AP Review Topic 3: Kinetics
Reaction Rate



Change in concentration of reactants or products over time
Can be measured as decrease in reactant concentration over time or increase in product
concentration over time.
Can be measured using specropotometer and using Beer's law, by measuring the change in
absorbance of a colored solution over time.
Collision Theory-

mechanisms that increase the number of effective collisions (collisions with the proper
orientation, and with sufficient energy to overcome activation energy) will increase reaction
rate
Conditions that effect rate:
1. Increasing surface area of reactants
2. Increasing the temperature
3. Increasing the concentration of reactants
4. Adding a catayst will lower the activation energy
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Energy Pathway diagram
Free Response Example
.
H2(gv
)
+ I2(g)  2 HI(g)
For the exothermic reaction represented above, carried out at 298K, the rate law is as follows.
Rate = k[H2][I2]
Predict the effect of each of the following changes on the initial rate of the reaction and explain your
prediction.
(a) Addition of hydrogen gas at constant temperature and volume
(b) Increase in volume of the reaction vessel at constant temperature
(c) Addition of catalyst. In your explanation, include a diagram of potential energy versus
reaction coordinate.
(d) Increase in temperature. In your explanation, include a diagram showing the number of
molecules as a function of energy.
The differential rate law
C
aA + bB  xX
Where C is the catalyst
Initial rxn rate= k[A]m [B]n [C]p
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Orders of reaction



Are determined by experimentation
The order with respect to a certain reactant is simply the exponent on its concentration term in
the rate law
We analyze concentration and rate data to determine the order
The overall order of a reaction is the sum of the orders in the rate expression
1.
zero order- Changing the concentration of the reactant has no effect on the rate.
Not very common.
Rate law : rate =k
2.
first order- rate is directly proportional to the concentration of the reactant.
These are very common! Nuclear decay is a first order reaction.
Rate law : rate=k[A]1 or rate = k[A]
3.
Second order- rate is quadrupled hese are common in gas phase reactions.
Rate Law: rate= k [A]2 or rate = k [A][B]
Orders can be fractional, but this is rare!!!
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Free Response Example
2A+BC+D
The following results were obtained when the reaction represented above was studied at 25C.
Experiment
Initial
[A]
Initial
[B]
Initial Rate of
Formation of C
(mol L-1 min-1)
1
0.25
0.75
4.310-4
2
0.75
0.75
1.310-3
3
1.50
1.50
5.310-3
4
1.75
?
8.010-3
(a) Determine the order of the reaction with respect to A and to B. Justify your answer.
(b) Write the rate law for the reaction. Calculate the value of the rate constant, specifying units.
(c) Determine the initial rate of change of [A] in Experiment 3.
(d) Determine the initial value of [B] in Experiment 4.
(e) Identify which of the reaction mechanisms represented below is consistent with the rate law
developed in part (b). Justify your choice.
1. A + B  C + M
Fast
M+AD
Slow
2. B  M
Fast equilibrium
M+AC+X
Slow
A+XD
Fast
3. A + B  M
Fast equilibrium
M+AC+X
Slow
XD
Fast
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Integrated Rate Law Uses graphs to determine order of reactions
•
Time is always on x axis
•
Plot concentration on y axis of 1st graph -- linear- zero order
•
Plot ln [A] on the y axis of the second graph-- linear- first order
•
Plot 1/[A] on the y axis of third graph-- linear-- second order
Zero Order
•
time vs concentration= line
y = mx+ b
[A]= -kt + [A0 ]
A- reactant A,
A0 - initial concentration of A at t=0
l slope l (abs value)= k, since k cannot be negative, and k will have a negative slope
Rate law will be rate=k[A]0
First Order
time vs ln[ ] is linear
y=
mx+ b
ln [A]t - ln [A0 ] = -kt -- on equation sheet!!!!
A- reactant A,
[A]0 - initial concentration of A at t=0
l slope l= k, since k cannot be negative, and k will have a negative slope
Rate law will be rate=k[A]1
Second Order
• time vs 1/ [ ]= line
y= mx+ b
1/[A]= kt + 1/ [A0 ]
k=slope
Rate law will be rate=k[A]2
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Graphs:
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.
•
First order decay is what is seen in radioactive decay -- constant 1/2 life!!
0.693 = t1/2
k
Example
A certain first-order reaction has a half-life of 20.0 minutes.
a. Calculate the rate constant for this reaction.
b. How much time is required for this reaction to be 75% complete?
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Reaction Mechanisms



A reaction mechanism represents the sequence of ______making and _________
breaking steps that occur during the conversion of reactants to products.
Each step is called a _______________________ step
These elementary steps are determined by _____________
To determine if a reaction mechanism is correct for a particular reaction, the reaction
mechanism must
 Agree with the overall ___________________ of your reaction
 Agree with the ___________________ of your reaction
Elementary steps are described in terms of their molecularity
Molecularity describes the number of molecules that are participating in atomic
reaarangement.
 Unimolecular elementary steps- __________ reactant molecule collides with a
solvent or a background molecule to become collisionally activated
 Bimolecular – involves a collision between ____________
 Termolecular-involves a collision between _____________
o Very rare—why??
Example #2
The reaction below
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A + B C + D
Has the following mechanism
A ↔Q
fast equilibrium
Q + B  C + D slow
Here the slow step contains Q and B, and ______________________is an intermediate .
Can intermediates be featured the rate equation? _____________
. Since the formation of Q is dependent on A, Q can be replaced by A in the rate
equation. Therefore the rate equation is given as_________________ The orders w.r.t A and B
are________________________________
since the stoichiometric coefficient of B in the rate determining step is 1, and the
stoichiometric coefficient of A (which Q depends upon) is also 1.
Note:
1. In all valid mechanisms the sum of the individual fast and slow steps must be the same as the
overall chemical equation.
2. The stoichiometric number of a substance that appears in the slow step is the power that the
concentration of that substance is raised to in the rate equation.
3. If a substance is present at the beginning of a reaction AND present in the same form at the end of the
reaction, it can be identified as _______________________!!
Catalysis
Catalysts – increase rate of a chemical reaction
Not consumed in a reaction
Do not change the ΔH of the reaction
Lower the activation energy in an elementary step
Provide a new (and faster) reaction mechanism
Maxwell-Boltzman Distribution:
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How do catalysts do their job?
The addition of a catalyst provides an alternative pathway with a lower Eact. More particles
will possess this lower, minimum energy and , as a result, a greater number of particles will
have enough energy to overcome the lower Eact and a greater number of successful collisions
will occur (remember collision theory??)
Arrhenius Equation
This equation relates the rate constant k to temperature and activation energy Ea
k= Ae(-Ea/RT)
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Free Response Practice
1.
2 ClO2(g) + F2(g)  2 ClO2F(g)
The following results were obtained when the reaction represented above was studied at 25C.
Initial [ClO2],
Initial [F2],
(mol.L-1)
(mol.L-1)
Initial Rate of Increase of
[ClO2F], (mol.L-1.sec-1)
1
0.010
0.10
2.410-3
2
0.010
0.40
9.610-3
3
0.020
0.20
9.610-3
Experiment
(a)
(b)
(c)
(d)
Write the rate law expression for the reaction above.
Calculate the numerical value of the rate constant and specify the units.
In experiment 2, what is the initial rate of decrease of [F2]?
Which of the following reaction mechanisms is consistent with the rate law developed in (a).
Justify your choice.
I. ClO2 + F2  ClO2F2
(fast)
ClO2F2  ClO2F + F
(slow)
ClO2 + F  ClO2F
(fast)
II. F2  2 F
(slow)
2 (ClO2 + F  ClO2F)
(fast)
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2.
Graphical methods are frequently used to analyze data and obtain desired quantities.
2 HI(g)  H2(g) + I2(g)
(a)
The following data give the value of the rate constant at various temperatures for the gas
phase reaction above.
T (K)
k (litre/mol sec)
647
8.5810-5
666
2.1910-4
683
5.1110-4
700
1.1710-3
716
2.5010-3
Describe, without doing any calculations, how a graphical method can be used to obtain the
activation energy for this reaction.
A(g)  B(g) + C(g)
(b)
The following data give the partial pressure of A as a function of time and were obtained at
100C for the reaction above.
PA (mm Hg)
t (sec)
348
0
247
600
185
1200
105
2400
58
3600
Describe, without doing any calculations, how graphs can be used to determine whether this
reaction is first or second order in A and how these graphs are used to determine the rate
constant.
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3.
C2H4(g) + H2(g)  C2H6(g) H = -137 kJ
Account for the following observations regarding the exothermic reaction represented by the
equation above.
(a) An increase in the pressure of the reactants causes an increase in the reaction rate.
(b) A small increase in temperature causes a large increase in the reaction rate.
(c) The presence of metallic nickel causes an increase in reaction rate.
(d) The presence of powdered nickel causes a larger increase in reaction rate than does the
presence of a single piece of nickel of the same mass.
4.
Answer the following questions regarding the kinetics of chemical reactions.
(a) The diagram below at right shows the energy pathway for the reaction O 3 + NO  NO2 +
O2. Clearly label the following directly on the diagram.
(i) The activation energy (Ea) for the forward reaction
(ii) The enthalpy change (H) for the reaction
(b) The reaction 2 N2O5  4 NO2 + O2 is first order with respect to N2O5.
(i) Using the axes at right, complete the graph that represents the change in [N2O5] over
time as the reaction proceeds.
Initial
[N2O3 ]•
Time
(ii) Describe how the graph in (i) could be used to find the reaction rate at a given time, t.
(iii) Considering the rate law and the graph in (i), describe how the value of the rate
constant, k, could be determined.
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(iv) If more N2O5 were added to the reaction mixture at constant temperature, what would
be the effect on the rate constant, k ? Explain.
(c) Data for the chemical reaction 2A  B + C were collected by measuring the concentration
of A at 10-minute intervals for 80 minutes. The following graphs were generated from
analysis of the data.
Use the information in the graphs above to answer the following.
(i) Write the rate-law expression for the reaction. Justify your answer.
(ii) Describe how to determine the value of the rate constant for the reaction.
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