Question

Using the equation of state, PV = n RT, show that at a given temperature, density of a gas is proportional to gas pressure, P.

Answer 1

From the given equation it is clear that pressure is directly proportional to temperature...

P=dRT/M

From the above equation.... Pressure is directly proportional to density

Answer 2

The given equation of is pV = nRT ……….. (i)

Here,

P = Pressure of gas

V = Volume of gas

n = Number of moles of gas

R = Gas constant

T = Temperature of gas

From equation (i)  

We know,

                            $p = \frac { nRT }{ V }$

Where, n = Mass of gas(m) or Molar mass of gas(M)

Substitute the value of n in the equation (i)

We get,

                            $p = \frac { mRT }{ MV } …… (ii)$

Now density,

                            $(\rho) = \frac { m }{ V } …… (iii)$

Substitute (iii) in (ii)

We get,

                            $P = \frac { \rho RT }{ M }  \\Or\quad \rho = \frac { PM }{ RT }$

Hence, at a given temperature, the density (ρ) of gas is proportional to its pressure (P).