Prove that density of an ideal gas is proportional to pressure dont spam give right derivation

The density of an ideal gas is proportional to its pressure through ideal gas equation in the mentioned below steps.

Explanation:

For an ideal gas, we know that  pV=nRT

where p= pressure of the gas

V-volume of the gas

n- no of moles of the gas in consideration

R= Gas constant

T= temperature of the gas

Thus

pressure (p)= nRT/V  -- equation 1

we know that no of moles of any gas= mass of the gas(m)/ Molar mass of the gas (M)

Putting the value of n in the equation 1

p= mRT/MV   -- equation 2

We know that density (ρ)= mass/volume

equation 2 can be re-arranged as

p=RT.m/V.M

Substituing, m/v in equation 2 by density (ρ)

p=ρRT/M   --equation 3

Equation 3 can be re-written as

ρ=pM/RT

where

ρ= density of the gas concerned

p=pressure of the gas

M=molar mass of the gas

R= Gas constant

T= Temperature of the gas concerned

Hence in the final equation density of the gas is directly proportional to the pressure