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
