Transcript Teaching Physical Chemistry Without Lectures

Teaching Physical Chemistry Without
Lectures
or the Power of Cooperative Learning in Chemistry
Julanna V. Gilbert
Department of Chemistry & Biochemistry
Physical Chemistry
Junior/senior level course for chemistry/biochemistry majors
Requirements: 1yr calculus, 1 yr physics, general chemistry & equilibrium
systems.
•
Introduction to Physical Chemistry
– Thermodynamics
– Applications
•
Physical Chemistry II
– Kinetics
– Quantum Mechanics
•
Physical Chemistry III
– Spectroscopy
– Photochemistry
– Statistical Mechanics
Why not just lecture?
Student perspective
 Material tends to be presented too quickly.
 Limited access to other students & the instructor outside class time.
 Class time may not provide opportunity for students to discuss what
they need to discuss (which varies by student).
 Little time for individualized help during class.
 Students need to learn how to learn on their own
Why not just lecture?
Instructor perspective
 Most students don’t or can’t answer questions during class.
 May not find what students are really learning until an exam.
 Individualized help difficult, tend to “lecture at everyone”.
 Hard to know when misconceptions exist, don’t hear from most
of the students.
 Students need to learn how to learn on their own
Class Format
 Meets for two 2-hr sessions per week
 Class divided into groups
 Each group completes a “worksheet” during class
 Worksheets lead students through the material
Student Groups
 As much diversity as possible – set by instructor & explained to
students
 Three students per group (optimum size)
 Rotate the “scribe” duty.
Grading
• Group work (worksheets) – 40% of total grade
• Individual work (homework + exams) – 50% of grade
• Peer review – 10% of grade
Typical Session
 Students are eager to start working on the worksheets (really!).
 Students refer to their textbooks, talk to each other, ask the
instructor questions.
 Room gets noisy, groups interact with each other, instructor
circulates to monitor progress and answers questions.
 Sometimes class is stopped to clear up common misconceptions
that arise.
Class time is defined by the students’ needs first, not by
the need to cover a given amount of material.
Tools
Textbook
Excel, MathCad
Course web site
 Syllabus, Worksheets, Review sheets
 Discussion forums
 Internet resources
The students’ minds
Examples of materials created
for Thermodynamics
Physical Chemistry I, Fall 2003
INTRODUCTION
Tues Sept 9
Worksheet 1: Calculus review, Introduction to exact and
inexact differentials (Further information 1.5 & 1.7)
Thurs Sept 11
Worksheet 2: Real and ideal gases (Chapter 1)
THERMODYNAMICS - THE FIRST LAW
Tues Sept 15
Worksheet 3: Work, heat and the first law of thermodynamics
(Chapter 2.1-2.4)
Thurs Sept 18
Worksheet 4: Enthalpy & heat capacities, the equipartition of
energy theorem (Chapter 2.5 – 2.6, handout)
Tues Sept 23
Worksheet 5: Understanding thermochemistry & enthalpies
and fun with thermodynamic relationships (Chapter
2.7-2.9, Chapter 3)
Thurs Sept 25
Discussion and review
Tues Sept 31
Exam # 1
Physical Chemistry I, Fall 2003
THERMODYNAMICS - THE SECOND LAW
Thurs Oct 2
Worksheet 6: Spontaneous direction of processes, Carnot cycles, entropy, & the
second law of thermodynamics (Chapter 4.1 & 4.2)
Tues Oct 7
Worksheet 7: S for processes involving gases, phase transitions, and chemical
reactions, entropy & probability, the third law of thermodynamics
(Chapter 4.3 & 4.4)
Thurs Oct 9
Worksheet 8: Predicting spontaneous processes: Gibbs & Helmholtz energies (Chapter 4.5 & 4.6, Thermodynamics in a Nutshell)
Tues Oct 14
Worksheet 9: Properties of the Gibbs energy and more fun with thermodynamic
relationships (Chapter 5 & Thermodynamics in a Nutshell)
APPLICATIONS OF THERMODYNAMICS
Thurs Oct 16
Worksheet 10: Phase diagrams for pure substances (Chapter 6.1-6.7)
Tues Oct 21
Worksheet 11: Thermodynamic description of mixtures (Chapter 7.1-7.3)
Thurs Oct 23
Discussion and review
Tues Oct 28
Exam #2
Finding expressions for PV work.
• All of the PV expressions for work in one table.
• Makes it easy for students to grasp how to know
when to use what expression for calculating
work.
• Allow students to concentrate on the system and
meaning.
E. Finding expressions for PV work.
Fill in the table below - show your work.
(The entries in the1st column will be identical – likewise for the entries in the 2nd column.)
PROCESS
Free expansion
Differential
Integral
Pext
Evaluate integral
dw = -PextdV
-Pext dV
Pext = 0
w =-Pext dV
w = -Pext  dV
w =0 since Pext= 0
Expansion against
a constant
external
pressure,
any gas
Reversible
isothermal
expansion,
ideal gas
Reversible
isothermal
expansion,
VDW gas
A change at
constant
volume any
gas
Adiabatic
expansion,
ideal gas
dw = -PextdV
-Pext dV
Pext=
Pint
=
nR
T/
V
STOP! T is not constant!
We must find a new
relationship between
T and V to evaluate
the integral:
(nRT/V) dV. We
will find this
relationship in a
later worksheet.
The Nutshell Sheet
A one-page organizational scheme for equilibrium
thermodynamics.
Demystifies the math for students so they can
concentrate on the content
Equilibrium Thermodynamics in a Nutshell
Energy
1. Write the state function
definition
2. Write the differential
form of the state
function
3. Write the differential
form assuming a
reversible process
(dqrev=TdS), and PdV
work only
4. Write the exact
differential with the
“natural variables”
(from 3)
5. Write the new
relationships
(from 3 & 4)
6. Apply Euler's criterion
for exact differentials
to the expression in 4
above
7. Write the new
relationships from 5 &
6 (called Maxwell's
Relations)
8. Determine the condition
for equilibrium
dU =
Enthalpy
H=
Gibbs Energy
G=
Helmholtz Energy
A=
EQUILIBRIUM THERMODYNAMICS IN A NUTSHELL
Enthalpy
Gibbs Energy
Helmholtz Energy
Energy
1. Write the state
function definition
dU = dq + dw
H = U + PV
G = H - TS
A = U - TS
2. Write the differential
form of the state
function
dU = dq + dw
dH = dU + PdV +VdP
dG = dH – TdS – SdT
dA = dU – TdS – SdT
3. Write the differential
form assuming a
reversible process
(dqrev=TdS), and
PdV work only
dU = TdS – PdV
dH =TdS – PdV
+PdV + VdP
dH = TdS + VdP
dG = dU+PdV+VdP
– TdS – SdT
dG = TdS –PdV
+PdV + VdP
– TdS – SdT
dG = VdP – SdT
dA = TdS – PdV
– TdS – SdT
dA = -PdV-SdT
dH = (H/S)P dS
+ (H/P)S dP
dG = (G/P)T dP
+ (G/T)P
dT
dA = (A/V)T dV
+ (A/T)V dT
4. Write the exact
differential with the
“natural variables”
(from 3)
5. Write the new
relationships
(from 3 & 4)
6. Apply Euler's criterion
for exact
differentials to the
expression in 4
above
7. Write the new
relationships from 5
& 6 (called
Maxwell's
Relations)
8. Determine the
condition for
dU = (U/S)VdS
+
(U/V)SdV
T = (U/S)V
–-P = (U/V)S
(U2/SV)=
T = (H/S)P
V = (H/P)S
(H2/SP)=
(H2/PS)
V = (G/P)T
–S = (G/T)P
(G2/PT)=
(G2/TP)
–P = (A/V)T
–S = (A/T)V
(A2/VT)=
(A2/TV)
(U2/VS)
(T/V)s = –
(P/S)V
(T/P)S = (V/S)P
dU=0 at constant
V and S
dH=0 at constant
P and S
(V/T)P = –
(S/P)T
dG=0 at constant
P and T
(P/T)V =(S/V)T
dA=0 at constant
V and T
The third “law” of thermodynamics
• Hard for students to grasp.
• Work the exercise in class so there is lots
of interaction between instructor and
students.
• Students get it!!
Find S for lead at various T’s
using Excel
Visualization of:
–
Cp vs. T for Lead
CP,T experimental data
30
–
Cp (J/K mole)
25
The 3rd Law of
Thermodynamics
(limT0S 0)
20
15
10
5
–
dS = (CP/T)dT,
S =(CP/T)dT
and S = ST-S0
0
0
50
100
150
200
250
300
350
Temperature (Kelvin)
Cp/T vs. T for Lead
–
S is the area under the
curve of CP/T vs. T.
0.6
0.5
Cp/T (J/KKmole)
•
0.4
0.3
0.2
0.1
0
0
50
100
150
200
250
Temperature (Kelvin)
300
350
Cp vs. T for Lead
30
Cp (J/K mole)
25
20
15
10
5
0
0
50
100
150
200
Temperature (Kelvin)
250
300
350
Cp/T vs. T for Lead
0.6
Cp/T (J/KKmole)
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
Temperature (Kelvin)
250
300
350
Physical Chemistry II Mathcad exercises
 Particle in a 2-dimensional box
 Plots of wavefunctions
 Solving rate equations
General impressions of teaching without
lectures
 Find out what students are really learning
 Get students to talk in class about
chemistry
 Intervene frequently to minimize
misconceptions
 Provide more individualized help
Does it work???
Lots of qualitative feedback from students
suggests “yes”.
– Students
answer questions in class, are
able to think “on their feet”
– Students gain self-confidence, are
willing to ask questions in class
– Students come up with creative problem
solving methods
– Students are fully engaged with the
course material.
Comparison of exam averages
from lecture-based and group-based methods
in Physical Chemistry I
80
Exam 1
Exam 2
Final
75
70
65
60
55
50
Fall 1993-1996 (n=40)
Fall 2000-03 (n=58)
LECTURES
GROUP WORK
Comparison of Exam Averages
Physical Chemistry III
90
85
80
Exam 1
Exam 2
Final
75
70
65
60
55
50
Spring, 1994,95,97 (n=12)
Spring, 2001(n=4)
What the instructor experiences





Instructor gets all kinds of questions from
students.
Additional grading.
More interaction with students.
Students get used to participating.
Students who miss a lot of sessions get left
behind in many ways.
What do the students say?
Students’ Comments

(first 2 years) Need lectures & shorter worksheets

Course seemed too easy – Gilbert thinks everyone can learn
thermodynamics but that’s just not true.

(last year & this year) I thought I would want lectures, but I
prefer the groups. I learned more this way especially since the
course is so difficult.

I leaned a lot, I tried hard.

I like the format & learned a lot even though it was tough.

Use of worksheets enables us to get a better grasp on what we
are covering.
Conclusions
 Requires the instructor to determine which course topics are
truly essential and how to guide students through them.
 Students discover that they and their peers can work together to
gain understanding of even complicated concepts.
 Students become active participants and take responsibility for
learning the material
 Students are definitely better able to demonstrate their learning
with this format than with the lecture format