Title
Outline
History
Pedagogical Continuity
Errant topics in chemistry
Roy Jensen, M.Sc., Ph.D.
Grant MacEwan College
JensenRH@MacEwan.ca
Thinking bigger
ÄKnowledge Crystal
ÄInitiatives at Grant MacEwan College
ÄGuiding principles
Errant examples
Äformatting standards
Äimplicit simplifications
Äwork in progress
Errant: straying from the proper course or standards.
History
The enlightening high school teacher.
Crystal Knowledge
Crystal Knowledge is a metaphor for the overall
learning process.
ÄCrystals grow by accreting material; we accrete information.
• We learn by adding information to our existing knowledge base.
ÄImpurities, be them chemical or inaccurate information, lead
to defects and weaknesses in the crystal and in our
understanding.
• Radiance is dramatically reduced.
ÄThe best way to grow crystals and develop true understanding
is
• to maintain optimal growth conditions,
• to not introduce defects in the first place, and
• to correct defects before they are deeply buried.
Education doesn't cost ... it pays! Univ. of Mississippi postmark, Dec 78.
understanding + recall = knowledge
Initiatives
MacEwan Initiatives
Äcontinuing education program for science teachers
Äscience seminars for the general public
Collaboration with Alberta Education
Äreviewers for the provincial exam
Äcontent experts and reviewers for textbook
Äworkshops for science teachers
Äon-call persons (also with ESON)
Edmonton Science Outreach Network (ESON)
Äpublic school science demonstrations
Ä(proposed) Science Festival
If you think education is expensive, try ignorance. Derek Bok
Guiding principles
Documents referencing ISO standards
• Chemistry: IUPAC
○ Mills, I.; et al. Quantities, Units, and Symbols in Physical
Chemistry, 2nd ed., Blackwell Science, 1993.
• Physics: IUPAP
○ Report on Symbols, Units, Nomenclature, Atomic Masses and
Constants, IUPAP Commission, 1999.
• Biology
○ Kotyk, A. Quantities, Symbols, Units and Abbreviations in the
Life Sciences: A Guide for Authors and Editors, Humana Press,
1999.
• NIST
○ NIST Special Publication 811, Taylor, B. N., (ed.) Guide for the
Use of the International System of Units (SI), 1995.
Those that can...do. Those that understand...teach.
Guiding principles
The story of Dr. Jeremy Tatum.
There are established standards.
ÄThe Bureau International des Poids et Mesures (BIPM) is a
intergovernmental body established by the Meter Convention
in Paris on 20 May 1875.
ÄInternational Organization for Standards (ISO) (from Greek, ISOS, equal)
• NGO coordinating international standards
• Representation from academia, industry, and government
• ISO 31:1998 Quantities and Units. (13 sub reports)
• ISO 1000:1992 SI units and recommendations for the use
of their multiples and of certain other units.
• www.iso.org
Try not to have a good time...this is supposed to be educational.
Guiding principles
Example: chemical syntax
Example: chemical syntax
Consider the following chemical reactions:
Consider the following chemical reactions:
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
2HCl(aq) + Zn(s)
H2(g) + 2ZnCl2(aq)
Which is written according to adopted standards?
Which is used in your textbook?
A four number bank machine password is as secure as a two digit computer password.
FYI: rules for scientific syntax
SO24−
(not SO )
People learn because of LOVE [of subject] or FEAR [of failure].
Guiding principles
• Scalar quantities and variables are set as regular weight italicized
serif font: A
• Functions, units, and labels are set as regular weight serif upright
font: A
• Vectors and matrices are set as bold weight italicized serif font: A
• Tensors are set as bold weight italicized sans-serif font: A
T = 273 K
• States of matter are a label and presented in roman upright font and
inline with the text.
• Subscripting only refers to the preceding atom.
d[A]
= −k t
dt
a 
a
A =  11 12 
 a21 a22 
2−
Educational material often contains implicit and explicit
simplifications due to the educational level of the learner and
complexity of the system. Occasionally, these simplifications
become entrenched in the material and future educators are
unaware of the implicit simplifications.
• It is only when we ask ‘why?’ that we face the limitations of our
understanding.
• Textbooks often fail to explain the concept or they provide poor,
incomplete, and contradictory explanations.
4
1.02 cm × 1.83 cm
The baby was 4.8 kg at birth!
R = 8.314 51 J mol−1 K −1
= 8.314 51 J / (mol K )
≠ 8.314 51 J / mol / K
I have never let my schooling interfere with my learning. Mark Twain
The real object of education is to leave a person in the condition of continually asking questions.
Bishop Creighton
Example: significant figures
Example: standard states
How many significant figures are in 6 °C?
What is challenging about the following question?
Answer: 1 or 3
3. The true, thermodynamic temperature (kelvin) is obtained
by adding exactly 273.15 to the temperature in degrees
Celsius.
T / K = t / °C + 273.15
6 °C
=
+ 273.15 = 279.15
°C
T = 279 K
Graph ΔrG°(T) for the following reaction from 0 K to 500 K.
2SO2 + O2
The obvious answer is to calculate ΔrH° and ΔrS°.
2SO2(g) + O2(g)
2SO3(g)
ΔfH°
S°
Example: standard states
0
205
-396
257
kJ/mol
J/(mol K)
Confidence is what you feel before you fully comprehend the situation.
Example: standard states
Graph ΔrG°(T) for the following reaction from 0 K to 500 K.
However, the reagent standard states are not gaseous over the (0
– 500) K range.
-75
-75
2SO2(g) + O2(g)
2SO3(g)
-100
ΔrG °(T ) /(kJ/mol)
-100
ΔrG °(T ) /(kJ/mol)
-297
248
ΔrG° is calculated from ΔrG°(T) = ΔrH° – T ΔrS°, again
assuming that ΔrH° and ΔrS° are independent of temperature.
1. If a change in temperature is being measured, there is only
one significant figure: 295 K – 289 K = 6 K or 6 °C
Mathematically, if you end up with the incorrect answer, try multiplying by the page number.
2SO3
-125
-150
-175
-200
2SO2(g) + O2(g)
2SO2(g) + O2(g)
-150
2SO2(g) + O2(g)
-175
2SO2(l) + O2(g)
-200
-225
2SO3(g)
-125
2SO3(s)
2SO3(l)
2SO3(s)
No data on
O2(s) and O2(l).
-225
0
100
200
300
400
500
Temp. /K
If I had to live my life over again, I’d make the same mistakes...only sooner. Tallulah Bankhead
0
100
200
300
400
500
Temp. /K
The real voyage of discovery consists not in seeking new landscapes, but in having new eyes.
Example: standard conditions
Example: activities
Standard reaction conditions
•
•
•
•
What is the activity of pure solids and pure liquids?
pure solids and pure liquids
unit activity for solutes (≈ 1 mol/L)
unit fugacity for gases (≈ 1 bar)
temperature is not specified!
Considering the general reaction
aA(w) + bB(x)
The equilibrium constant expression is given by
K (T ) =
What is ‘standard’ has changed over time:
• 16O → 12C
• atmosphere → 105 Pa (bar)
• molality or molarity?
cC(y) + dD(z)
(1961)
(1982)
(λC )c (λD )d
(λA )a (λB )b
What is K(298 K) for the following reaction?
C(s,graphite)
ΔfH°
S°
When things disappear in water, there must be a solution. the Magic School Bus
Example: activities
∆ r G°(T ) = ∆ r H ° − T ∆ r S °
C(s,diamond)
1.9
2.4
kJ/mol
J/(mol K)
Confidence is what you feel before you fully comprehend the situation.
What is the specific heat capacity of liquid water?
4.23
4.0
4.22
3.0
CP /(J/(g K))
ΔrG °(T ) /(kJ/mol)
5.0
Never spontaneous under
standard conditions.
2.0
1.0
0.0
0
K (T )
0.0
5.7
Example: constants
6.0
C(s,graphite)
C(s,diamond)
200
400
600
800
1000
0.4
∆ r G°(T ) = − R T ln (K (T ))
4.21
4.20
4.19
Average heat capacity
(4.191 ± 0.011) J/(g K)
4.18
0.2
4.17
0.0
0
200
400
600
800
1000
Temp. /K
It is the mark of an educated mind to be able to entertain a thought without accepting it.
0
20
40
60
Temperature /°C
KNOWING is a barrier that prevents LEARNING.
80
100
Example: electrochemistry
Example: dimensionality
o
What is Ecell
(298 K ) for the reaction
AgCl(s)
How is dimensionality treated in logarithm operations?
Ag+(aq) + Cl–(aq)
k (T ) = A e
o
(298 K ) = 0.222 V
AgCl(s) + e–
Ag(s) + Cl–(aq) Ered
o
+
–
Ered (298 K ) = 0.800 V
Ag(s)
Ag (aq) + e
————————————————————————
o
(298 K ) = −0.578 V
Ecell
AgCl(s)
Ag+(aq) + Cl–(aq)
ln(k (T )) =
-Ea
L
L
k (T ) = κ (T )
; A=α
+ ln( A)
mol s
mol s
RT
 L  -Ea
 L 
 =

ln (κ (T )) + ln
+ ln(α ) + ln
 mol s  R T
 mol s 
ln(κ (T )) =
For every reaction, it is possible to determine
• the reaction free energy, ΔrG(T);
• the equilibrium constant, K(T); and
• the cell potential, Ecell(T).
∆G o (T ) = − R T ln (K (T ))
∆G o (T ) = −n F E o (T )
Minds are like parachutes. they only function when they are open.
each term is dimensionless
• Dimensionality is ‘lost’ during logarithm operations.
• Any consistent set of units may be introduced when taking the inverse
logarithm.
Example: equilibrium expression order
Consider the equilibrium and questions:
N2O4(g)
-Ea
+ ln(α )
RT
Those who say it cannot be done should not interrupt those who are doing it. George Bernard Shaw
Example: equilibrium systems
2NO2(g)
-Ea
RT
K(298 K) = 3.2
Determine the equilibrium concentrations of NO2 and N2O4 after
0.10 mol of each are added to a 5.00 L evacuated flask at 298 K.
Considering a general reaction
aA + bB
kf
kr
cC + dD
The reaction rate expression is given by
m
n
p
q
vf (T ) = kf (T )(λA ) (λB ) (λC ) (λD )
vr (T ) = k r (T )(λA ) (λB ) (λC ) (λD )
w
Determine the equilibrium concentrations of NO2 and N2O4 after
0.10 mol of each are added to a 5.00 L flask (filled with air at
one bar pressure) at 298 K.
Considering le Châteliers Principle, what effect does adding an
inert gas have on an equilibrium?
It is what you learn after you know it all that counts. Harry S. Truman
(states of matter removed)
x
y
z
m, n, p, q 

∈ℜ
w, x, y, z 
The equilibrium expression is given by
(λ )c (λ )d k (T ) = (λA )w (λB )x (λC )y (λD )z
K (T ) = C a D b = f
(λA ) (λB ) kr (T ) (λA )m (λB )n (λC ) p (λD )q
Why are the reagents in the equilibrium expression
always raised to their stoichiometric coefficients?
Forgive my nonsense as I also forgive those who think they talk sense. Robert Frost
Example: equilibrium expression order
Issue: activity and fugacity
Resolution is obtained by considering the Principle of
Microscopic Reversibility. Expanding the overall equilibrium
into a series of elementary equilibria gives
α1A + bB
pP + qQ
K1 (T ) =
(λP ) p (λQ )q
(λA )α (λB )b
pP + qQ
rR + δ1D
K 2 (T ) =
(λR )r (λD )δ
(λP )p (λQ )q
1
Activity is the effective concentration of a solute.
Activity is dimensionless.
λA = γ A [A]
Fugacity is the effective pressure of a gas.
f A = φA PA
Fugacity has dimension of pressure (Pa).
1
(λ )c (λ )δ
K3 (T ) = C r D α
rR + α2A
cC + δ2D
(λR ) (λA )
———————————————————————
aA + bB
cC + dD
K (T ) = K1 (T ) K 2 (T ) K 3 (T )
γ and φ are dimensionless.
2
2
=
(λC )c (λD )d
(λA )a (λB )b
Those who will not learn cannot be taught. Benjamin Franklin
Issue: equil. expression dimensionality
What dimensionality is associated
with the equilibrium expression?
Entities are made dimensionless, apparently ad hoc, by dividing
by the standard state.
x
F= o
x
I have learned silence from the talkative, toleration from the intolerant, and kindness from the
unkind; yet, strange, I am ungrateful to these teachers.
Issue: equil. expression dimensionality
What dimensionality is associated with the
equilibrium expression?
Considering the general reaction
aA(w) + bB(x)
K=
Today nearly everyone can read, but only a few people can think. Cardinal Alfredo Ottaviani (1956!)
cC(y) + dD(z)
(λC )c (λD )d = (γ C )c (γ D )d [C]c [D]d
(λA )a (λB )b (γ A )a (γ B )b [A]a [B]b
Kc =
[C]c [D]d
[A]a [B]b
KP =
(PC )c (PD )d
(PA )a (PB )b
K=
Let my words today be tender and tasty, for I may have to eat them tomorrow.
Kc
(c )
o ∑ν
Issue: equil. expression dimensionality
A dimensionless quantity is the same in all reference frames
(standard states). Considering the NO2, N2O4 equilibrium,
2NO2(g)
N2O4(g)
K(298 K) = 3.2
Solving using bar as the standard state gives
PNO2 = 0.6110 bar, PN 2O 4 = 1.1945 bar
Converting to other states
K (298 K ) = 3.16
PNO = 0.619 1 atm, PN O = 1.210 3 atm
Äatm:
−5
PNO = 6.110 ⋅105 Pa, PN O = 1.194 5 ⋅106 Pa K (298 K ) = 3.2 ⋅10
ÄPa:
−3
ÄmmHg: PNO = 470.5 mmHg, PN O = 919.9 mmHg K (298 K ) = 4.2 ⋅10
2
2
Standards exist
ÄContinuity and consistency are problems that impede
understanding of science — problems that can be readily
rectified with consistent use of standards.
ÄUnless someone can present a reasoned scientific argument
for changing a standard, the standard should be followed…
• …to maintain pedagogical continuity.
• …because science is sufficiently challenging without the introduction
of artificial learning barriers.
• …because people expect consistency in science.
4
2
2
4
2
2
4
Information is lost if dimensionality is not included with equilibrium data.
You can lead a person to the university, but you can't make them think. Finley Peter Dunne
Acknowledgements
Grant MacEwan College
•
•
•
•
•
Conclusions
Dr. Lucio Gelmini
Dr. Robert Hilts
Ms. Mary Sheppard
Dr. Patrick Sullivan
Faculty of Arts & Science
Alberta Education
• Ms. Debra Campbell
• Ms. Caroline Nixon
Edmonton Science Outreach Network
• Dr. Michael Caley
Education is not the filling of a pail, but the lighting of a fire. W.B. Yeats
Pedagogical simplifications exist
ÄWe need to be cognizant of implicit simplifications.
You know you've spoken too long when the audience stops looking at their watches and starts shaking them.
Title
Pedagogical Continuity
Errant topics in chemistry
Thank-you!
Roy Jensen, M.Sc., Ph.D.
Grant MacEwan College
JensenRH@MacEwan.ca