Calculate mass of air in a tyre from pressure

You need an equation for the density of the gas as a function of temperature and pressure. Assuming the tyre is full of air, this is reasonably close to an ideal gas so the molar volume is given by:

$$V_m = \frac{RT}{P}$$

where R is the ideal gas constant and and the average molecular weight of air (20% O$_2$, 80% N$_2$) is about 28.8. From this you can work out the density at the pressure and temperature of your car tyre, and since you know the volume this immediately gives you the mass.