PV=RT
$$6.02\times10^{23}$$
PV=nRT
$$R=8.31 J/(mol\cdotK)$$
$$\Delta P=-\rho\Delta z\cdot g$$
$$\frac{n}{V}=\frac{P}{RV}$$
$$\rho=\frac{M}{1000}\cdot\frac{n}{V}=\frac{\frac{PM}{1000}}{RT}$$
$$\Delta P=-\left(\frac{\frac{PM}{1000}}{RT}\right)\Delta z\cdot g$$
$$\frac{\Delta P}{P}=$-$\frac{\frac{gM}{1000}}{RT}\Delta z$$
$$\int\frac{1}{P}dP=-\frac{\frac{gM}{1000}}{RT}\int dz$$
