This will
be a very rough estimate but it is a fascinating question.
The wear will depend on
how the car is driven, road conditions, braking, make of tyre etc. but roughly car tyres wear
down by about 6 mm over 20 000 miles of driving.
My car tyres have a radius of
about 0.6 m and a width of 0.15 m and so for 0.006 m (6 mm) of rubber to wear off them they
must have lost 0.0017 cubic metres of rubber.
The density of rubber is a little less
than water (to test this will a car tyre float in water? If yes then its density is less than water).
Lets say 950 kg/cubic metre.
So the mass of rubber worn away = 0.0017x950 = 1.62
kg
Each molecule of rubber (assuming that the tyres are pure rubber) is a chain
molecule of many units, each unit is 5 carbons and 8 hydrogens. Therefore 60/68 of the
mass is carbon.
Therefore 1.6x60/68 = 1.4118 kg is carbon.
The mass of a
carbon atom is 12x1.6x10-27 kg = 1.92x10-26 kg
So the number of
carbon atoms rubbed off is 1.4118/1.92x10-26 = 7.35x1025 atoms
The circumference of the tyre is 1.9 m and therefore in travelling 20 000 miles (or 32 000
km = 32 000 000) they will have rotated 32 000 000/1.9 = almost 17 million
times!
Therefore in one rotation the tyre will lose 7.35x1025/17 million =
4.3x1018 carbon atoms.
Roughly 4 million million million carbon atoms will
be rubbed off every rotation!
This is a very rough estimate that all depends on my
guess as to molecular weight and structure of the rubber used in car tyres. Actually it is even
worse because tyres are made of 28% carbon black, 27% synthetic polymer, 14% natural
rubber, 10% wire, 10% oil, and 11% other materials.