Transcript Kinetics - MullisChemistry

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Mullis
Kinetics
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Concept of rate of reaction
Use of differential rate laws to determine
order of reaction and rate constant from
experimental data
Effect of temperature change on rates
Energy of activation; the role of catalysts
The relationship between the ratedetermining step and a mechanism
Mullis
Rate of Reaction
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Rate = Δ[concentration] or d [product]
Δ time
dt
Rate of appearance of a product = rate of
disappearance of a reactant
Rate of change for any species is inversely
proportional to its coefficient in a balanced
equation.
Mullis
Rate of Reaction
Assumes nonreversible forward reaction
 Rate of change for any species is inversely
proportional to its coefficient in a balanced
equation.
 2N2O5  4NO2 + O2
 Rate of reaction = -Δ[N2O5] = Δ[NO2] = Δ[O2]
2 Δt
4 Δt
Δt
where [x] is concentration of x (M) and t is time (s)
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Mullis
Reaction of phenolphthalein in excess
base
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Use the data in the table to
calculate the rate at which
phenolphthalein reacts with the
OH- ion during each of the
following periods:
(a) During the first time interval,
when the phenolphthalein
concentration falls from 0.0050
M to 0.0045 M.
(b) During the second interval,
when the concentration falls
from 0.0045 M to 0.0040 M.
(c) During the third interval,
when the concentration falls
from 0.0040 M to 0.0035 M.
Conc. (M)
0.0050
0.0045
Time (s)
0
10.5
0.0040
0.0035
0.0030
0.0025
22.3
35.7
51.1
69.3
0.0020
91.6
Mullis
Reactant Concentration by Time
Phenolphthalein Concentation in Basic Solution
Over Time
0.006
Conc. (M)
0.005
0.004
0.003
0.002
0.001
0
0
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10 20 30 40 50 60 70 80 90 10
0
Time (s)
Mullis
Finding k given time and concentration
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Create a graph with time on x-axis.
Plot each vs. time to determine the graph that gives
the best line:
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[A]
ln[A]
1/[A]
(Use LinReg and find the r value closest to 1)
k is detemined by the slope of best line (“a” in the linear
regression equation on TI-83)
1st order (ln[A] vs. t): k is –slope
2nd order (1/[A] vs t: k is slope)
Mullis
Rate Law Expression
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As concentrations of reactants change at constant
temperature, the rate of reaction changes. According
to this expression.
Rate = k[A]x[B]y…
Where k is an experimentally determined rate
constant, [ ] is concentration of product and x and y
are orders related to the concentration of A and B,
respectively. These are determined by looking at
measured rate values to determine the order of the
reaction.
Mullis
Finding Order of a Reactant - Example
2ClO2 + 2OH-  ClO3- + ClO2- + H2O
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Start with a table of experimental values:
[ClO2] (M)
[OH-] (M)
Rate (mol/L-s)
0.010
0.030
6.00x10-4
2x
0.010
0.060
1.20x10-3
0.030
0.060
1.08x10-2
To find effect of [OH-] compare change in rate to
change in concentration.
When [OH-] doubles, rate doubles. Order is the
power: 2x = 2. x is 1. This is 1st order for [OH-].
Mullis
2x
Finding Order of a Reactant - Example
2ClO2 + 2OH-  ClO3- + ClO2- + H2O
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Start with a table of experimental values:
[ClO2] (M)
[OH-] (M)
Rate (mol/L-s-1)
0.010
0.030
6.00x10-4
0.010
0.060
1.20x10-3
0.060
1.08x10-2
0.030
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3x
9x
To find effect of [ClO2] compare change in rate to
change in concentration.
When [ClO2] triples, rate increases 9 times. Order is
the power: 3y = 9. y is 2. This is 2nd order for [ClO2].
Mullis
Finding Order of a Reactant - Example
2ClO2 + 2OH-  ClO3- + ClO2- + H2O
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Can use algebraic method instead. This is useful when there are
not constant concentrations of one or more reactants. This
example assumes you found that reaction is first order for [OH-] .
[ClO2] (M)
[OH-] (M)
Rate (mol/L-s-1)
0.010
0.030
6.00x10-4
0.010
0.060
1.20x10-3
0.030
0.060
1.08x10-2
6.00 x 10-4=k(0.010)x(.030)1
1.08 x 10-2 = k (0.030)x(.060)1
0.0556 = .333x(.5)
For [ClO2]x , x = 2
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Mullis
Rate Law:
2ClO2 + 2OH-  ClO3- + ClO2- + H2O
Rate = k[ClO2]2[OH-]
To find k, substitute in any one set of
experimental data from the table. For
example, using the first row:
k = rate/[ClO2]2[OH-]
k = 6.00x10-4Ms-1
= 200 M-2s-1
[0.010M]2[0.030M]
Overall reaction order is 2+1=3. Note units of k.
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Mullis
Determining k Given Overall Reaction
Order
Rate(M/s) = k[A]x
x = overall order of reaction
[A] = the reactant concentration (M)
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Overall reaction order
Example
Units of k
1
Rate=k[A]
(M/s)/M = s-1
2
Rate=k[A]2
(M/s)/M2 = M-1s-1
3
Rate=k[A]3
(M/s)/M3 = M-2s-1
1.5
Rate=k[A]1.5
(M/s)/M1.5 = M-0.5s-1
Mullis
Determine Reaction Order
From the following experimental data, determine the order of the reaction and
the rate constant for the reaction:
C4H8 (g) → 2C2H4 (g)
The reaction was carried out in a constant volume container at 532 °C.
Time (s)
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P (mm Hg)
0
800
200
732
400
496
600
392
800
310
1000
244
Mullis
Another Reaction Order Example
The following data were collected during a study of its
decomposition at a certain temperature:
[H2O2] (M)
0.100
0.088
0.070
0.050
0.025
0.006
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Time (s)
0
120
300
600
1200
2400
Mullis
Integrated Rate Law
Use when time is given or requested
Relates concentration and time to rate
 1st order: ln[A] = -kt +
ln[A]0 or [A]=[A]0e-kT
 2nd order: 1__ = kt + 1__
[B]
[B]0
Wow!
y
= mx + b
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Both equations can be used with linear regression
to solve for slope, or k.
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Mullis
Half life for 1st vs 2nd Order Reactions
1st order:
t1/2 = 0.693
k
2nd order: t1/2 = 1__
k[A]0
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Mullis
Order
1
2
Rate Law
Rate = k[A]
Rate = k[A]2
Concentration-Time
Equation
ln
At
= – kt
A0
1
1
= kt +
At
A0
Half-life
Equation
t½ =
t½
0.693
k
1
=k A
 0
Graphical Analysis
Graph
ln[A]
ln[A] vs. time
slope = –k
1
A
vs. time
t
1
At
t
slope = k
[A]
0
Rate = k[A]0
[A] = –kt + [A]0
t½ = [ A ] 0
2k
t
[A] vs. t
slope = –k
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Mullis
The Arrhenius Equation and Finding Ea
k=Ae-Ea/RT
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Where A is the frequency factor
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Related to frequency of collisions and favorable
orientation of collisions
Ea is activation energy in J
R = 8.314 J/mol-K
T is temp in K
k is the rate constant
Mullis
Using the Arrhenius equation
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As Ea increases, rate decreases.
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As temp increases, rate increases
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Fewer molecules have the needed energy to react.
More collisions occur and increased kinetic energy
means more collisions have enough energy to react.
Mathematically, T is in denominator of the power
–Ea/T.
ln k =
-Ea + lnA
T
Mullis
Activation Energy: Energy vs.
Reaction Progress
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Ea is lowered with the
addition of a catalyst.
Peak is where collisions
of reactants have
achieved enough
energy to react
The arrangement of
atoms at the peak is
activated complex or
the transition state.
A+B --> C+D
400
no catalyst
Energy (kJ)
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300
with catalyst
200
Ea
A+ B
ΔH
100
C+D
0
0
2
4
Reaction path
Mullis
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Temperature effects on a reaction
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Two factors account for increased rate of reaction.
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Energy factor: When enough energy is in collision for
formation of activation complex, bonds break to begin
reaction. With higher temp, more collisions have this
energy.
Frequency of collision: Particles move faster and collide
more frequently with higher temp, increasing chance of
reaction.
Increasing temperature increases the rate of a
reaction more if the reaction is endothermic to start
with.
K increases according to k=Ae-Ea/RT
Mullis
Finding Ea given info at two temperatures
ln k1 =
k2
Ea [ 1_ - 1_ ]
R
T2
T1
Similar to vapor pressure equation, Clausius-Clapeyron Equation:
ln PvapT1 = ΔHvap [ 1_ - 1_ ]
PvapT2 R
T2
T1
In both cases, use R = 8.3145 J/K-mol and be
sure Ea or ΔHvap are in J, not kJ.
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Mullis
Mechanisms: Multistep Reactions
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The following reaction occurs in a single step.
CH3Br (aq) + OH-(aq)  CH3OH(aq) + Br-(aq)
Rate = k(CH3Br)(OH-)
This one occurs in several steps:
(CH3) 3CBr(aq) + OH-(aq) (CH3) 3COH (aq) + Br- (aq)
1. (CH3)3CBr  (CH3) 3C+ + BrSlow step
2. (CH3)3C+ + H2O  (CH3)COH2+ Fast step
3. (CH3)3COH2+ + OH-  (CH3)3COH + H2O Fast step
– Rate = k((CH3)3CBr)
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Mullis
Mechanisms: Multistep Reactions
The overall rate of reaction is more or less equal to the rate of the slowest step.
(rate-limiting step)
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If only one reagent is involved in the rate-limiting step, the overall rate of
reaction is proportional to the concentration of only this reagent.
Ex. For the reaction with Rate = k((CH3) 3CBr)
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Although the reaction consumes both (CH3) 3CBr and OH-, the rate of the
reaction is only proportional to the concentration of (CH3)3CBr.
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The rate laws for chemical reactions can be explained by the following general
rules.
– The rate of any step in a reaction is directly proportional to the
concentrations of the reagents consumed in that step.
– The overall rate law for a reaction is determined by the sequence of steps,
or the mechanism, by which the reactants are converted into the products
of the reaction.
– The overall rate law for a reaction is dominated by the rate law for the
slowest step in the reaction.
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch22/rateframe.html
Mullis
Substituting for an Intermediate
Step 1 : N2H2O2  N2HO2- + H +
Step 2: N2HO2-  N2O + OHStep 3: H+ + OH-  H2O
fast equilibrium
slow
fast
Requirement: A fast equilibrium prior to the rate determining (slow) step
that contains the intermediate for which you wish to substitute.
1. N2H2O2 N2HO2- + H+
fast equilibrium
For the fast equilibrium, write the rate law (leaving out the k and R) for
the reactants and set it equal to the rate law for the products. This can
be done because in an equilibrium reaction the forward rate must be
equal to the reverse rate.
[N2H2O2] = [N2HO2-] [H+]
3. Algebraically solve for the intermediate, N2HO2[N2H2O2] / [H+] = [N2HO2-]
4. Algebraically substitute into the rate law for N2HO2Rate law with intermediate is: R = k [N2HO2-] , so R = k [N2H2O2] / [H+]
2.
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Mullis