Using the equation of state PV = nRT, show that at given temperature density of gas is directly proportional to gas pressure.

Explanation

The density of an ideal gas can be calculated by using ideal gas equation. This equation is useful to study the behaviour of ideal gases. The ideal gas equation is as below.
`pV = nRT " " ....(i)`
or, `p=(nRT)/(V) " " ...(ii)`
Here, p = Pressure of gas
V = Volume of gas
T = Temperature
R = Gas constant and n= Number of moles of gas
Number of mole can be calculated as,
`n=("Mass of gas")/("Molar mass of gas")=(m)/(M)" " ...(iii)`
By putting value of (n) in equation (ii), we get `p=(m)/(M) (RT)/(V)" " ...(iv)`
We know that density of gas `(rho)= ("mass")/("volume")=(m)/(V)" " ...(v)`
`:.` from equation (iv), we get `p=(rhoRT)/(M) or rho=(pM)/(RT)`