Chemistry and Mathematics
– the Perfect Couple?
Michael Springborg
Physical and Theoretical Chemistry
University of Saarland
66123 Saarbrücken
Germany
Farmaceuticals:
Functionality?
Side effects?
Washing powder:
Do they clean?
Colours?
Environment?
Elctronic
components;
Plastics:
Waste?
Replace expensive elements
through cheaper ones.
Stability (atmosphere,
environment, time, light,
weather, …)
Are they (only)
healthy?
Accordingly:
Not only synthesis in the lab
But also:
Study of properties:
•Costs
•Risks for environment, health
•Stability (mechanical, thermal, light, atmosphere)
•Leftovers of products, educts, …
•Wanted / required properties?
No yes/no questions! Instead quantitive studies!
The determination of
properties is often indirect.
Based on mathematical
identities.
Ideal gas law:
P V = n R T
n = m / M
Then:
P = (R T m) / (M V)
P: pressure
V: volume:
n: # mol
R: Gas constant
T: abs. temperature
m: mass
M: molar mass
Our „laws“ are not exact – but
idealizations that may or may not be
sufficiently accurate.
(„Essentially all models are wrong but
some are useful“)
If ideal gas law is not suffieciently
accurate, one may restore to other
laws. For instance van der Waals
law:
Important: when to use which
approximation.
Typical procedure
Scientific
question
Mathematical
question
Scientific
answer
Mathematical
answer
Mathematics is the language of
science
Scientific
question
Mathematical
question
Scientific
answer
Mathematical
answer
Where do chemistry
students have
problems?Where can Math-Bridge
help?
Why do chemistry students have
problems with mathematics?
Unrealistic ideas about chemistry.
Inadequate background knowledge.
Interest in science but not at all in
mathematics.
Mathematics is the language of
science.
If you do not understand the
language, you do not understand
the science.
We expect from the students that they
master simple mathematics:
1. Simple arithmetics (+,-,*,/,**)
2. Simple functions (cos, sin, exp, ln, log, powers, polynomials)
3. Differentiation
4. Integration
5. (Linear) differential equations
6. Linear equations
7. Quadratic equations
8. Sums and series
9. Linearization
10. Minimization and fitting
11. Complex numbers
12. Discrete probability distributions
13. Vectors
14. Matrices
Study of Chemistry
Classical fields of chemistry:
Inorganic chemistry
Organic chemistry
Physical chemistry
Synthesis – matches typical
expectations
Properties – surprise; contains
physics and mathematics; often
problematic
Since some years:
new 1st semester course
Introduction to Physical Chemistry
(contains a little of everything in PC plus of
mathematics and of English)
Experience with
Math-Bridge / Active-Math
The students of „Introduction to PC“ were offered access
to Active-Math
Active training was awarded extra credit points in
examination (125 / 100 possible; 50 necessary; 5 extra)
Students had to accept that activity was monitored
individually
Performance and skills were not monitored
Only few made use of the offer
Experience with
Math-Bridge / Active-MathWhy so few?
Not part of the lectures / exercises
Not well-known
Problematic attitude towards mathematics
Next attempt:
Use Math-Bridge directly in bridge course before lectures
start
Scientific
question
Mathematical
question
Scientific
answer
Mathematical
answer
Here Math-Bridge
can helpHere Math-Bridge
could be extended
Concluding:
Chemistry and Mathematics – the
Perfect Couple?
Not really – their relation is rather
based on necessity than love. A ”family”
therapy (= Mathe-Bridge) could help.