
• units for k are 1/{concentration•time} (e.g., M-1•s-1)
Chem 1AA3Chem 1AA3
51
14-6. Second-order reactions
v0 = k[MeOH][Me-Cl] (15)
• units for v are concentration/time (e.g., M/s)
• units of [MeOH] and [Me-Cl] are concentration (e.g., M)
Concept check:
What are the units of k for a second-order reaction?
• units for k are 1/{concentration•time} (e.g., M-1•s-1)
Chem 1AA3Chem 1AA3
52
14-6. Second-order reactions
• example from the textbook:
2A . products (16)
•where:
v0 = k[A]2 (17, 14.17)
•SN2 example: A + B . products,
•where:
v0 = k[A][B] (17a) Chem 1AA3Chem 1AA3
53
14-6. Second-order reactions
Pseudo first-order reactions
–2nd-order reaction rates become very slow as
reactants are depleted
• e.g.:
H3C O
O
R + H2O H3C OH
O
+ HO-R
H+
Chem 1AA3Chem 1AA3
53
14-6. Second-order reactions
Pseudo first-order reactions
–2nd-order reaction rates become very slow as
reactants are depleted
• e.g.:
H3C O
O
R + H2O H3C OH
O
+ HO-R
H+ Chem 1AA3Chem 1AA3
54
time (min)
[ester]
(M)
0.00
0.05
0.10
time (min)
[water]
(M)
0.00
0.05
0.10
14-6. Second-order reactions
• e.g., reaction of 0.1 M ester and 0.1 M H2O in acetone*:
H3C O
O
R + H2O H3C OH
O
+ HO-R
H+
* calculations neglect reversibility of reaction, which will slow it
even more Chem 1AA3Chem 1AA3
55
14-6. Second-order reactions
• Pseudo first-order reactions
– Run ester hydrolysis reaction in dilute aqueous acid.
– Change in [H2O] is negligible.
– Reaction appears to be first order.
– behaves like a 1st-order irreversible reaction:
v = k[ester]
0.1 M0.1 M55.4 M0 Mfinal
0 M0 M55.5 M0.1 Minitial
[HO-R][AcOH][H2O][ester]
Chem 1AA3Chem 1AA3
55
14-6. Second-order reactions
• Pseudo first-order reactions
– Run ester hydrolysis reaction in dilute aqueous acid.
– Change in [H2O] is negligible.
– Reaction appears to be first order.
– behaves like a 1st-order irreversible reaction:
v = k[ester]
0.1 M0.1 M55.4 M0 Mfinal
0 M0 M55.5 M0.1 Minitial
[HO-R][AcOH][H2O][ester]
Chem 1AA3Chem 1AA3
56 14-6. Second-order reactions
• Pseudo first-order reactions
time (min)
[ester]
or
[water]
(M)
0
0.05
0.1
20
40
60
H3C O
O
R + H2O H3C OH
O
+ HO-R
H+ Chem 1AA3Chem 1AA3
57
14-6. Second-order reactions
• Key concepts:
– rate depends on both reactants (or [A]2)
– make pseudo-1st order with one excess reagent
Chem 1AA3Chem 1AA3
57
14-6. Second-order reactions
• Key concepts:
– rate depends on both reactants (or [A]2)
– make pseudo-1st order with one excess reagent
Chem 1AA3Chem 1AA3
58
PH
Formative iClicker Question #20
What is the rate constant, k, for a reaction with the following
relationship between reactant concentration, [A], and initial
velocity, v0?
(a) k = 1.0 s-1
(b) k = 10 M•s-1
(c) k = 1.0 M•s-1
(d) k = 10 M-1•s-1
0.4 M•s-10.2 M
0.1 M•s-10.1 M
v0[A] Chem 1AA3Chem 1AA3
59
PB
Formative iClicker Question #20
What is the rate constant, k, for a reaction with the following
relationship between reactant concentration, [A], and initial
velocity, v0?
(a) k = 100 s-1
(b) k = 1000 M-1•s-1
(c) k = 100 M•s-1
(d) k = 1000 M•s-1
90 M•s-10.3 M
10 M•s-10.1 M
v0[A]
Chem 1AA3Chem 1AA3
59
PB
Formative iClicker Question #20
What is the rate constant, k, for a reaction with the following
relationship between reactant concentration, [A], and initial
velocity, v0?
(a) k = 100 s-1
(b) k = 1000 M-1•s-1
(c) k = 100 M•s-1
(d) k = 1000 M•s-1
90 M•s-10.3 M 10 M•s-10.1 M
v0[A]
Chem 1AA3Chem 1AA3
60
JV
Formative iClicker Question #20
What is the rate constant, k, for a reaction with the following
relationship between reactant concentration, [A], and initial
velocity, v0?
(a) k = 10-3 M-1•s-1
(b) k = 10 M-1•s-1
(c) k = 0.01 s-1
(d) k = 10 s-1
20 mM•s-12 M
10 mM•s-11 M
v0[A] HS
Formative iClicker Question #20
velocity, v0?
(a) k = 0.01 M-1•s-1
2 M
1 M
[A]
4 mM•s-1
1 mM•s-1
v0
(b) k = 1.0 M-1•s-1
(c) k = 10-3 M-1•s-1
(d) k = 10 M-1•s-1
Chem 1AA3Chem 1AA3
61
What is the rate constant, k, for a reaction with the following
relationship between reactant concentration, [A], and initial
Chem 1AA3Chem 1AA3
62
14-7. Reaction kinetics: A summary
Things you can calculate:
(1) v0 when the rate law is known: v0 = k[A]m[B]n...
(2) Instantaneous rate (v) from:
(i) tangent to line in graph of [A] vs. t,
(ii) -.[A]/.t (average rate) for short .t
(iii) rate law
(3) Order of reaction from:
(i) v0 vs. concentration
(ii) graph that gives a straight line
(iii) constant t1/2 (1st-order)
(iv) integrated rate law which gives a constant k Chem 1AA3Chem 1AA3
63
14-7. Reaction kinetics: A summary
Things you can calculate:
(4) k from:
(i) slope of line in an appropriate graph
(ii) substitute data into the appropriate integrated rate
law
(iii) from t1/2 (1st-order)
(5) use integrated rate law to give [A]t and [G]t from k and
[A]0.
Chem 1AA3Chem 1AA3
63
14-7. Reaction kinetics: A summary
Things you can calculate:
(4) k from:
(i) slope of line in an appropriate graph
(ii) substitute data into the appropriate integrated rate
law
(iii) from t1/2 (1st-order)
(5) use i

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