Why don't they use normal air in race car tires?
(by Lawrence R. Sperberg)

Many race car teams use nitrogen instead of air in their tires because nitrogen has a much more consistent rate of expansion and contraction compared to the usual air. Often, a half pound of pressure will radically affect traction and handling. With track and tire temperatures varying over the duration of a race, the consistency of is needed.

"Oxygen and Moisture - the Killer of Tires"

All pneumatic tires have suffered from a deterioration starting the day that tires were invented. That deterioration is chemical oxidation masquerading under the name of "tire fatigue".

Causing the deterioration are oxygen molecules contained in the inflating air which is a mixture of gases - nitrogen 78%, oxygen 21%, argon 0.9%, and miscellaneous O.1%. Tires are designed to be protected from this deterioration by their liners which are supposed to keep air from percolating through them into the tire body, which they never do, and by chemicals called antioxidants or age resisters whose job is to intercept and neutralize any invading oxygen - which they do until they are themselves used up, which occurs too soon after a tire enters into service.

So the deterioration spreads. It starts within the tire interior and moves outward. it first invades and consumes the tire liner. It then ravages the insulation rubber adjacent the liner. It marches inexorably outward - because of the pressure differential of the tire inflation on the inside and the atmospheric pressure on the outside. As the decay moves ever outward - the oxygen molecules react chemically with the unsaturated double valence bonds present in all rubbers, causing the rubber molecules to lose their strength and their elasticity, so that they no longer act as rubbers, but instead take on the characteristics of a non rigid plastic. The decay is constantly being fueled by the fresh all too often moist air being injected into the air chamber to maintain the desired inflation pressure. Moisture inside a tire is bad because it causes pressure fluctuations and corrodes rims.