In order for high-ability students to feel academically
challenged in secondary schools, many look to Advanced
Placement courses. Success in an AP classroom is often
an indicator of success in the future.
College students :
1) who have NOT taken an AP course have only a
33% chance of completing a Bachelor’s Degree
2) who have completed ONE AP course have a 59%
chance of completing a Bachelor’s Degree
3) who have completed TWO or MORE AP courses
have a 76% chance of completing a Bachelor’s
Degree --Statistics from Answers in the Tool Box: Academic
Intensity, Attendance Patterns, and Bachelor’s Attainment
AP* CHEMISTRY
KINETICS
Rate Laws, Differential, Integrated,
and
Arrhenius
KINETICS: Rate Laws, Differential, Integrated, and Arrhenius
Objective
To review the student on the concepts, processes and problem
solving strategies necessary to successfully answer questions over
principles of reaction rates.
Standards
The topic of kinetics is addressed in the topic outline of the College
Board AP Chemistry Course Description Guide as described below.
III Reactions D. Kinetics
1. Concept of rate of reaction
2. Use of experimental data and graphical analysis to determine
reactant order, rate constants, and reaction rate laws
3. Effect of temperature change on rates
4. Energy of activation; the role of catalysts
5. The relationship between the rate-determining step and a
mechanism
AP Chemistry Exam Connections
The topic of kinetics is tested every year on the multiple
choice and many years on the free response portions of the
exam. The list below identifies free response questions that
have been previously asked recently. These questions are
available from the College Board and can be downloaded free
of charge from AP Central http://apcentral.collegeboard.com.
Free Response Questions
2008 Question 3 (parts d−f)
2008 B Question 2
2006 Question 6 (part d) 2005 B Question 3
2005 Question 3 2004 B
Question 3 (part b)
2004 Question 3 (part e) 2003 B Question 8 (part d)
2003 Question 3
2002 Question 7
2001 Question 6
2000 Question 6 (parts d−e)
What I Absolutely Have to Know to Survive the AP Exam
The following might indicate the question deals with kinetics:
Rate; time; concentration; order; rate constant; mechanisms;
rate determining step; intermediate; catalyst; half-life;
instantaneous rate; relative rate; activation energy; integrated
rate law; rate expression; rate law
FACTORS THAT AFFECT REACTION RATE
Temperature Reaction rate increases with increasing
temperature
Concentration Reaction rate typically increases with
increasing concentration of reactants (pressure
changes have the same effect on gaseous
reactions)
Catalyst Reaction rate increases with the addition of a
catalyst
Surface Area Reaction rate increases with increased surface
area of the reactant.
EXPRESSING REACTION RATE
Reaction rate is expressed in terms of how fast the concentration
of a substance changes; which is expressed mathematically as
shown below. It does not whether you measure the products or the
reactants as they are stoichiometrically linked.
Translated… The rate of consumption of N2O5 is equal to half the rate of
the production of NO2 and equal to twice the production of O2 ……Or
better yet…
 NO2 is produced at twice the rate at which N2O5 is consumed
 O2 is produced at the half the rate at which N2O5 is consumed
Instantaneous Rate: Instantaneous rate is the rate at any one
point and time during the experiment. To find instantaneous
rate you find the slope of the curve at the time in question (for
those of you in calculus aka…derivative) i.e. the slope of the
tangent line to that point in time.
Notice: The rate at any point is
constantly decreasing
over time; because the
concentration of reactants
is constantly decreasing
as the reaction proceeds.
Rate Laws
The reaction rate depends only on the concentration of the reactants
(assuming the reverse reaction does not contribute to the rate)
For the following reaction… 2 X + Y → Z
The general form of the rate is…
rate = k[X]m [Y]n
Where…
 k is the rate constant
 The exponent m represents the order of the reaction with respect
to reactant X
 The exponent n represents the order of the reaction with respect to
reactant Y
 The sum of m + n represents the overall order of the reaction.
Reactant orders must be determined experimentally;
they cannot be written from a balanced equation.
Rate generally refers to the initial rate.
 The initial rate is the fastest rate of the reaction and
occurs at the very beginning of the reaction. At this point
there are few competing reactions. It should be noted when
using the initial rate the concentration of the reactants are
initial concentrations.
 The rate law is a mathematical equation which relates the
instantaneous rate at a particular point in the progress of
a chemical reaction to the concentration of the reacting
specie(s).
Integrated Rate
The rate law expresses rate as a function of reactant
concentration(s) at an instant in time (hence instantaneous
rate)
Integrated rates express the reactant concentrations as a
function of time.
Graphical Analysis
It is imperative that you can determine reaction order simply by analyzing a
graph.What is important?
 What is plotted on each axis?
 What does the slope of the line indicate?
If you know this, the order and rate constant can easily be
determined.
Reaction Mechanisms
 Rxn mechanisms attempt to describe the stepwise sequence
of elementary reactions that take reactants to products.
 The mechanism describes in detail the bonds that are
broken and formed as the reaction proceeds.
 Each elementary step of a mechanism typically involves
1, 2, or 3 reactants combining to form products.
 Every mechanism consists of a series of stepwise reactions.
Each reaction in a mechanism has a rate associated
with it.
 The overall speed of the reaction depends upon the slowest
step of the mechanism. The rate law of this step is
identical to the experimental rate law. The slow step of
the mechanism is also called the rate determining step of
the mechanism.
 The sum of all the steps of the mechanism must equal the
overall balanced chemical equation.
Reaction Mechanisms (cont.)
The coefficients of the reactants in the rate determining step
of the mechanism must correspond to the exponents or order
of the reactants in the experimental rate law.
Catalysts and Intermediates…
 A catalyst is used up early in a reaction (reactant) and is
regenerated (product) in a subsequent step.
 A catalyst is a substance that acts to increase the rate of a
chemical reaction by providing an alternate path for the
reaction to occur. This means that there will be a change in
the magnitude of the rate constant and possibly achange in
the order of the reaction.
 An intermediate is produced early in the reaction (product)
and used up (reactant) in a subsequent step.
Collision Theory and Activation Energy
For a reaction to happen two things must occur:
1. Molecules must collide with enough kinetic energy to react
– i.e. they must meet or exceed the energy of activation, Ea.
2. The molecules must collide with the appropriate orientation
for a reaction to occur, i.e. the collisions MUST BE
EFFECTIVE.
These two factors are summarized in the Arrhenius equation:
 k is the rate constant(s)
 T is the temperature in Kelvin
 R is the gas constant 8.341 J mol−1 K−1
 Ea is the activation energy
 A is the Arrhenius constant − it describes how
many collisions have the appropriate orientation.
Two simple atoms that can collide in any
Orientation will have a very high A value, while
two very complex molecules that
must collide in a very specific way will
have a low A value.
Ea − the activation energy…
 Is a measure of the energy barrier colliding
molecules must overcome if they are to react
rather than recoil from one another.
 It is assumed that every pair of reacting species
with energy less than Ea will not react and
every pair with energy greater than Ea and the
proper orientation will react.
 See graph on next page
Kinetics Cheat Sheet (cont.)
 Be able to explain with algebraic equations or words how an
order is determined. It is important to state which
concentration(s) is/are held constant and which
concentration is varied as well the effect that has on the
rate of the reaction if you choose not to justify without
algebraic equations.
 Mechanisms – must agree with the stoichiometry of the
reaction and the “summary rate law” must agree up to
and including the slow step; identify intermediates and
catalysts and clearly state that the correct mechanism
“agrees with the experimentally determined rate law”.
Kinetics Cheat Sheet (cont.)
 Discuss number of effective collisions in relation to
increasing or decreasing rates
 Arrhenius – magnitude of k relates directly to the
speed of the reaction; large = fast; small = slow
 Ea also predicts speed but the relationship is an
inverse one; high = slow rate; low = fast rate
 “rate in terms of” is code for “relative rates” – use
stoichiometry ratios on rate value
 instantaneous rate = slope of the line tangent to
the time point in question
Connections
Stoichiometry − “using up” one component of
the system might indicate a limiting reactant in
effect
Electrochemistry − if reaction is redox in
nature rate problems could come in play
Thermochemistry − Ea and ΔH°rxn and
reaction diagrams
Potential Pitfalls
Units on k = always time−1 and one
less M−1 than overall order.
Ex: 2nd order overall has a k with
units of M −1 s −1
2x= 2
4
4
E If it is zero order with respect to [A],
then A0 equals one, thus [A] is not
included in the rate expression.
D To be second order with respect to A and
third order overall, reactant B must be first
order.
B The rate law expression shows that reactant X is
second order, therefore a plot of reciprocal
concentration vs. time will yield a straight line.
B The rate law expression shows that reactant X is
second order, therefore a plot of reciprocal
concentration vs. time will yield a straight line.
B I is incorrect. The reactant graphed is first order, if it were 2nd order the graph
would have reciprocal concentration on the y-axis and have a straight line with a
positive slope. II is a correct statement. III is incorrect, for a 1st order reaction the
units for k are time−1
7. Each of the following factors can affect the rate
of a chemical reaction EXCEPT
(A) increasing temperature
(B) decreasing reactant concentration
(C) adding a catalyst
(D) removing products
(E) breaking up solid reactants
D Chemical reactions occur because molecules collide
with sufficient energy and orientation to break and
make bonds. Heat ‘em up and speed ‘em up. The
reactions are more energetic with an increase in
temperature, more effectively oriented in the
presence of a catalyst, more common if the
container is crowded or the reactants have more
surface area.
8. As the above reaction proceeds at constant temperature, the reaction
rate
(A) remains the same since there is no catalyst present
(B) remains the same since the temperature is constant
(C) increases because the rate constant is a large number
(D) increases because the rate of effective collisions increases over time
(E) decreases because the concentrations of the reactants decrease as
the reaction progresses
8. As the above reaction proceeds at constant temperature, the reaction rate
(A) remains the same since there is no catalyst present
(B) remains the same since the temperature is constant
(C) increases because the rate constant is a large number
(D) increases because the rate of effective collisions increases over time
(E) decreases because the concentrations of the reactants decrease as the reaction progresses
E As the reaction proceeds at constant temperature, the
concentration of its reactants are decreasing thus the
reaction rate is decreasing. The rate of effective
collisions remains constant at constant temperature with
no catalyst.
C Trials 1 & 2 held [B] constant and double the [A];
the rate doubled therefore the reaction is 1st order
for reactant A. Trials 1 & 3 held [A] constant and
doubled [B]; the rate doubled therefore the reaction
is 1st order for reactant B.
C Cross off any intermediates, in this case F
atoms. Focus on only the slow or rate
determining step. In this case it is the first step.
therefore the mechanism gives an overall rate
law as shown. Rate = k[NO2][F2]