Preview – Look through the PP slides BEFORE the class (spend roughly 15-25 minutes to have a general sense of what
concepts I will be covering)
Attend Class – OR make sure you watch the video that I post.
Review After Class – This will help you connect the dots, reinforce the concepts you learned or teach you the concepts you
DID not learn.
Study
i) Form study groups (if possible in the current situation)
ii) Question “Am I understanding the material?” “What am I not understanding”
iii) Have I memorized what I am supposed to?
iv) Solve problems without looking at an example.
v) DO NOT just highlight or re-read the material.
vi) Explain your material to your friend or someone else.
Assess
i) Can you solve random ALEKS’ questions?
ii) Can you solve Exam Practice problems?
iii) Can you rework the problems I worked out in class without looking at the answers?
Week 2- Chapter 12 and 13
CHAPTER 12: CHEMICAL KINETICS
Learning objectives:
1. Derive rate expressions from the balanced equation for a given chemical reaction
2. Calculate reaction rates from experimental data
3. Describe the effects of chemical nature, physical state, temperature, concentration, and
catalysis on reaction rates
4. Use rate and concentration data to identify reaction orders and derive rate laws
5. Perform integrated rate law calculations for zero-, first-, and second-order reactions
6. Define half-life and carry out related calculations
7. Use the postulates of collision theory to explain the effects of physical state, temperature, and
concentration on reaction rates
8. Use the Arrhenius equation in calculations relating rate constants to temperature
9. Explain the function of a catalyst in terms of reaction mechanisms and potential energy
diagrams
Chemical Kinetics and Reaction Rates
• Chemical kinetics: The study of reaction rates
• Reaction rates: The changes in concentrations of reactants and
products with time (units for reaction rate??)
• Reaction rates are expressed as the concentration of reactant
consumed or the concentration of product formed per unit time
• For the reaction, A → B
14-4
Writing Rate Expressions
2N2O5(g) → 4NO2(g) + O2(g)
• Write the rate expression in terms of each species.
• Rate of N2O5 decomposition =
• Rate of NO2 formation =
• Rate of O2 formation =
Figure: The Progress of a Simple Reaction (A → B)
14-6
Reaction rates
Decomposition of Hydrogen peroxide: 2H2O2 → 2H2O + O2
Rate decreases as the concentration of H2O2 decreases.
∆[𝐻2 𝑂2 ]
𝑅𝑎𝑡𝑒 = −
∆𝑡
14-7
Average Reaction Rate
• The reaction rate calculated for a given time interval from the
concentrations at the beginning of the interval time (ti) and at the end
of the interval (tf)
𝑅𝑎𝑡𝑒𝑡=0.00ℎ−6.00ℎ = ?
14-8
Knowledge Check 1
• Calculate the average reaction rate for the H2O2 reaction from the
earlier two slides from the time interval of t= 6 to t=24.
Instantaneous Reaction Rate
The reaction rate of a chemical
reaction at any given point in time
• e.g. Instantaneous rate at 10 h
∆ 𝐻2 𝑂2
∆𝑡
=−
= slope of tangent
14-10
ALEKS problem (calculating rates from a graph)
Relative Reaction Rate
Using the data in the following table, prove the relationship:
Rate = −
∆ 𝑆𝑂2
2∆𝑡
=−
∆ 𝑂2
∆𝑡
=
∆[𝑆𝑂3 ]
2∆𝑡
2SO2(g) + O2(g) → 2SO3(g)
Time (s)
[SO2] (M)
[O2] (M)
[SO3] (M)
300
0.0270
0.0500
0.0072
720
0.0194
0.0462
0.0148
14-12
Calculating the reaction rate of one species from that of
another
• For the reaction: 2H2O2 → 2H2O + O2
Rate= −
∆ 𝐻2 𝑂2
2∆𝑡
=
∆ 𝐻2 𝑂
2∆𝑡
=
∆[𝑂2 ]
∆𝑡
• If the rate of decomposition of H2O2 is 3.20 × 10−2
molL-1h-1, what is the rate of production of H2O?
14-13
Knowledge Check 2
• What is the rate of production of O2?
Factors affecting Reaction Rates
•
•
•
•
•
Concentration of reactants
Temperature and Pressure
Phase and surface area of the reactants
Nature of solvent
Catalyst
14-15
Knowledge Check 3
• How does the surface area of reactants and pressure affect the
reaction rate?
ALEKS problem (factors affecting reaction rate)
Rate Laws or Rate Equations
• Mathematical expressions that describe the relationship
between the rate of a chemical reaction and the
concentration of its reactants.
A+B→C
• In general, a rate law (or rate equation) takes this form:
Rate = k[A]m[B]n…
14-18
Order of reaction
• k, m and n are determined experimentally
• The rate constant k is independent of concentrations of A
and B whose value is characteristic of the reaction and the
reaction conditions. It does not change as the reaction
progresses under a given set of conditions
• If m = 0, the reaction is ????? with respect to A
• If m = 1, the reaction is ????? with respect to A
• If m = 2, the reaction is ????? with respect to A
• Rate = k[A]2[B]1
14-19
ALEKS problem (Using and understanding the rate law)
Knowledge Check 4
• For the same problem in the earlier slide, what is the new value of
the rate constant if the reaction order in nitrogen was 2 instead of 3
(assume everything else is constant)?
Order of reaction (& unit of rate constant)
An experiment shows that the reaction of nitrogen dioxide
with carbon monoxide is second order in NO2 and zero order
in CO at 100oC. What is the rate law for the reaction?
NO2(g) + CO(g)⟶ NO(g) + CO2(g)
Rate = k[NO2]?[CO]? = k[NO2]?
What will be the unit of rate constant k for this reaction?
14-22
Knowledge Check 5
• What will be the unit of rate constant “k” for the reaction in the
earlier slide if the reaction was first order in CO (assume everything
else is constant)?
But how do chemists determine a Reaction’s Rate Law?
• One way to determine the rate law of a reaction is to measure the
initial rate.
• The rate at time zero.
• If the initial rate is measured with a number of different initial
reactant concentrations then the rate law can be determined.
How to Determine a Rate Law
• The order with respect to a particular reactant can be determined by
varying its initial concentration while holding the initial
concentration(s) of the other reactant(s) constant.
• Experimentally measure the initial rate with each of the two different
concentrations.
• The change in rate is then a direct result of the reactant which changed in
concentration.
• The order with respect to that reactant can then be calculated.
• Repeat this process with all reactants.
ALEKS Problem (Rate Law Practice)
14-26
Knowledge Check 6
Determine the (a) rate law expression, (b) value of rate constant k with
appropriate units, and (c) overall rate for this reaction.
14-27
Integrated Rate Laws
• So far we have only talked about the concentration-rate relationship.
A → products
Rate = k[A]m
• The rate law can be integrated with respect to time to produce a
concentration-time relationship known as an integrated rate law.
• This relationship depends on the order of the reaction: Zero order, 1st
order, 2nd order, etc.
• A new term, the half-life, will also be introduced.
First-Order Reactions
• For 1st order reactions of the type A → products
rate = k[A]
Integration with respect to time gives us:
• k is the rate constant
• t is time
• [A]0 is the initial reactant conc.
• [A]t is the reactant conc. present at time t
[ A] 0
ln
= kt
[ A] t
Linear Form of the First-Order Integrated Rate Law
[ A] 0
ln
= kt
[ A] t
• We can put the first-order integrated rate law into the
form
ln[ A] t = - kt + ln[ A] 0
• y = mx + b
•
•
•
•
ln[A]t plotted on the y-axis
time (t) plotted on the x-axis
The slope of the line is –k
The y-intercept is ln[A]0
Knowledge Check 7
• For the linear form of first-order integrated rate law, what is plotted
on the y-axis and x-axis? Also, what is the slope of this linear form?
Integrated Rate Laws
• Note that when using all of the integrated rate laws
[ A] 0
ln
= kt
[ A] t
ln[ A] t = - kt + ln[ A] 0
• The amount of reactant (A) does not always need to be expressed in Molarity (M) as the
equations imply.
• The amount can also be expressed in
•
•
•
•
Mass (g, mg, etc.)
Number of molecules or atoms
Other conc. units such as g/L
Partial pressure if A is a gas (assuming volume and temperature remain constant).
Figure 12.9
The linear relationship between the ln[H2O2] and time shows that the decomposition of
hydrogen peroxide is a first-order reaction.
ALEKS (Linear Form of the First-Order Integrated Rate Law)
The Half Life: First-Order Reaction
• The half-life (t1/2) of a reaction is the
time it takes for one half of a given
amount of reactant to be consumed.
• For a first-order reaction, at the halflife, t1/2
• [A]t = ½[A]0
Solving for t in ln[A]t = –kt + ln[A]0
t1/ 2
ln 2 0.693
=
=
k
k
Figure 12.12
The decomposition of H2O2 (2H2O2 ⟶ 2H2O + O2) at 40 °C is illustrated. The intensity of the
color symbolizes the concentration of H2O2 at the indicated times; H2O2 is actually colorless.
The Half Life: First-Order Reaction
t1/ 2
ln 2 0.693
=
=
k
k
• Notice that for a first-order reaction, the half-life is independent on
the initial concentration
of reactant.
ALEKS (The Half Life: First-Order Reaction)
The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of
82 minutes.
Suppose in a particular patient the concentration of this drug in the bloodstream immediately after
injection is 1.7 microgram/mL. What will the concentration be 328 minutes later?
Knowledge Check 8
What is half-life for the first order decay of 14C according to the reaction, 146C → 147N
+ e- ? The rate constant for the decay is 1.21 ×10-4 year-1.
14-39
Second-Order Integrated Rate Law
• For A → products, Rate = k[A]2
• Integration with respect to time gives us:
1
1
= kt +
At
A0
t1/ 2
1
=
k[A]0
• The half-life of a second-order reaction does depend on
the initial concentration of reactant.
Figure 12.10
.
Knowledge Check 9
• For the linear form of second-order integrated rate law, what is
plotted on the y-axis and x-axis? Also, what is the slope of this linear
form and what is the y-intercept?
Zero-Order Integrated Rate Law
• For a zero-order reaction: A → products
rate = k[ A]0 = k
• Integration with respect to time gives us:
[ A]t = - kt + [ A]0
[ A]0
t1/ 2 =
2k
• Note that the half-life of a zero-order reaction DOES
DEPEND on the initial concentration of reactant.
Summary: Properties of Reactions that Obey Zeroth-, First-,
and Second-Order Rate Laws
14-44
SUMMARY: Properties of Reactions That Obey Zeroth-,
First-, and Second-Order Rate Laws
14-45
ALEKS (Deducing a rate law from the change in concentration
over time)
Learning Objectives
12.5 Collision Theory
• Use the postulates of collision theory to explain the effects of physical state,
temperature, and concentration on reaction rates
• Define the concepts of activation energy and transition state
• Use the Arrhenius equation in calculations relating rate constants to
temperature
Collision Theory
• Collision theory: Reactants (atoms, molecules, or ions) must collide in
order to react with each other.
• Postulates of Collision theory:
1) Rate of Reaction is proportional to the rate of reactant collisions.
Collisions: Effective and Ineffective
• Why does every collision not lead to a reaction?
2) Molecules must be oriented properly when they collide.
Collisions: Effective and Ineffective
Why does every collision not lead to a reaction?
3) Molecules must have adequate kinetic energy to react.
• The kinetic energy supplied must be high enough to break the chemical
bonds.
• Molecules with kinetic energies too small just bounce off each other and
don’t react.
• This required energy is called the activation energy
• Activation energy (Ea): minimum energy necessary to form a
product during a collision between reactants.
Think about these questions
What is the difference between effective and ineffective collisions?
Why does all the collisions does not form products?
Transition-State Model
• Reaction energy diagram
• Potential energy is plotted on the y-axis
• Reaction path (or extent of reaction) is plotted on the x-axis.
• The reactants form an intermediate called an activated complex.
• The state of the system at the activated complex is called a transition state.
Figure 12.14
This graph shows the potential energy relationships for the reaction A + B ⟶ C + D. The dashed
portion of the curve represents the energy of the system with a molecule of A and a molecule
of B present, and the solid portion the energy of the system with a molecule of C and a
molecule of D present. The activation energy for the forward reaction is represented by Ea. The
activation energy for the reverse reaction is greater than that for the forward reaction by an
amount equal to ΔH. The curve’s peak is represented the transition state.
ALEKS (Understanding the features of an energy diagram)
Reaction Rate and Temperature
Thus far we have discussed:
• The concentration-rate relationship
• The concentration-time relationship
• Now we will look at the temperature–rate relationship.
Reaction rate ordinarily increases with temperature.
• To cook food more quickly, raise the oven temperature.
• To slow the reactions that lead to food spoilage, put food in the refrigerator.
• To really slow the reactions down, put food in the freezer.
Kinetic Theory
• Higher temperatures mean higher kinetic energies.
• The higher the temperature, the larger the fraction of molecules with
kinetic energies equal to or greater than the activation energy (Ea).
• With a larger fraction of molecules possessing Ea, a larger fraction of
collisions lead to product formation, resulting in a higher rate of reaction.
Kinetic Theory
• Consider the following equation:
k = Ae
−E a / RT
• A is a constant called the frequency factor and is related to the frequency of collision and
orientation.
• The rate constant (k) is dependent on the activation energy of the reaction and the
temperature.
Kinetic Theory
k = Ae −E a / RT
• Consider two different reactions that occur at the same temperature.
Each reaction has a different Ea.
Kinetic Theory
k = Ae −E a / RT
• Consider the same reaction at two different temperatures. Ea is
independent of temperature.
Arrhenius Equation
k = Ae
−E a / RT
• Taking the natural logarithm of both sides of the equation gives the
Arrhenius equation.
æ -E a öæ 1 ö
ln(k) = ç
÷ç ÷ + ln(A)
è R øè T ø
Figure 12.16
This graph shows the linear relationship between ln k and 1/T for the reaction 2HI ⟶ H2 + I2
according to the Arrhenius equation.
Knowledge Check 10
14-62
Two-Point Form of the Arrhenius Equation
æ -E a öæ 1 ö
ln(k) = ç
÷ç ÷ + ln(A)
è R øè T ø
k2 E a 1 1
ln =
−
k1 R T1 T2
• This form of the Arrhenius equation can be used with two k values and
two corresponding temperatures to calculate Ea.
• You do not need to know the value of the constant, A, to use this
equation.
• Make sure that the energy units on Ea and R are identical.
ALEKS (calculate k at one temperature from k at another)
Reaction Mechanisms—A Microscopic View
• The mechanism of the reaction describes how individual atoms, ions, or
molecules interact to form particular products
• The stepwise changes are collectively called the reaction mechanism
O3(g)⟶O2(g)+O
O+O3(g)⟶2O2(g)
Overall: 2O3(g) ⟶ 3O2(g)
Elementary reaction: Each of the series of reactions that take place in a stepwise
fashion to convert reactants to products
14-65
ALEKS (Identifying intermediates and writing overall reaction)
Rate-Determining Step
• Rate-determining step: The slowest step in a reaction mechanism
14-67
Catalysis
• Catalyst: A substance that participates in a reaction and causes it to
occur more rapidly but that can be recovered unchanged at the end
of the reaction and reused
• A catalyst lowers the
Activation energy and
thus facilitates the
reaction → →
14-68
Knowledge Check 11
• How does a catalyst speed up the reaction? (Look at the earlier slide
to help you answer this question.)
Heterogeneous Catalysis
• Heterogeneous catalysis: A catalytic reaction in which the catalyst is in
a different phase from the reactants
14-70
Homogeneous Catalysis
• Homogeneous catalysis: A catalytic reaction in which the catalyst is
uniformly dispersed throughout the reactant mixture to form a solution
14-71
Enzymes as Catalysts
14-72
Chapter 13: Chemical Equilibrium
Learning Objectives
By the end of this section, you will be able to:
▪ Describe the nature of equilibrium systems
▪ Explain the dynamic nature of a chemical equilibrium
▪ Derive reaction quotients from chemical equations representing
homogeneous and heterogeneous reactions
▪ Calculate values of reaction quotients and equilibrium constants,
using concentrations and pressures
▪ Describe the ways in which an equilibrium system can be stressed
▪ Predict the response of a stressed equilibrium using Le Châtelier’s
principle
▪ Calculate equilibrium concentrations or pressures and equilibrium
constants, using various algebraic approaches
15-73
Chemical Equilibrium
• The point at which the forward and reverse reaction rates become the same so that
the net composition of the system no longer changes with time
2NO2(g) ⇌
Brown
N2O4(g)
Colorless
• Chemical Equilibrium is the phenomenon observed in reversible reactions.
15-74
Concept of Equilibrium
A two-person juggling act illustrates the dynamic aspect of chemical
equilibria. Each person is throwing and catching clubs at the same rate,
and each holds a (approximately) constant number of clubs.
15-75
The Concept of Chemical Equilibrium
15-76
Chemical Equilibrium in Biological Systems
Transport of carbon dioxide in the body involves several reversible
chemical reactions, including hydrolysis and acid ionization (among
others).
15-77
The Reaction Quotient Qc
What is Q?
Q measures the relative amounts of products and reactants present during a reaction at a particular point in time.
Qc: The ratio of the product concentrations (multiplied together) to the reactant
concentrations (also multiplied together), with each concentrations raised to the power
equal to the coefficients in a balanced chemical equation.
For the reaction, 𝑁2 𝑔 + 3𝐻2 𝑔 ⇌ 2𝑁𝐻3 (𝑔) 𝑸𝒄 =
[𝑵𝑯𝟑 ]𝟐
[𝑵𝟐 ][𝑯𝟐 ]𝟑
15-78
The Reaction Quotient Qp
Qp: The ratio of the partial pressure of products (multiplied together)
to the partial pressure of reactants (also multiplied together), with each
partial pressures raised to the power equal to the coefficients in a
balanced chemical equation.
• For the reaction, 𝑁2 𝑔 + 3𝐻2 𝑔 ⇌ 2𝑁𝐻3 (𝑔)
𝑸𝒑 =
(𝑷𝑵𝑯𝟑 )𝟐
(𝑷𝑵𝟐 ) (𝑷𝑯𝟐 )𝟑
Knowledge Check 12
• Suppose you run this reaction in a chemistry lab:
CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (g)
Write down the reaction quotient (Qp) for this reaction.
The Reaction Quotients Qc and Qp
The Equilibrium Constant K
15-82
ALEKS (Calculating an equilibrium constant from an
equilibrium composition)
Equilibrium Constant Practice (Q relation to K)
Consider the equation: 2NO2(g) ⇌ N2O4(g)
When 0.10 mol NO2 is added to a 1.0-L flask at
25°C, the concentration changes so that at
equilibrium, [NO2] = 0.016 M and [N2O4] =
0.042 M.
(a) What is the value of the reaction quotient
before any reaction occurs?
(b) What is the value of the equilibrium
constant for the reaction?
Knowledge Check 13
• For the question in the earlier slide, let us assume the concentration
changes so that at equilibrium, [NO2] = 0.042 M and [N2O4] = 0.016 M
(temperature and the volume of the flask is constant).
(a) What is the value of the reaction quotient before any reaction
occurs?
(b) What is the value of the equilibrium constant for the reaction?

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