Question

Prove that at a given temp density of a gas is proportional to the gas pressure by using the equation of state pV = nRT​

Answer 1

Explanation:

The equation of state is given by,

pV = nRT ……..(1)

Where, p = pressure

V = volume

N = number of moles

R = Gas constant

T = temp

\frac{n}{V}

V

n

= \frac{p}{RT}

RT

p

Replace n with \frac{m}{M}

M

m

, therefore,

\frac{m}{MV}

MV

m

= \frac{p}{RT}

RT

p

……..(2)

Where, m = mass

M = molar mass

But, \frac{m}{V}

V

m

= d

Where, d = density

Therefore, from equation (2), we get

\frac{d}{M}

M

d

= \frac{p}{RT}

RT

p

d = (\frac{M}{RT}

RT

M

) p

d \propto∝ p

Therefore, at a given temp, the density of gas (d) is proportional to its pressure (p).