If you define N as number of particles (as opposed to number of moles), the ideal gas law is PV = NkT where k is the Boltzmann constant, a fundamental physical constant. Divide both sides by V and you get
P = nkT
Where n = N/V is the number of particles per unit volume. Multiply n by m, the mass per particle, and you get the mass
per unit volume (aka density) rho. Hence n = rho/m and the ideal gas law becomes
P = (rho/m)kT
For air, there is more than one type of particle so m is a weighted average of the masses of the different molecules.