Chemistry and Mathematics

– the Perfect Couple?

Michael Springborg

Physical and Theoretical Chemistry

University of Saarland

66123 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 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!

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: pressure

V: volume:

n: # mol

R: Gas constant

T: abs. temperature

m: mass

M: 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. 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

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-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.

Thank you very much!