A correct relationship between density and pressure of a gas is

A relationship can be obtained between density and pressure of a gas by using Boyle's law,

$\mathrm{p}={\mathrm{K}}_1·\frac{1}{\mathrm{V}} \left(\mathrm{d}=\frac{\mathrm{m}}{\mathrm{V}},\mathrm{d}=\text{ density }\right)$

$\therefore \mathrm{V}=\frac{{\displaystyle \mathrm{m}}}{{\displaystyle \mathrm{d}}}, \mathrm{p}={\mathrm{K}}_1·\frac{{\displaystyle \mathrm{d}}}{{\displaystyle \mathrm{m}}}$

$\therefore \mathrm{d}=\left(\frac{{\displaystyle \mathrm{m}}}{{\displaystyle {\mathrm{K}}_1}}\right)·\mathrm{p}={\mathrm{K}}^{\text{'}}\mathrm{p}$

This shows that at a constant temperature, pressure is directly proportional to the density of a fixed mass of the gas.