Download University Studies Chem. 414 Math

MATHEMATICS/STATISTICS FLAG COURSE PROPOSAL
Chemistry 414: Physical Chemistry II (3 s.h.)
Chemistry is the science of matter and the changes matter can undergo. Physical chemistry deals with the
physical principles underlying chemistry and seeks to account for the properties of matter (such as atoms,
electrons, and energy) in terms of fundamental concepts. It provides the basic framework for branches of
chemistry such as inorganic chemistry, organic chemistry, biochemistry, geochemistry, and chemical
engineering. It also provides the basis for modern methods of analysis, the determination of structure, and
the elucidation of the manner in which chemical reactions occur. Physical chemistry is divided into four
majors areas: thermodynamics, quantum chemistry, kinetics, and statistical mechanics. This course provides
an in-depth study of chemical kinetics, and an introduction to quantum chemistry and statistical distributions.
The application of quantum mechanics to atomic structure, molecular bonding, and spectroscopy gives rise to
the study of quantum chemistry. The study of statistical mechanics provides insights into why the laws of
thermodynamics hold and allows calculation of macroscopic thermodynamic properties from molecular
properties. Kinetics is the study of rate processes such as chemical reactions, diffusions, and the flow of
charges in an electrochemical cell. All four major concepts will be applied toward ideal and dilute solutions
at the end of this course. Mathematics is one the most important tools of physical chemistry. Much of
physical chemistry involves casting physical problems into mathematical language. This involves
development of mathematical models starting with microscopic predictions and correlating derived equations
with macroscopic observations. Mathematical approaches include applications such as multi-variable
functions, differential and integral calculus, differential equations, power series, and operator algebra.
Computational data analysis via graphical and statistical treatments involves the use of software packages
such as Mathcad, Excel, and HyperChem. The latter software also enables molecular visualization and
enhances students’ abilities to correlate molecular structure to macroscopic behavior. As such, this course
emphasizes a significant practice in the application of mathematical/statistical approaches to physical
chemistry principles, thereby empowering the intellectual/critical thinking development of students in
physical chemistry and enhancing their understanding of the chemical universe.
Catalog Description:
Quantum Chemistry. Chemical Kinetics: rate laws, mechanisms, temperature-dependence, catalysis.
Boltzmann’s distribution. Theories of reaction rates: collision model, transition state theory, diffusion &
activation-controlled reactions, quantum mechanical tunneling, isotope effects. Properties of multicomponent solutions. Electrochemistry. Statistical Mechanics. Meets University Studies
Mathematics/Statistics Flag requirement. Prerequisites: CHEM 412, one year each of college chemistry,
physics, and calculus. Offered yearly.
This course includes requirements and learning activities that promote students' abilities to...
a.
practice the correct application of mathematical or statistical models that are appropriate to their
prerequisite knowledge of those areas; and
Requirements: Students are expected to apply various mathematical approaches in derivations of relevant
macroscopic equations starting with fundamental concepts and principles in physical chemistry.
Activities:
Students are provided with many opportunities (such as in-class discussions/exercises, problem
sets, and quizzes/tests/examinations) to practice the correct applications of various
mathematical approaches (such as multi-variable functions, differential and integral calculus,
differential equations, power series, and operator algebra) in derivations and the manipulations
of equations for systems under different constraints. The derivations begin with microscopic
predictions/expectations and end with macroscopic results; results that can be compared to real
world experimental observations.
1
Sample Activity:
Starting with microscopic motions (translations, rotations, vibrations) of gaseous
molecules, students apply the techniques of multi-variable calculus using the
Schrödinger equation, =E, where the 3-dimensional kinetic-energy Hamiltonian 
is given by:
^
H 
2   2
2 2 
 2  2  2
2  m  x
y z 
where:

h
2
Derivations will
give rise to wavefunction  and macroscopic equations such as total energy ( E =
n2h2/8ma2 ), momentum (p) and velocity (v). Data will be provided to test the validity
of model equations.
b.
make proper use of modern mathematical or statistical methods appropriate to their level of
prerequisite knowledge, to include, if statistics is used in a substantive way, the use of a statistical
package with graphics capability when appropriate;
Requirements: Students are expected to make proper use of modern mathematical and/or statistical methods
in the derivation and analysis of various physical chemistry principles. The applications of
these methods will include both mathematical techniques and computational software.
Activities:
Students will use mathematical approaches such as differential equations in the derivations of
fundamental equations. Data analysis of real world problems will involve graphical and
statistical software packages, such as Mathcad, Excel, and HyperChem. Mathcad and
HyperChem will enable visualization of system properties (such as graphical interpretations of
energy distributions and predications of molecular properties). Excel will provide both tabular
and graphical calculations, in addition to statistical treatments of application problems.
Students will choose appropriate mathematical/statistical techniques and applications in solving
different problems in order to understand the relationships between microscopic and
macroscopic properties. Laptops will be used in and outside the classroom for various
applications.
2
Sample Activity:
Students will be given kinetic data and then use Mathcad and Excel to derive/model
appropriate rate laws for the SO2Cl2 reaction. The following is a sample Mathcad page.
1.
First-order reaction: SO 2 Cl2 ---> SO 2 + Cl 2
C
Co e
.
The Non-linear IRL is:
C = concentration of reactant remaining at time t
 k t
w here:
Co = initial concentration of reactant = 1.00 mol L
-5
k = rate constant = 2.20x10
s-1 = 7.92x10
-2
hr -1
______________________________________________________________________________
Co  1
5 1
2.20 10
ks
s
khr
2
k  7.92 10
2
7.92 10
1
 hr
C( t)  Co e
 k t
(A) Plot of non-linear IRL
C( t )
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
30
35
40
45
50
t
(B) Plot of linear IRL
0
0.4
0.8
1.2
1.6
ln( C( t ) ) 2
2.4
2.8
3.2
3.6
4
0
[ Take natural log of non-linear IRL: ln(C) = -kt + ln(C
5
10
15
20
25
t
3
30
35
40
o)
45
]
50
-1
Sample Syllabus
WINONA STATE UNIVERSITY
Chem. 414 - Fall Semester 20XX
Physical Chemistry II - 3 S.H.
Instructor:
Dr. C.B. W. Ng (PA312G, 457-5293)
e-mail:
[email protected]
Or [email protected]
Web-site:
http://course1.winona.msus.edu/wng/
Lectures:
M W F 9:00 - 9:50 a.m. PA309
Required Text:
J. H. Noggle, Physical Chemistry, 3rd ed., Harper Collins (1996).
Recommended Reference:
Course Purpose:
R. G. Mortimer, Mathematics for Physical Chemistry, 2nd ed., Harcourt
Academic Press (1999).
Chemistry is the science of matter and the changes matter can undergo. Physical
chemistry deals with the physical principles underlying chemistry and seeks to account
for the properties of matter (such as atoms, electrons, and energy) in terms of
fundamental concepts. It provides the basic framework for branches of chemistry such
as inorganic chemistry, organic chemistry, biochemistry, geochemistry, and chemical
engineering. It also provides the basis for modern methods of analysis, the
determination of structure, and the elucidation of the manner in which chemical
reactions occur. Physical chemistry is divided into four majors areas:
thermodynamics, quantum chemistry, kinetics, and statistical mechanics. This course
provides an in-depth study of chemical kinetics, and an introduction to quantum
chemistry and statistical distributions. The application of quantum mechanics to
atomic structure, molecular bonding, and spectroscopy gives rise to the study of
quantum chemistry. The study of statistical mechanics provides insights into why the
laws of thermodynamics hold and allows calculation of macroscopic thermodynamic
properties from molecular properties. Kinetics is the study of rate processes such as
chemical reactions, diffusions, and the flow of charges in an electrochemical cell. All
four major concepts will be applied toward ideal and dilute solutions at the end of this
course. Mathematics is one the most important tools of physical chemistry. Much of
physical chemistry involves casting physical problems into mathematical language.
This involves development of mathematical models starting with microscopic
predictions and correlating derived equations with macroscopic observations.
Mathematical approaches include applications such as multi-variable functions,
differential and integral calculus, differential equations, power series, and operator
algebra. Computational data analysis via graphical and statistical treatments involves
the use of software packages such as Mathcad, Excel, and HyperChem. The latter
software also enables molecular visualization and enhances students’ abilities to
correlate molecular structure to macroscopic behavior. As such, this course
emphasizes a significant practice in the application of mathematical/statistical
approaches to physical chemistry principles, thereby empowering the
intellectual/critical thinking development of students in physical chemistry and
enhancing their understanding of the chemical universe.
4
Course Description:
Quantum Chemistry. Chemical Kinetics: rate laws, mechanisms, temperaturedependence, catalysis. Boltzmann’s distribution. Theories of reaction rates: collision
model, transition state theory, diffusion & activation-controlled reactions, quantum
mechanical tunneling, isotope effects. Properties of multi-component solutions.
Electrochemistry. Statistical Mechanics. Meets University Studies
Mathematics/Statistics Flag requirement. Prerequisites: CHEM 412, one year each of
college chemistry, physics, and calculus. Offered yearly.
Completion of this course will include requirements and learning activities that promote students’
abilities to achieve the following Outcomes:
a.
practice the correct application of mathematical or statistical models that are appropriate to prerequisite
knowledge of physical chemistry; and
b.
make proper use of modern mathematical or statistical methods appropriate to students’ level of
prerequisite knowledge, to include, if statistics is used in a substantive way, the use of a statistical
package with graphics capability when appropriate;
Completion of this course will satisfy the Mathematics/Statistics Flag Requirement in the University Studies
Program.
Course Details/Requirements/Activities:
In order to pass the course, students are expected to:
1.
attend and participate in lecture-discussion-problem solving sessions, [Outcomes a, b]
2.
complete and turn in assigned problem sets, [Outcomes a, b]
3.
read assigned chapters and attempt text problems, [Outcomes a, b]
4.
use Mathcad and HyperChem in visualizations, calculations, and interpretations of system properties,
[Outcome b]
5.
utilize Excel in data, graphical, and statistical analysis of sample and real-world examples, [Outcome b]
6.
collaborate/discuss in problem solving and model analysis sessions, [Outcome a, b] and
7.
pass, in general, quizzes, tests, and final examination. [Outcomes a, b].
The two-hour final examination will cover the whole course, the two one-hour tests will cover only
certain chapters, and the problem sets will cover certain selected topic(s). There will be points
deducted for late problem sets.
Marking Distribution
Date(s)
Problem Sets (8)
20%
due ~every 2 weeks
Tests (2)
50%
TBA (25% each)
Final Examination
30%
April XX (Day) 8 a.m.
These assessments will give your level of achievement relative to Outcomes a and b.
Grading Scale: A ( 85%) , B (70-85%), C (55-70%), D (45-55%), F (<45%).
5
Title/Topic(s)
Chapter(s)
1. Quantum Chemistry
(2) Brief Historical Perspectives
(3) Operator Algebra
(1) Postulates of Quantum Theory
(4) Particle in a Box (Translational)
(1) Harmonic Oscillator (Vibrational)
Angular Momentum (Rotational)
Spectroscopic Applications
Lectures
11 , 12
13 , 14
(optional)
11
2. Kinetics: Empirical Laws, Applications, and Mechanisms
(1) Concepts of Chemical Kinetics
(1) Rate Measurements & Rate Laws
(3) Simple Integer-Order Reactions
(4) Mechanisms and Rate Laws
(1) Temperature Dependence of Reaction Rates
(1) Applications/Catalysis
[Test #1]
3. Theories of Reaction Rates
(3) Boltzmann Distributions (Velocities and Temperature)
Mean Free path, Collision Numbers and Viscosity
(2) Collision Theory & Transition State Theory
Unimolecular and Bimolecular Reactions
(3) Reactions in Solutions
Diffusion & Activation Controlled Reactions
[Test #2]
Quantum Mechanical Tunneling, Isotope Effects, Muonium
Kinetics
4. Ideal and Dilute Solutions
(1) Gibb’s Energy in Systems of Variable Compositions
Partial Molar/Molal Quantities
(3) Henry’s and Raoult’s Laws
(3) Thermodynamics of an Ideal Solution
(1) Phase Diagrams of Multi-components
(3) Colligative Properties: b.pt. Elevation, f.pt. Depression, Osm
Pressure
5. Electrochemistry and Statistical Mechanics
Faraday’s Law, Conductivity, Ionic Strength, Debye-Huckel
Theory
Ensembles & Partition Functions, Statistical Thermodynamics
10
11
(1.5) , 1.6
5.2 , 5.3
9.1 , 9.3 ,
9.4
10.4
JPC
(Ng,’81)
8
7
11
8 , 15
optional
The study of these physical chemistry concepts requires purposeful readings of your textbook, attendance and
participation in lecture-discussion sessions, and completion of problem set assignments. The lecture material
is complemented by in-class chemical demonstrations/simulations, video media, computer visualizations
(molecular modeling and graphical interpretations), web/internet supplements, active participation using
laptops in and outside the classroom, and the correct application and proper use of mathematical methods
appropriate to physical chemistry. Furthermore, these chemistry concepts are supplemented with hands-on
laboratory experiments in Chemistry 415. Successful completion of studies of these lecture topics will
promote your ability to achieve Outcomes a and b for the Mathematics/Statistics Flag Requirement in
the University Studies Program.
Completion of this course will satisfy the Mathematics/Statistics Flag Requirement in the University Studies
Program.
6
Additional course information can be accessed via the webpage:
http://course1.winona.edu/wng/
Documentation:
Sample Final Examination
Chem.414
PChem. II
Winona State University
May 1, 20XX
Dr. Ng
Final Examination - 60 Marks
PART A:
1.
2.
3.
4.
5.
PART B:
Briefly, but clearly, using statements, equations and/or diagrams , describe any two of the
following five topics. ( 2 x 5 each = 10 marks )
Raoult’s Law, Henry’s Law, and the Ideal Solution.
The Four Major Principles of Physical Chemistry.
The Schrödinger Equation.
The Transition State Theory.
Applications of First-Order Kinetics.
Attempt all questions. ( 5 x 10 each = 50 marks)
1.
At 20C the vapor pressure of benzene (species B) is 13.3 kPa and that of octane (species A) is 2.66
kPa. If 1.00 mol of octane is dissolved in 4.00 mol of benzene, and the solution is ideal, calculate the
total vapor pressure of the solution and the composition of the vapor.
2.
Given that:
h  x 2  d 2 and
(A)
Is
  7 x e

x2
2
(B)
Is
  7 x e

x2
2
3.
B  x  d
an eigenfunction of
an eigenfunction of
h-hat ? Show your work.
For the reaction, 2 Fe(CN)63- + 2 I-
 2 Fe(CN)
B-hat ? Show your work.
4-
6
+ I2
the following mechanism was proposed:
k1
^
B 
^
^
x d
 Fe(CN ) 46  I 2 (fast)
Fe(CN ) 36  2 I 
k-1

k2

3
(slow)
I 2  Fe(CN ) 6  Fe(CN ) 46  I 2
The rate law, d[I2]/dt = kobs [Fe(CN)63-]2 [I-]2 [Fe(CN)64-]-1 , was obtained experimentally. Explicitly
show that the proposed mechanism is consistent with the observed rate law.
7
4.
The following is a normalized energy distribution from 0 to :
2
E
dN  1 

    E  e kT  dE
N  kT 
5.
(A)
Show that this energy distribution is normalized. ( Let:
a = 1/kT )
(B)
Determine an expression for the average energy ( E avg ) .
(C)
Show that the root-mean-square energy ( Erms ) is equal to 2.45kT .
(D)
Determine an expression for the most probable energy ( Emp ) .
(E)
Sketch this energy distribution and identify the three energy values.
An ideal binary A-B mixture follows Raoult’s law and Dalton’s law. The vapor pressure of the liquid
composition (liquidus curve) is represented by:
P = [ ( PB - PA )*B ] + PA
where:
P = total pressure
PB = vapor pressure of pure component B
PA = vapor pressure of pure component A
B = mole fraction of component B
The vapor pressure in terms of the vapor composition (vapor curve) is represented by:
P 
PA  PB
[  B  ( PB  PA ]  PB
By defining kPa=103 Pa and setting PB = 192 kPa and PA = 76.0 kPa , use Mathcad to plot both
the liquidus and vapor curves on one phase diagram of P versus B .
8