Using the equation of state pV = nRT shows that at a given temperature density of a gas is proportional to gas pressure p.

Asked by Pragya Singh | 1 year ago |  71

##### Solution :-

The equation of state is given by,

pV = nRT ……..(1)

Where, p = pressure

V = volume

N = number of moles

R = Gas constant

T = temp

$$\dfrac{n}{V} = \dfrac{p}{RT}$$

Replace n with $$\dfrac{m}{M},$$ therefore,

$$\dfrac{m}{MV} = \dfrac{p}{RT}$$​……..(2)

Where, m = mass

M = molar mass

But, $$\dfrac{m}{V}$$​ = d

Where, d = density

Therefore, from equation (2), we get

$$\dfrac{d}{M} = \dfrac{p}{RT}$$

d = $$(\dfrac{M}{RT}) p$$

d$$\propto$$ p

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

Answered by Abhisek | 1 year ago

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