Chemistry and Mathematics – the Perfect Couple?

Michael SpringborgPhysical and Theoretical Chemistry

University of Saarland66123 Saarbrücken

Germany

What is chemistry?

What is chemistry?

What is chemistry?

Chemistry is, however, also related to mathematics and data

manipulation!

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 labBut 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!

Also the development of theoretical methods is important

Keto – Enol Tautomers of

Acetone

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: pressureV: volume:n: # molR: Gas constantT: abs. temperaturem: massM: molar mass

Units are very important

Our „laws“ are not exact – but idealizations that may or may not be

sufficiently accurate.(„Essentially all models are wrong but

some are useful“)

Again ideal gas law:

P V = n R T

or

Z = (P V) / (n R T) = 1

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.

Accuracy is an issue:

1.03 m/s ≠ 1.030 m/s

Measured quantities have error bars

Manipulation of measured date

is an issue

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. Differentiation4. Integration5. (Linear) differential equations6. Linear equations7. Quadratic equations8. Sums and series9. Linearization10. Minimization and fitting11. Complex numbers12. Discrete probability distributions13. Vectors14. Matrices

And that they can read and understand mathematical

expressions:

P V = n R T

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-Math

Why 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 help

Here 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.

Thank you very much!