NCHE 312 EC
PHYSICAL CHEMISTRY
Faculty of Natural and Agricultural Sciences
Study guide compiled by: RJ Kriek
Copyright © 2022 edition. Review date 2022.
North-West University
No part of this study guide may be reproduced in any form or in any way without the written permission of the publishers.
It all starts here
•
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Ranked in the top 5% of universities globally by the QS-rankings
Contributes the second largest number of graduates annually to the labour market
Dit begin alles hier
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As een van die top 5% universiteite wêreldwyd deur die QS-ranglys aangewys
Lewer jaarliks die tweede meeste graduandi aan die arbeidsmark
Gotlhe go simolola fano
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•
Re beilwe mo gare ga diyunibesiti tse 5% tse di kwa godimo go ya ka peo ya
maemo ya QS
Ngwaga le ngwaga go abelwa palo ya bobedi ka bogolo ya badiri mo maketeng ya
badiri
MODULE CONTENTS
Module information ................................................................................................................ iii
A word of welcome................................................................................................................. iii
Module outcomes................................................................................................................... v
Prior learning ......................................................................................................................... v
Teaching details ..................................................................................................................... vi
Study material ....................................................................................................................... vii
How to study ......................................................................................................................... vii
Assessment ......................................................................................................................... viii
How to use this study guide ................................................................................................... ix
Action words .......................................................................................................................... ix
Icons ...................................................................................................................................... x
Warning against plagiarism .................................................................................................... xi
Study Division 1: Structure: Quantum theory and spectroscopy ............................................ 1
Study Unit 1
Quantum theory and molecular spectroscopy ................................... 2
Study unit plan ....................................................................................................................... 3
Study Section 1.1 Origin of quantum mechanics ................................................................. 4
1.1.1
Failures of classical mechanics .............................................................. 4
1.1.2
Quantization of energy ........................................................................... 5
1.1.3
Wave-particle-duality.............................................................................. 5
Study Section 1.2 Dynamics of microscopic systems .......................................................... 6
Priorities ................................................................................................................................. 6
1.2.1
Schrödinger equation ............................................................................. 6
1.2.2
Interpretation of wavefunction ................................................................ 7
Study Section 1.3 Molecular vibration and infrared spectroscopy ........................................ 8
1.3.1
Properties of a harmonic oscillator ......................................................... 8
1.3.2
Features of vibration spectra .................................................................. 9
Study Section 1.4 Molecular rotation and microwave spectroscopy .................................. 10
1.4.1
Properties of a rigid rotor ...................................................................... 10
1.4.2
Features of rotation spectra (also including distortion) .......................... 11
Study Section 1.5 Vibration-rotation spectra ..................................................................... 12
1.5.1
Vibration-rotation spectra ..................................................................... 12
Study division 2 Non-ideality:
Gases
and
solutions .............................................................................................................................. 14
Study Unit 2
Real gases and solutions .................................................................. 15
Study unit plan ..................................................................................................................... 16
Study Section 2.1 Adaptions for non-ideal gases .............................................................. 17
Priorities ............................................................................................................................... 18
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2.1.1
Equations of state, compression factor, and Van der Waals constants. 18
2.1.2
Temperature dependance of Cp and value of Cp – CV ............................................ 18
2.1.3
Joule-Thomson effect ........................................................................... 19
Study Section 2.2 Compensation for deviations of non-ideal solutions .............................. 20
Priorities ............................................................................................................................... 20
2.2.1
Definitions: activity, activity coefficient, ionic strength ........................... 20
2.2.2
Electrochemical measurement of activity coefficients ........................... 21
Study division 3 Change: Chemical kinetics ......................................................................... 22
Study Unit 3
Rate of chemical reactions ................................................................ 23
Study unit plan ..................................................................................................................... 24
Study Section 3.1 Principles of kinetics ............................................................................. 25
Priorities ............................................................................................................................... 25
3.1.1
Measuring reaction rates ...................................................................... 25
3.1.2
Integrated rate laws.............................................................................. 26
3.1.3
Steady-state approximation .................................................................. 26
3.1.4
Activation parameters .......................................................................... 26
Study Section 3.2 Kinetics of electrode reactions .............................................................. 28
3.2.1
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Dynamics of electrode reactions .......................................................... 28
Module information
Module code
NCHE312
Module Credits
16
Module name
Physical Chemistry
Lecturers:
Name of lecturer
Prof Cobus Kriek, Potchefstroom
Office telephone
018 299 2345
Email address
cobus.kriek@nwu.ac.za
Building and Office nr
Natural Science Building G8, Room 107
Consulting hours
By appointment and e-mail
Name of lecturer
Dr Mawethu Bilibana, Mafikeng
Office telephone
018 389 2867
Email address
Mawethu.Bilibana@nwu.ac.za
Building and Office nr
Old Science Building A4, Room 2064
Consulting hours
By appointment and e-mail
A word of welcome
Welcome to all who have enrolled for module NCHE312, physical chemistry on thirdyear level, in 2022. This module is presented with an open-textbook approach and your
Atkins’ Physical Chemistry International Edition (2018) will be with you whenever you
write a class test, a semester assessment (or more extensive test), or write an exam
paper! In this way you are much more suitably equipped for the real-world where it is
expected of you to independently consult sources of information and to retrieve data from
the literature to solve a problem rather than to rely on partly forgotten memorised
knowledge. Samuel Johnson once said: Knowledge is of two kinds. We know the subject
ourselves, or we know where we can find information upon it. You should decide yourself
what information (physical constants, enthalpies, activation parameters) you need to
solve a specific problem, and where (textbook, library, internet) such information can be
found, so that one day you as an employee of a company, a consultant in public life or a
lecturer at a university may use with confidence available sources of information to solve
problems.
The open-book approach requires more thorough preparation and more practice than
the traditional closed-book approach. The open-book approach will change the way in
which you utilise your textbook. For the first time ever you will really use it, index it, and
consult it so regularly that it may fall apart towards the end of the semester. You will
discover the textbook to be an asset which you would like to keep ready throughout your
career as a chemist. The open-book approach lastly implies that class tests, the
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semester assessment (or more extensive test) and exam papers may look different from
what you are used to, since the emphasis is now on insight and application rather than
on memorisation and reproduction of study material.
Apart from the open-book approach, you have probably also discovered that chemistry
generally demands a study method different from that required for subjects having a lot
to memorise, and this applies especially to physical chemistry with its emphasis on
problem-solving. It is not the easiest subject around, and instead of mastering the theory
first and then apply it, you should rather start with problem-solving and discover the
underlying theoretical principles as you progress. You may compare it to a situation
where somebody who wants to play soccer, starts practising the game on the soccer
field and gradually becomes familiar with the rules instead of starting with the rules of
the game by memorising them from an instruction book. The successful physical
chemistry student is one who makes the important paradigm shift to tackle the subject in
a problem-solving mode rather than a theory- memorising mode. This study guide is
intended to help you to achieve this by listing under the heading “priorities” the items you
should be capable of doing.
Physical chemistry serves the purpose of teaching you to think logically, a capability
which is more important than the content of the subject. For this reason, you should
regard physical chemistry as a discipline of exceptional educational significance and not
reject it too quickly. Many students in other careers have confirmed that physical
chemistry taught them to think scientifically. I would like to equip you by virtue of this
advanced module in physical chemistry to think scientifically and not to rely on
memorised knowledge only.
Finally, I would like to relate the known expression no pain, no gain to physical chemistry.
The key to success is to be prepared to take the “pain” required to master physical
chemistry. Good luck with that!
Further module information
NCHE312 is based on selected chapters from the prescribed textbook (Atkins’ Physical
Chemistry, International Edition, 2018) within the three principal theories of chemistry
(quantum mechanics or “structure”, thermodynamics or “equilibrium” and reaction
kinetics or “change”). The contents of the module is an extension of the physical
chemistry of the ideal state, as presented introductorily in NCHE111 and more
completely in NCHE212, to the physical chemistry of the non-ideal (real) state. It includes
topics of non-ideality within advanced thermodynamics (extended law of Kirchhoff, CpCv for real gases, Joule-Thomson effect, activity coefficients of concentrated solutions,
Debye-Hückel extrapolation for determination of activity coefficients), and mnore
complex process kinetics. Additionally, it offers a first aquaintance with quantum
mechanical principles in order to make molecular spectroscopy (vibration or infrared
spectra, rotation or microwave spectra and vibration-rotation spectra) understandable on
third-year level and to serve as a point of departure for molecular modelling on
postgraduate level.
In a nutshell, the objective with NCHE312 is to aquaint you with
•
quantum mechanical principles and the origin of molecular spectra;
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advanced thermodynamic theory for the non-ideal (real) state;
•
complex process kinetics of selected types of reaction.
The module is simultaneously an in-depth continuation of the preceding module
NCHE212 and a forerunner to the more advanced postgraduate follow-on module
NCHE612, all based upon the three principal theories of chemistry.
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The module has a credit value of 16 and represents 160 supposed hours of study, of
which 100 hours are assigned to theory (study and practising) and 60 hours to practicals
(execution and report writing).
Module outcomes
Knowledge:
On completion of the module you should have the knowledge and insight
1.
to perform calculations based on introductory quantum chemical principles;
2.
to explain the origin of vibration, rotation and vibration-rotation spectra, and to
calculate molecular quantities and spectroscopic constants from these spectra;
3.
to calculate thermodynamic quantities for real (non-ideal) gases by using tabled
data in equations based on deviations from ideal gas behaviour;
4.
to utilise the Debye-Hückel theory to determine thermodynamic quantities for real
(non-ideal) solutions;
5.
to determine kinetic quantities and activation parameters of complex reactions both
numerically and graphically.
Capabilities:
On completion of the module you should be able
1.
to apply a few important physical-chemical methods of investigation and laboratory
techniques;
2.
to perform the prescribed experiments as illustrations of the three chemical models
(equilibrium, structure and change) taught in the theory part of the module;
3.
to analyse and interpret measured physical-chemical data by using the prescribed
practical manual, a suitable calculator and computer software (Microsoft Word,
Microsoft Excel);
4.
to consult sources of information (library, internet, databases) in order to find
answers to questions related to the prescribed experiments;
5.
to work with other students within a group in the laboratory as will probably be
required in a future career position.
Prior learning
A student who enrols for NCHE312 needs to have passed the preceding module
NCHE212. Other prior learning includes
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•
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basic computer skills, which include experience with Microsoft Word, Excel and
Powerpoint;
capability to use a calculator with built-in statistical functions and regression
routines;
familiarity with eFundi to download and use published material.
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Teaching details
Online Theoretical sessions
The lecturer presents you with recorded theoretical sessions, that is the core lectures,
each of which deals with one topic and which is summarised on one or more Powerpoint
slides. The presentation further supports the open-book approach for a real-world
scenario. The study guide contains assignments/problems, indicated as priorities, which
you should work through to ensure that you achieve the module outcomes. The class
tests, semester assessment (or more extensive test) and exam papers are based on the
study material covered in these assignments.
Learning facilitation
The lecturer futhermore presents you with recorded solutions to the
assignments/problems to assist you (by virtue of exercises based on existing
assessment material) with the open-book approach and with practise in problem-solving.
Arrangements with regard to this additional tutorial period for problem solving will be
made during the first few contact sessions.
Consultation times
You are welcome to contact the lecturer via e-mail to discuss problems. Additional
contact between the lecturer and students will be investigated.
Workplan
A workplan will be provided that specifies the schedule of the theoretical online sessions
as well as the study sections dealt with during these sessions and the dates on which
class tests are written. It is expected of you to prepare in accordance with this workplan.
Practicals
The theoretical and practical sections of the module are not mutually separated but form
an integrated unity. The purpose of the practicals is to demonstrate some of the
principles from theory and to offer you the opportunity to think creatively and innovatively.
The prescribed experiments are a capita selecta based on the prescribed study material
and are performed during the practical cycle for NCHE312 on a rotation basis according
to a pre-prepared schedule. These experiments are described and bound together in a
practical manual, which includes pro forma report forms to familiarise you with the
compilation of a practical report. The report forms are also available in electronic format
on eFundi in case you prefer to complete your report on your computer. The advantage
is that you then have the software on your computer available for data processing (e.g.
Iinear regression), statistical calculations (e.g. standard deviation) and word processing
(e.g. answers to questions).
The practicals consist of six experiments, which are executed by subdevided groups of
students persuant to a rotation schedule. It is foreseen that these experiments will
take place on campus so that students can generate their own data (for this you
will therefore have to come to Chemistry Department, A4 building). Although
students work together in groups, each individual is expected to complete an own report
by using the report formsin the practical manual or on eFundi.
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NB! Each student must have his/her own laboratory jacket and face shield. No
safety glasses are necessary as the faceshield is sufficient. Disposable gloves and
masks will be provided at the laboratories. Closed shoes are compulsory.
Study material
Textbooks
The prescribed textbook for theory is Atkins’ Physical Chemistry, International Edition
(2018), Peter Atkins, Julio de Paula and James Keeler. Publisher: Oxford University
Press. The textbook is complemented by additional study material which can be
accessed at the following website www.oup.com/uk/pchem11exe/, in order to achieve
deeper insight into physical chemistry.
The prescribed practical manual/guide will be made available online.
Study guide
The study guide is used throughout the presentation of the module. It has been revised
for 2022 and is based on the prescribed textbook mentioned above.
Calculator
Use of a more advanced calculator than those capable of performing basic arithmetical
operations only, could be helpful for calculations in both the theoretical and practical
components of the module, but is not essential. Examples include the HP35S and
HP50G of Hewlett-Packard.
How to study
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•
•
•
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Read the introductory section of this study guide. This is the first step to
successfully complete this module, since you then know exactly what is expected
of you and how you should proceed to achieve that.
Prepare for each online session by using the workplan and this study guide.
Consider the study material as comparable to the rules of a type of sport (soccer)
- you should not only study them (knowledge), but also practise them (insight) by
working through examples and problems while preparing for online sessions and
assessments.
Your objective should be to understand the work presented during each online
session and to take with you a “take-home message”. The purpose of the online
sessions is to guide you to get used to self-learning.
Check your progress. Class tests may help to ascertain whether you have achieved
the outcomes. Download the class tests of last year from eFundi, answer them and
check your answers against the supplied memoranda/marking schemes. Do the
same with the semester assessment and final exam papers. If you are not doing
well, study the material again and seek help from your lecturer. Also take
confidence in asking questions.
Try to keep on track. Once you have fallen behind the schedule, is it difficult to
catch up.
It may also help to index your textbook with “thumbnails” to enable you to quickly
find information.
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Assessment
Smaller class tests and more extensive assessment
You write a number of class tests in the course of the semester. Consult the workplan
as well as eFundi for the dates on which class tests are written. There is also a more
extensive assessment, which covers approximately half of the work to be done to
complete the module. The average mark for the class tests, the mark for the semester
assessment and the mark for the practicals each contribute one-third towards the
participation mark. The mark required for admission to the exam is 40%.
Practical tests and reports
At the start of a practical session each student writes a short preparatory test on the
technical aspects of the experiment he/she is doing on a particular day. The practical
reports are handed in weekly to be marked by the student assistents.
The mark for each experiment consists of the marks for the preparatory test, the
experimental results and the general impression of the report. The average mark for the
six practicals accounts for one-third of the participation mark.
Participation and module marks
The participation mark, which should be 40% for admission to the exam, is calculated by
combining the practical mark (⅓), the mark for the more extensive assessment (⅓) and
the average mark for the class tests (⅓). In order to pass the module, you must obtain a
subminimum of 40% in the exam and a final module mark (average of participation and
exam mark) of 50%.
Examination
It planned to write a sitdown exam on campus. The date and time of the two exam
opportunities are determined by the examination office. You may utilise any of the two
(or both) exam opportunities. If you utilise both, the rules of the university state that the
mark for the second opportunity will be the final module mark. No proof of absence for
the first opportunity is required to turn up for the second opportunity. It is risky, however,
not to utilise the first opportunity since, if you turn ill during the second opportunity, there
is no further (third) exam opportunity. A student who misses out on both opportunities,
or who has not passed the module after the second opportunity, must register again, pay
tuition fees, attend contact sessions and get a new participation mark.
Absence
You write a number of class tests of which at least one normally falls away. In the event
of not writing a class test, you need to hand in a medical certificate or other supporting
document for exemption from that test, which then becomes the one that falls away.
If you miss out on the more extensive assessment, you lose an important opportunity to
get a good participation mark and do not gain experience in writing an open-book paper.
If you are absent from a practical session, you should submit a medical certificate or
other supporting document to your lecturer within one week after the date of absence. If
you fail to do so, you forfeit the mark for that practical. The practical report still needs to
be completed and handed in, which means that you are only exempted from writing the
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preparatory test. Completion of the practical component of module NCHE312 is
compulsory for acquiring proof of participation.
How to use this study guide
The aim of this study guide is to guide you through the study contents of NCHE312. You
should therefore use the study guide as efficiently as possible. You may use the following
as guidelines:
•
•
•
•
check thoroughly the outcomes stated in the different sections (study division,
study unit, study section) so that you are well informed of what you should finally
achieve,
check in advance the contents of a study unit - it gives a general overview of what
you may expect,
study the material of each study section according to the priorities given and make
sure that you do all the assignments, and
prepare well for each contact session, facilitation opportunity or practical according
to the workplan supplied.
Action words
Questions in class tests, semester assessments and exams contain certain action words,
the meaning of which you must know in order to answer questions correctly. With this in
view a short list of such action words is given below.
Study
Work through repeatedly until you fully grasp the meaning and are
capable of doing a specific assignment or example yourself.
Know
Learn/memorise until you are able to reproduce the information.
Assign mechanism
Give a reaction scheme by means of a few steps or by using an
arrow notation.
Apply
Use a formula/principle to solve a given problem.
Understand
Know exactly what something means; illustrate a theoretical
principle with a practical example.
Name/Give
Write down facts or statements.
Describe
Give properties, facts or results in a logical, well-formulated manner
without comments or discussion.
Define
Give a clear, short and authoritative description of a concept such
that its meaning becomes clear.
Explain
State a matter with illustrations, descriptions and examples such
that the reader can understand it.
Proof
Support a statement by logical and acceptable facts.
Compare
Contrast facts, events or problems and highlight differences and
similarities.
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Discuss
Formulate/debate various aspects of a matter in an analytical
manner.
Complete
Add a word, number, phrase, chemical formula, reaction, or
mechanism, to finish a statement.
Show relationship
Explain, if two statements are made, the connection between them.
Icons
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Time allocation
Learning outcomes
Study material
Assessment /
Assignments
Individual exercise
Group Activity
Example
Reflection
Warning against plagiarism
ASSIGNMENTS ARE INDIVIDUAL TASKS AND NOT GROUP ACTIVITIES. (UNLESS
EXPLICITLY INDICATED AS GROUP ACTIVITIES)
Copying of text from other learners or from other sources (for instance the study guide,
prescribed material or directly from the internet) is not allowed – only brief quotations
are allowed and then only if indicated as such.
You should reformulate existing text and use your own words to explain what you have
read. It is not acceptable to retype existing text and just acknowledge the source in a
footnote – you should be able to relate the idea or concept, without repeating the original
author to the letter.
The aim of the assignments is not the reproduction of existing material, but to ascertain
whether you have the ability to integrate existing texts, add your own interpretation and/or
critique of the texts and offer a creative solution to existing problems.
Be warned: students who submit copied text will obtain a mark of zero for the
assignment and disciplinary steps may be taken by the Faculty and/or University.
It is also unacceptable to do somebody else’s work, to lend your work to them or
to make your work available to them to copy – be careful and do not make your
work available to anyone!
Plagiarism is a serious offence and you should familiarise yourself with the
plagiarism policy of the NWU. http://library.nwu.ac.za/copyright-and-plagiarism
Please refer to the Policy on Academic Integrity which is found on the following
website:
http://www.nwu.ac.za/sites/www.nwu.ac.za/files/files/i-governancemanagement/policy/2P-2.4.3.2_Academic%20integrity_e.pdf
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Study division 1
Study Division 1:
Structure: Quantum theory and spectroscopy
Study time
The time scheduled for this study division is 45 hours.
Study Material
Study Division 1 is based on parts from Focus 7, 8, and 11 of Atkins’ Physical
Chemistry.
Study outcomes
After completing this study division you should be able
•
to explain a few phenomena which cannot be explained by means of classical
mechanics;
•
to describe the contributions of Max Planck, Niels Bohr, Werner Heisenberg,
Louis De Broglie and Erwin Schrödinger to the development of quantum
mechanics;
•
to write down the Schrödinger equation for microscopic systems and to explain
the requirements for a wavefunction and how these imply energy quantisation;
•
to explain the basic principles of absorption and emission spectroscopy and the
classification of spectral regions in the electromagnetic spectrum;
•
to write down the Schrödinger equation for a harmonic oscillator and a rigid
rotor, and to use the expressions for the vibrational and rotational energy levels
of a diatomic molecule without taking into account and taking into account
anharmonicity and centrifugal distortion in order to calculate molecular
quantities from molecular spectra;
•
to mathematically describe the origin of P-, Q- and R-branches in a vibrationrotation spectrum and to calculate molecular quantities from it.
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Study unit 1
Study Unit 1
QUANTUM THEORY AND MOLECULAR SPECTROSCOPY
Study time
The time scheduled for this study unit is 45 hours.
Study material
Study unit 1 is based on parts from Focus 7 (p. 223-240, 243-245, 247-251, 259263, 267-271), Focus 8 (p. 284) and Focus 11 (p. 395-397, 406-413, 418-425) of
Atkins’ Physical Chemistry.
Study outcomes
After completing this study unit you should be able
•
to explain the failures of classical mechanics at the beginning of the previous
century;
•
to highlight the contribution of each co-worker (Max Planck, Niels Bohr, Werner
Heisenberg, Louis De Broglie and Erwin Schrödinger) to the development of the
quantum theory in words and by calculations;
•
to explain the basic principles of molecular spectroscopy and the classification
of spectral regions within the electromagnetic spectrum;
•
to apply expressions for the vibrational and rotational energy levels of a diatomic
molecule without taking into account and taking into account anharmonicity and
centrifugal distortion in order to calculate molecular quantities from molecular
spectra;
•
to mathematically describe the origin of P-, Q- and R-branches in a vibrationrotation spectrum and to calculate molecular quantities from such a spectrum.
The advent of quantum theory in the period 1900-1925 represents an important paradigm
shift by providing, as a substitute for the description of macroscopic objects by classical
mechanics, quantum mechanics for the description of microscopic systems. The five
scientists who largely contributed to the development of the new theory were all
physicists who at some stage were Nobel-prize awardees. Physics is for this reason
often referred to as the “Big Brother” of chemistry. Molecular spectroscopy is an
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Study unit 1
important application of the quantum theory and was made possible by solving the
Schrödinger equation for different molecular systems.
Study unit plan
Study Sections 1.1 - 1.2
SYSTEMS
Microscopic
Quantum Theory
Macroscopic
Classical Mechanics
Quantization
Dualization
Normalization
(Planck, Bohr,
Heisenberg)
(De Broglie)
(Schrödinger)
Study sections 1.3 - 1.5
MOLECULAR SPECTROSCOPY
Vibration Spectra
Rotation Spectra
Vibration-Rotation Spectra
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Study unit 1
Study Section 1.1
Origin of quantum mechanics
Study time
The time scheduled for this study section is 8 hours.
Study material
This study section is based on parts from Focus 7 (p. 223-240, 243-245) and Focus
8 (p. 284) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study section you should be able
•
•
•
•
to describe a few phenomena (black-body radiation, emission spectrum,
photoelectric effect), which cannot be explained by classical mechanics but by
quantisation of energy according to the hypothesis of Planck;
to calculate the spectral lines in the emission spectrum of hydrogen and explain
how the spectra of hydrogenic atoms according to Bohr bear witness of
quantization of energy;
to state and interpret the Heisenberg uncertainty principle;
to write down the de Broglie relation and to present experimental verification
(Davisson-Germer experiment) for wave-particle duality.
The quantum theory was developed by the contributions of five physicists. The nature of
the contributions is covered in this study section.
Priorities
1.1.1
Failures of classical mechanics
Study material
•
4
Study in broad outline black-body radiation (p. 223, etc.), atomic and molecular
spectra (p. 227, etc.) and photoelectric effect (p. 228, etc.) as failures of
classical physics (Par. 7A.1-7A.2).
Study unit 1
1.1.2
Quantization of energy
Study material
•
Study the hypothesis of Planck on quantization of energy (Eqn. 7A.5).
•
Study the introductory part of Focus 8 (p. 284) in order to calculate according
to Bohr the wave numbers of the spectral lines of the different series (Lyman,
Balmer, Paschen, Brackett, Pfund, Humphreys) of the emission spectrum of the
hydrogen atom as examples of quantized energy transitions.
•
Study the uncertainty principle of Heisenberg (Par. 7C.3) as a reason why the
Bohr theory could not be extended to other hydrogen type atoms. Study Eqn.
7C.13a that describes the principle quantitatively.
Individual activity
1.1.3
•
Work through Example 7A.1 (p. 228), 7A.2 (p. 230), and 7C.4 (p. 244) and do
Self-test 7A.1, 7A.2, and 7C.4 as additional calculations of the same type.
•
Do Exercise 9C.1(a) (p. 393, Atkins’ Physical Chemistry 10th Edition) as an
example of calculations based on the emission spectrum of the hydrogen atom,
i.e. “Identify the shortest and longest wavelength lines in the Lyman series”.
•
Do Problem 9C.1 (p. 393, Atkins’ Physical Chemistry 10th Edition) in order to
take note of the Humphreys series in the emission spectrum of the hydrogen
atom, i.e. “The Humphreys series is a group of lines in the spectrum of atomic
hydrogen. It begins at 12 368 nm and has been traced to 3281.4 nm. What are
the transitions involved? What are the wavelengths of the intermediate
transitions?”
Wave-particle-duality
Study material
•
Study wave-particle duality (Par. 7A.2) with emphasis on the experimental
evidence for it (Davisson-Germer experiment) and the De Broglie relation (Eqn.
7A.11) between the momentum of a particle and the wavelength of its
associated wave.
Individual activity
•
Work through Example 7A.3 (p. 231) and do Self-test 7A.3 as an additional
calculation of the same type.
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Study unit 1
Study Section 1.2
Dynamics of microscopic systems
Study time
The time scheduled for this study section is 8 hours.
Study material
This study section is based on parts from Focus 7 (p. 232-239, 247-251) of Atkins’
Physical Chemistry.
Study outcomes
After completing this study section you should be able
•
•
•
•
•
•
to describe the contribution of Schrödinger to the quantum theory;
to write down the general form of the Schrödinger equation and to explain the
meaning of the different symbols;
to explain the requirements for a wavefunction and how these imply
quantization;
to distinguish among the concepts of normalization, quantization and
dualization and to explain each of these;
to know the meaning of the concepts of operator, eigenfunction and eigenvalue;
to demonstrate the “particle in a potential well” scenario as an example of
solving the Schrödinger equation for translational motion.
Priorities
1.2.1
Schrödinger equation
Study material
6
•
Study Par. 7B.1 and 7B.2 (p. 232-236).
•
Take note of the following concepts: operator, eigenfunction, eigenvalue (Par.
7C.1)
Study unit 1
1.2.2
Interpretation of wavefunction
Study material
•
Study Par. 7B.2 (p. 233-236) on the interpretation of the wavefunction.
•
Take note of the following concepts: duality (p. 228), probability density (p. 233),
normalization (p. 234), and quantization (p. 236).
•
Study Par. 7D.1 and 7D.2 (p. 247-252) which illustrates a “particle in a potential
well” as an example of the interpretation of the wavefunction.
Individual activity
•
Work through Example 7B.1 (p. 234), 7B.2 (p. 234), and 7B.3 (p. 235), and
then do Self-test 7B.1, 7B.2 and 7B.3 for more practice.
•
List the mathematical requirements which, in addition to the normalization
requirement, apply to an acceptable wavefunction of the Schrödinger equation
(p. 235-236).
7
Study unit 1
Study Section 1.3
Molecular vibration and infrared spectroscopy
Study time
The time scheduled for this study section is 13 hours.
Study material
This study section is based on parts of Focus 7 (p. 259-263) and Focus 11 (p. 395397, 406-413, 418-425) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study section you should be able
•
•
•
•
•
to explain the basic principles of spectroscopy and to identify in the
electromagnetic spectrum the region in which transitions specifically between
vibrational energy levels occur;
to write down the Schrödinger equation for a harmonic oscillator, and to give
and to apply the expressions for the wavefunctions and energy levels obtained
by solving the equation;
to give the gross and specific selection rules for vibrational transitions;
to use the expression for the vibrational energy levels of a diatomic molecule
without taking into account and taking into account anharmonicity to calculate
molecular quantities from vibration spectra;
to calculate the number of vibrational modes of polyatomic molecules and to
relate this to their vibration spectra.
Priorities
1.3.1
Properties of a harmonic oscillator
Study material
•
8
Read the introduction to molecular spectroscopy (p. 395-397) and take note of
the electromagnetic radiation specifically involved in vibrational transitions (Par.
11A.1).
Study unit 1
•
Take note of the Schrödinger equation for a harmonic oscillator (Eqn. 7E.2,
11C.3a) and the expression for the wavefunctions (Eqn. 7E.7) and energy
levels (Eqn. 7E.3, 11C.4a) obtained by solving the equation.
•
Make sure of the distinction between gross and specific selection rules (Par.
11A.1(b)) and take note of the specific selection rule that applies to vibration
transitions (Eqn. 11C.5).
Individual activity
1.3.2
•
Work through the Brief Illustrations (7E.1) on p. 260 and in the centre of p.
419 (11C.1) to sense the usefulness of a harmonic oscillator as a model for
molecular vibration.
•
Study Par. 11C.2 to predict by virtue of the gross selection rule which vibrations
are infrared active.
Features of vibration spectra
Study material
•
Learn how to use the expressions for the vibrational energy levels of diatomic
molecules without taking anharmonicity into account (Eqn. 11C.4b) and taking
anharmonicity into account (Eqn. 11C.8) in order to calculate molecular
quantities such as those in Table 11C.1 (p. 836).
•
Study the section dealing with the number of vibrational modes of polyatomic
molecules (p. 427-429) and relate it to the infrared spectra of such molecules.
•
Study the graphical methods based on Eqn. 11C.9b and Eqn. 11C.11 (BirgeSponer plot) to determine molecular quantities.
Individual activity
•
Do Problem 12D.3 (p. 528 of Atkins’ Physical Chemistry 10th Edition) by
linear regression of the spectral data according to the equation given, i.e. “The
vibrational levels of NaI lie at the wavenumbers 142.81, 427.31, 710.31, and
1
1 2
991.81 cm-1. Show that they fit the expression
, and
�𝜐𝜐 + � 𝜈𝜈� − �𝜐𝜐 + � 𝑥𝑥𝑒𝑒 𝜈�
2
2
deduce the force constant, zero-point energy, and dissociation energy of the
molecule.”
•
Work through Example 11C.2 on p. 422, and do Self-test 11C.2 as further
practice to plot a Birge-Sponer graph and to calculate from it the dissociation
energy of the molecule.
•
Work through the Brief Illustration 11D.1 on p. 427 and the captions of Fig.
11D.2 and Fig. 11D.3 in order to relate the observed peaks to the infrared active
modes (normal modes) of vibration.
9
Study unit 1
Study Section 1.4
Molecular rotation and microwave spectroscopy
Study time
The time scheduled for this study section is 13 hours.
Study material
This study section is based on parts of Focus 7 (p. 267-274) and Focus 11 (p. 406415) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study section you should be able
•
to explain the basic principles of spectroscopy and to identify the spectral region
within the electromagnetic spectrum for transitions specifically between
rotational energy levels;
•
to write down and to use the Schrödinger equation for a rigid rotor rotating in
two dimensions, as well as the expression for the energy levels obtained by
solving the equation for rotation in three dimensions;
•
to state the general and specific selection rules for rotational transitions of
diatomic molecules;
•
to use the expression for the rotational energy levels of a diatomic molecule
without taking into account centrifugal distortion and taking into account
centrifugal distortion in order to calculate molecular quantities from rotation
spectra.
Priorities
1.4.1
Properties of a rigid rotor
Study material
10
•
Study the sections on the rotation of a rigid rotor in two dimensions (Par. 7F.1,
p. 267-271) and three dimensions (Par. 7F.2, p. 271-274) in order to realise its
usefulness as a model for molecular rotation.
•
Derive in a “classical” way the same expression (Eqn. 11B.8, p. 408) for the
rotational energy levels of a diatomic molecule as the one obtained “quantum
mechanically” by solving the Schrödinger equation for a rigid rotor.
Study unit 1
Individual activity
•
1.4.2
Work through the Brief Illustration 11B.4 on p. 411 to predict by virtue of the
gross selection rule for rotation (Par. 11B.2(a), p. 411) which molecules exhibit
rotation spectra.
Features of rotation spectra (also including distortion)
Study material
•
Do revision of the introduction to molecular spectroscopy (p. 395-397) and take
note of the electromagnetic radiation involved specifically in rotational
transitions (Par. 11A.1), and of the distinction between gross and specific
selection rules (Par. 11A.1(b)).
•
Practise to use the expression for the rotational energy levels of a diatomic
molecule without taking into account centrifugal distortion (Eqn. 11B.14) and
taking into account centrifugal distortion (Eqn. 11B.15) in order to calculate
molecular quantities like those in Table 11C.1 (p. 836).
•
Use an analytical method (Eqn. 11B.16) as well as a graphical method (Eqn.
11B.20b) to determine the centrifugal distortion constant.
Individual activity
•
Work through Brief Illustrations 11B.1, 11B.2, and 11B.3. In addition work
through Examples 11B.1, 11B.2, and 11B.3 to instill the underlying priniciples
of rotational spectroscopy.
•
Do Problem 12C.2 (p. 526 of Atkins’ Physical Chemistry 10th Edition) as an
illustration of the appearance of a rotation spectrum and how molecular
quantities can be calculated from it, i.e. “Rotational absorption lines from 1H35Cl
gas were found at the following wavenumbers (R.I. Hausler and R.A. Oetjen, J.
Chem. Phys. 21, 1340 (1953)): 83.32, 104.13, 124.73, 145.37, 165.89, 186.23,
206.60, 226.86 cm-1. Calculate the moment of inertia and the bond length of the
molecule. Predict the positions of the corresponding lines in 2H35Cl.”
11
Study unit 1
Study Section 1.5
Vibration-rotation spectra
Study time
The time scheduled for this study section is 3 hours.
Study material
This study section is based on parts from Focus 11 (p. 422-424) of Atkins’ Physical
Chemistry.
Study outcomes
After completing this study section you should be able
•
to explain the origin and appearance of a vibration-rotation spectrum of a
diatomic molecule;
•
to illustrate the usefulness of a vibration-rotation spectrum for the calculation of
molecular quantities.
The vibration-rotation spectrum of diatomic molecules is extremely useful since several
molecular quantities such as the wavenumber of the fundamental vibrational transition,
the force constant, the bond length and the rotational constant of the molecule can
readily be determined from it.
Priorities
1.5.1
Vibration-rotation spectra
Study material
12
•
Study Par. 11C.4 on p. 422-424.
•
Study Fig. 11C.9 and Fig. 11C.10 to understand the formation of P-, Q- and Rbranches of a vibration-rotation spectrum as the one shown in Fig. 11C.8.
Study unit 1
Individual activity
•
Work through Brief Illustrations 11C.2 and 11C.3 to instill the underlying
concepts of vibration-rotation spectra.
13
Study unit 1
Study division 2
Non-ideality: Gases and solutions
Study time
The time scheduled for this study division is 30 hours.
Study material
This study division is based on parts from Focus 1, 2, 5 and 6 of Atkins’ Physical
Chemistry.
Study outcomes
After completing this study division you should be able
•
to define the compression factor of gases and to state whether repulsive or
attractive forces are operative;
•
to give the virial and Van der Waals equations as examples of equations of
state;
•
to calculate reaction enthalpies by means of the law of Kirchhoff while taking
into account the temperature dependence of Cp;
•
to define expansion coefficient and isothermal compressibility and to write down
the relationship between CP and CV for a real gas in terms of these definitions;
•
to explain the Joule-Thomson effect and its technological significance for the
liquefaction of gases;
to define the Joule-Thomson coefficient and to explain how it is measured
experimentally;
to define activity, mean activity coefficient and ionic strength of real solutions;
to calculate the mean activity coefficient by means of the Debye-Hückel limiting
law and to indicate how this law can be extended for concentrated solutions;
to describe measurement of mean activity coefficients and of standard electrode
potentials by means of a Debye-Hückel extrapolation.
•
•
•
•
14
Study unit 2
Study Unit 2
REAL GASES AND SOLUTIONS
Study time
The time scheduled for this study unit is 30 hours.
Study material
This study unit is based on Focus 1 (p. 6-9, 19-27), Focus 2 (p. 46-47, 53-54, 5864), Focus 5 (p. 173-180) and Focus 6 (p. 210-213) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study unit you should be able
•
to define the compression factor of real gases and to state under which
conditions repulsive and attractive forces are operative;
•
to write down the virial and Van der Waals equations as two examples of
equations of state, and to list the properties of the virial coefficients and of the
Van der Waals constants;
•
to calculate reaction enthalpies by means of the law of Kirchhoff while taking
into account the temperature dependence of Cp;
•
•
•
•
•
to define expansion coefficient and isothermal compressibility, to write down the
relationship between CP and CV for a real gas in terms of these definitions, and
to perform calculations based on this relationship;
to explain the Joule-Thomson effect and its technological significance for the
liquefaction of gases;
to define the Joule-Thomson coefficient, and to explain how it is measured
experimentally;
to define and to calculate the activity, mean activity coefficient and ionic strength
of real solutions;
to calculate mean activity coefficient by means of the Debye-Hückel limiting law,
and to indicate how this law can be extended for concentrated solutions;
15
Study unit 2
•
to describe the measurement of mean activity coefficients and of standard
electrode potentials by means of electrochemical cells and a Debye-Hückel
extrapolation.
You are familiar with introductory physical chemistry where the ideal gas law was used
as a starting point or hypothesis. In this study unit attention is given to deviations from
ideal behaviour, and how these are compensated for in the case of real gases and more
concentrated solutions.
Study unit plan
NON-IDEALITY
Real gases
Virial
Cp, Cv
Real solutions
JT-effect
Activity centre
Activity
Coefficients
16
Study unit 2
Study Section 2.1
Adaptions for non-ideal gases
Study time
The time scheduled for this study section is 20 hours. Part of the study material is
revision of work done in previous modules.
Study material
This study section is based on parts from Focus 1 (p. 6-9, 19-27), and Focus 2 (p.
46-47, 53-54, 58-64) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study section you should be able
•
•
•
•
•
•
•
•
to define the compression factor Z for real gases;
to specify conditions at which Z < 1 and Z > 1;
to write down a few equations of state, and especially highlight the virial and
Van der Waals equations as typical examples;
to list the properties of virial coefficients and of the Van der Waals constants;
to calculate reaction enthalpies by means of the law of Kirchhoff while taking
into account the temperature dependence of Cp;
to define isobaric thermal expansion coefficient and isothermal compressibility,
to write down the relation between CP and CV for a real gas in terms of these
quantities, and to perform calculations based upon them;
to describe the Joule-Thomson effect, and to explain how the technique is
applied to liquefy a gas (e.g. nitrogen) at room temperature;
to define the isothermal Joule-Thomson coefficient and to explain how it is
measured;
17
Study unit 2
Priorities
2.1.1
Equations of state, compression factor, and Van der
Waals constants
Study material
•
Study Par. 1A.2(a), 1C.1 as well as 1C.2(a) and (b) and familiarise yourself with
quantities in Table 1C.1, 1C.2 and 1C.3 and their use in calculations. See Table
1C.4 for a selection of equations of state.
•
Read Par. 1C.2(c) as revision of previously studied lecture material on the
compensation for deviations from ideality, and take note of the use of reduced
variables to compensate for the differences among real gases according to the
principle of corresponding states (Fig. 1C.8, p. 26).
Individual activity
2.1.2
•
Work through Brief Illustrations 1C.1 and 1C.2 to familiarise yourself with the
content of this section.
•
Do Problem 1C.2 (p. 57 in Atkins’ Physical Chemistry 10th Edition) as an
additional example of the topics covered in this study section, i.e. “At 273 K
measurements on argon gave 𝐵𝐵 = -21.7 cm3 mol-1 and 𝐶𝐶 = 1200 cm6 mol-2,
where 𝐵𝐵 and 𝐶𝐶 are the second and third virial coefficients in the expansion of 𝑍𝑍
in powers of 1/𝑉𝑉𝑚𝑚 . Assuming that the perfect gas law holds sufficiently well for
the estimation of the second and third terms of the expansion, calculate the
compression factor of argon at 100 atm and 273 K. From your result, estimate
the molar volume of argon under these conditions.”
Temperature dependance of Cp and value of Cp – CV
Study material
18
•
Study Par. 2B.2 with special attention to Eqn. 2B.5 (definition of Cp) and Eqn.
2B.8 (temperature dependence of Cp). Work through Example 2B.2 (p. 47) in
which the integrated form of Eqn. 2B.8 is derived.
•
Take note of the values of the empirical parameters a, b and c (see Table 2B.1)
in Eqn. 2B.8, and how these are used in Kirchhoff calculations of reaction
enthalpies at alternative temperatures where, unlike in Example 2C.2 (p. 54),
Cp is not independent of the temperature.
•
Learn the definitions for isobaric thermal expansion coefficient (Eqn. 2D.6) and
isothermal compressibility coefficient (Eqn. 2D.7) on p. 60 with which a
universally true expression (Eqn. 2D.11, p. 61) for Cp – Cv of real gases can be
derived. Take note of literature values for these two quantities in Table 2D.1.
Study unit 2
Individual activity
2.1.3
•
Do Self-test 2B.2 (p. 47) as practice to derive on your own the integrated form
of Eqn. 2B.8.
•
Verify the small difference between Cp and Cv for water as specified in Brief
Illustration 2D.1 (p. 61) by calculating it with Eqn. 2D.11 and values from Table
2D.1. Explain why the value is so small in comparison to differences as large
as 30% in a few cases.
•
Do Self-test 2D.3 (p. 94 in Atkins’ Physical Chemistry 10th Edition), i.e.
“Evaluate the difference in molar heat capacities for benzene.”
Joule-Thomson effect
Study material
•
Study Par. 2D.3 and 2D.4 (p. 61-64). Learn the definition for the isenthalpic
Joule-Thomson coefficient (Eqn. 2D.12, p. 61). Take note of the requirements
for an expanding gas to exhibit the Joule-Thomson effect, and of the values the
coefficient may adopt in relation to the inverse temperature.
Individual activity
•
Work through Brief Illustration 2D.2 (p. 61) to illustrate the practical application
of the Joule-Thomson effect.
19
Study unit 2
Study Section 2.2
Compensation for deviations of non-ideal solutions
Study time
The time scheduled for this study section is 10 hours.
Study material
This study section is based on parts from Focus 5 (p. 173-180) and Focus 6 (p. 210213) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study section you should be able
•
•
•
to define activity, mean activity coefficient and ionic strength of real solutions;
to calculate mean activity coefficients by means of the Debye-Hückel limiting
law, and to show how this law can be extended for concentrated solutions;
to determine experimentally mean activity coefficients and standard electrode
potentials by means of electrochemical cells and a Debye-Hückel extrapolation.
Priorities
2.2.1
Definitions: activity, activity coefficient, ionic strength
Study material
•
Study Par. 5F.1, Par. 5F.2 and Par. 5F.4, with special attention to the definitions
for activity (Eqn. 5F.14), mean activity coefficient (Eqn. 5F.25) and ionic
strength (Eqn. 5F.28) and to calculation of mean activity coefficient from the
Debye-Hückel limiting law (Eqn. 5F.27) and the extended Debye-Hückel law
(Eqn. 5F.30a) as well as the Davies equation (Eqn. 5F.30b).
Individual activity
•
20
Work through Brief Illustration 5F.4 on p. 178 as an example of how to
calculate the quantities defined above.
Study unit 2
2.2.2
Electrochemical measurement of activity coefficients
Study material
•
Do revision of electrochemical cells and their operation by reading and
familiarising yourself with Par. 6C.1, Par. 6C.2 and Par. 6C.3. Then study Par.
6D.1 and 6D.2 with special attention to determination of standard cell potential
by means of a Debye-Hückel extrapolation (Eqn. 6D.4) and, as soon as this is
known, calculation of the mean activity coefficient (Eqn. 6D.7) for a given
molality.
Individual activity
•
Work through Example 6D.1 on p. 211, and pay attention to the determination
of the standard cell potential by graphical extrapolation of the data in Fig. 6D.1.
Then do Self-test 6D.1 to further practice the procedure. Show how the mean
activity coefficient of a given solution of HBr can be determined from the
available data.
21
Study unit 2
Study division 3
Change: Chemical kinetics
Study time
The time scheduled for this study division is 25 hours.
Study material
Study division 3 is based on parts from Focus 14, 15 and 19 of Atkins’ Physical
Chemistry.
Study outcomes
After completing this study division you should be able
•
•
•
•
•
•
•
22
to give reasons why kinetic studies are performed;
to present and explain a flow diagram for a kinetic study;
to describe measurement of the rate of chemical reactions of different time
scales with different techniques either in situ or a posteriori;
to apply your knowledge of the integrated rate laws of zero-order, first-order and
second-order reactions after revision of previously studied material;
to use the steady-state approximation to derive the rate law for mechanisms
consisting of several elementary steps in which intermediates occur;
to use collision theory and transition state theory to calculate activation
parameters;
to mathematically derive the rate laws of the mechanisms proposed for selected
complex reactions.
Study unit 3
Study Unit 3
RATE OF CHEMICAL REACTIONS
Study time
The time scheduled for this study unit is 25 hours.
Study material
Study unit 3 is based on parts of Focus 14 (p. 539-552, 557-561, 562-568), Focus
15 (p. 604-609), and Focus 19 (p. 797-804) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study unit you should be able
•
to give reasons why kinetic studies are performed;
•
to present and to interpret a flow diagram for a kinetic study;
•
to explain measurement of reaction rate by in situ (real time) or a posteriori
analysis (after quenching) with different techniques for different time scales;
•
•
•
•
•
•
to apply integrated rate laws of zero-order, first-order and second-order
reactions to kinetic data;
to explain concepts such as preequilibrium and rate-controlling step;
to apply the steady-state approximation to derive the rate law for reaction
mechanisms with several rate-controlling steps or in which different kinds of
intermediate occur;
to use collision theory and transition-state theory to calculate activation
parameters and to interpret the values of these parameters;
to derive rate laws from mechanisms proposed for complex reactions;
to extend reaction dynamics to reactions occurring at electrode surfaces.
Chemical kinetics is a subdivision of chemistry dealing with the rate of chemical
reactions, the factors which determine reaction rate, and an explanation of the course of
a reaction in terms of a proposed mechanism. A kinetic study is performed according to
a flow diagram, a copy of which will be issued to you. The mechanism usually consists
of more than one elementary step, and more than one of these may be rate-controlling.
23
Study unit 3
The steady-state approximation enables determination of the approximate concentration
of the intermediates occurring in a complex mechanism.
Study unit plan
•
Study section 3.1
PRINCIPLES OF KINETICS
Measuring Reaction
Rate
stopped-flow, flash
photolysis,
quenching, T- and
P-jump
•
Integrated Rate
Laws
zero-order, first-order,
second-order
Study section 3.2
KINETICS OF ELECTRODE REACTIONS
24
Steady-State
Approximation
Activation Parameters
concentration of
intermediates
Ea, A, H, S, V
Study unit 3
Study Section 3.1
Principles of kinetics
Study time
The time scheduled for this study section is 20 hours.
Study material
Study section 3.1 is based on parts of Focus 14 (p. 539-552, 557-561, 562-568) and
Focus 15 (p. 604-609) of Atkins’ Physical Chemistry.
Study outcomes
After completing this study section you should be able
•
•
•
•
•
•
•
to state reasons why kinetic studies are performed;
to present and to interpret a flow diagram for a kinetic study;
to explain how reaction rate is measured in situ (real time) or a posteriori (after
quenching) by different techniques based on different time scales;
to apply, after revision of previously studied work, integrated rate laws of zeroorder, first-order and second-order reactions to experimental data;
to utilise the stationary-state approximation to derive the rate law for reactions
in which more than one rate-controlling step or an intermediate occur;
to understand concepts like preequilibrium and rate-controlling step;
to use collision theory (Arrhenius) and transition state theory (Eyring) to
calculate activation parameters.
Priorities
3.1.1
Measuring reaction rates
Study material
•
Read the introduction to Focus 14 to get an understanding of the scope of
chemical kinetics, and why the rate of chemical reactions is measured.
•
Study Par. 14A.1 (p. 539-541) in order to get an overview of different
experimental techniques by virtue of which reaction rates can be measured.
25
Study unit 3
Individual activity
•
3.1.2
Compile a list of apparatus suitable for measuring the rates of chemical
reactions having significantly different time scales.
Integrated rate laws
Study material
•
Read Par. 14A.2, Par. 14B.1, 14B.2 and Par. 14B.3 to refresh your memory
about rates of reaction and the associated terminology, and to revise the
integrated rate laws which you studied previously.
Individual activity
3.1.3
•
Work through Example 14B.1 (p. 548) as revision of first-order reactions, and
then do Self-test 14B.1 for further practice.
•
Table 14B.3 lists the integrated rate laws for different reaction orders. Check
that you know the first four entries and are capable of applying them.
Steady-state approximation
Study material
•
Study Par. 14E.1-5 (p. 562-567) in order to apply the steady-state
approximation to derive the rate law for a process comprising more than one
rate-controlling step and/or a pre-equilibrium.
Individual activity
•
3.1.4
Work through Brief Ilustration 14E.1 and 14E.2. Work through Examples
14E.1, 14E.2 and 14E.3 and then do Self-test 14E.2, 14E.2 and 14E.3 for
further practice.
Activation parameters
Study material
•
26
Study Par. 14D.1 and 14D.2 (p. 557-561) and Par. 15C.1(a)-(d) and Par.
15C.2(a) (p. 604-607, 607-609) to familiarise yourself with the collision theory
of Arrhenius and the transition state theory of Eyring, and with the determination
of activation parameters from the temperature dependence of the rate constant
Study unit 3
by graphs based on Eqn. 14D.1 and Eqn. 15C.16, respectively. Take note of
the relation between Ea and H (p. 608, for solution-phase and gas-phase
reactions), and between A and S (Eqn. 15C.15a & b).
Individual activity
•
Work through Example 14D.1 and then do Self-test 14D.1 to gain experience
in determining Arrhenius parameters graphically. Work through Brief
Illustration 14D.1 for additional insight and practice.
•
Do Problem 21C.1 (p. 932, in Atkins’ Physical Chemistry 10th Edition), i.e.
“The rates of thermolysis of a variety of cis- and trans-azoalkanes have been
measured over a range of temperatures in order to settle a controversy
concerning the mechanism of the reaction. In ethanol an unstable cis-azoalkane
decomposed at a rate that was followed by observing the N2 evolution, and this
led to the rate constants given in the following table (P.S. Engel and D.J. Bishop,
J. Amer. Chem. Soc. 97, 6754 (1975)). Calculate the enthalpy, entropy, energy,
and Gibbs energy of activation at -20C.
 / C
4
-1
10 x kr / s
-24.82
-20.73
-17.02
-13.00
-8.95
1.22
2.31
4.39
8.50
14.3
as an exercise to determine activation parameters by virtue of a graph based
on the Eyring equation (Eqn. 15C.16).
27
Study unit 3
Study Section 3.2
Kinetics of electrode reactions
Study time
The time scheduled for this study section is 5 hours.
Study material
Study section 3.2 is based on parts of Focus 19 (p. 797-804) of Atkins’ Physical
Chemistry.
Study outcomes
After completing this study section you should be able
•
•
•
•
To show understanding of the electrode-solution interface;
to apply the Butler-Volmer equation in accordance with the value of the
overpotential;
to determine the Butler-Volmer parameters (exchange current density and
transfer coefficient) for an electrode reaction by a graph based on one of the
Tafel equations;
to exhibit a general understanding of voltammetry and linear scanning
voltammetry.
Priorities
3.2.1
Dynamics of electrode reactions
Study material
28
•
Study Par. 19D.1 (p. 797-798) so as to be able to describe the electrode solution
interface employing different models.
•
Study Par. 19D.2 (p. 798-802) so as to describe electron transfer at the
electrode solution interface using the Butler-Volmer equation (Eqn. 19D.2) and
Tafel plots (Eqn. 19D.5a and Eqn. 19D.5b).
•
Use the Butler-Volmer equation (Eqn. 19D.2) for the determination of exchange
current density and charge transfer coefficient as electrode kinetic quantities.
Take note of the numerical values of these parameters for a few electrode
reactions in Table 19D.1.
Study unit 3
•
Study Par 19D.3 (p. 802-804) so as to describe the use of cyclic voltammetry
as a technique to obtain information on the kinetics of electrode processes.
Individual activity
•
Work through Brief Illustration 19D.1 on p. 801 to illustrate the use of the
exchange current density (Butler-Volmer parameter).
•
Work through Example 19D.1 (p. 802) in order to master the use of the Tafel
plot. Work through Self-Test 19D.1.
•
Work through Example 19D.2 (p. 804) so as to further master the use of cyclic
voltammetry.
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